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## Robot.icra.it

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Recent results and perspectives on cosmology and fundamental physics
from microwave surveys∗
Carlo Burigana,1,2,3,a Elia Stefano Battistelli,4,b Micol Benetti,5,c
Giovanni Cabass,4,d Paolo De Bernardis,4,e
Sperello Di Serego Alighieri,6,f Eleonora Di Valentino,7,g
Martina Gerbino,8,9,4,h Elena Giusarma,4,i Alessandro Gruppuso,1,3,j
Michele Liguori,10,11,k Silvia Masi,4,l Hans Ulrik Norgaard-Nielsen,12,m
Piero Rosati,2,n Laura Salvati,4,o
Tiziana Trombetti,1,2,p Patricio Vielva13,q
1INAF–IASF Bologna, Via Piero Gobetti 101, I-40129 Bologna, Italy †
2Dipartimento di Fisica e Scienze della Terra, Universit
a degli Studi di Ferrara,
Via Giuseppe Saragat 1, I-44122 Ferrara, Italy
3INFN, Sezione di Bologna, Via Irnerio 46, I-40126, Bologna, Italy
4Dipartimento di Fisica e INFN, Universit
a di Roma "La Sapienza",
P.le Aldo Moro 2, 00185, Rome, Italy
orio Nacional, 20921-400, Rio de Janeiro, RJ, Brazil
6INAF–Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy
7Institut d'Astrophysique de Paris
(UMR7095: CNRS & UPMC – Sorbonne Universities), F-75014, Paris, France
8The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics,
Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden
9Nordita (Nordic Institute for Theoretical Physics), Roslagstullsbacken 23, SE-106 91
Stockholm, Sweden
10Dipartimento di Fisica e Astronomia G. Galilei, Universit
a degli Studi di Padova,
Via Marzolo 8, 35131 Padova, Italy
11INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova, Italy
12DTU Space, Elektrovej, DK - 2800 Kgs. Lyngby, Denmark
13Instituto de F´ısica de Cantabria (CSIC-UC), Santander, 39005, Spain
aburigana@iasfbo.inaf.it − belia.battistelli@roma1.infn.it − cmicolbenetti@on.br
dgiovanni.cabass@gmail.com − epaolo.debernardis@roma1.infn.it − f sperello@arcetri.astro.it
g valentin@iap.fr − hmartina.gerbino@uniroma1.it − ielena.giusarma@roma1.infn.it
j gruppuso@iasfbo.inaf.it − kmichele.liguori@pd.infn.it − lsilvia.masi@roma1.infn.it
mhunn@space.dtu.dk − nrosati@fe.infn.it − olaura.salvati@roma1.infn.it
Recent cosmic microwave background data in temperature and polarization have reachedhigh precision in estimating all the parameters that describe the current so-called stan-dard cosmological model. Recent results about the integrated Sachs-Wolfe effect fromcosmic microwave background anisotropies, galaxy surveys, and their cross-correlationsare presented. Looking at fine signatures in the cosmic microwave background, such asthe lack of power at low multipoles, the primordial power spectrum and the bounds onnon-Gaussianities, complemented by galaxy surveys, we discuss inflationary physics andthe generation of primordial perturbations in the early Universe. Three important topicsin particle physics, the bounds on neutrinos masses and parameters, on thermal axionmass and on the neutron lifetime derived from cosmological data are reviewed, withattention to the comparison with laboratory experiment results. Recent results fromcosmic polarization rotation analyses aimed at testing the Einstein equivalence princi-
∗Based on contributions presented at the Fourteenth Marcel Grossmann Meeting on GeneralRelativity, Rome, July 2015.

†Istituto Nazionale di Astrofisica – Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna,Via Piero Gobetti 101, I-40129 Bologna, Italy
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ple are presented. Finally, we discuss the perspectives of next radio facilities for theimprovement of the analysis of future cosmic microwave background spectral distortionexperiments.

Keywords: Cosmology; Background radiations; Radio, microwave; Origin and formationof the Universe; Particle-theory and field-theory models of the early Universe; Obser-vational cosmology; Large scale structure of the Universe; Dark matter; Dark energy;Elementary particle processes.

Latest measurements of cosmic microwave background (CMB) anisotropies in tem-perature and polarization from Planck satellite,a 1 complemented at smaller scalesby recent ground-based experiments (see e.g. Refs. [2, 3, 4, 5]) and combined withother cosmological information coming from e.g. type-Ia supernovae, galaxy andgalaxy cluster surveys, have reached high precision in estimating all the parametersthat describe the current so-called standard cosmological model. Far from repre-senting a fully, physically exhaustive interpretation of the Universe properties, thecosmological constant plus cold dark matter (ΛCDM) model phenomenologicallydescribes reasonably well existing data with a simple set of six parameters (see e.g.

the lectures by M. Bersanelli and J.-L. Puget on Planck resultsb in this Meeting).

The integrated Sachs-Wolfe effect, discussed here in Sect. 2, represents a remark-able example of the success of current cosmology, since a such intrinsically weakpredicted signal is clearly recognized in two classical cosmological probes, like CMBanisotropies and galaxy surveys, and in their cross-correlations. Looking at finesignatures in the CMB it is possible to derive more hints on early Universe andinflationary physics as well as to carry out a sort of laboratory tests to constrainparticle and fundamental physics. In Sec. 3 the "lack of power" in the large scalepattern (i.e. low multipole region) of CMB anisotropy angular power spectrum(APS) is investigated to link the inflationary phase to the string theory while CMBdata and galaxy surveys are jointly analyzed in Sec. 4 to constrain inflationarymodels predicting localized ‘features' in the primordial power spectrum (PPS). Go-ing beyond power spectrum (PS) analyses, the study of primordial non-Gaussianity(PNG), discussed in Sec. 5, allows to test mechanisms for the generation of pri-mordial perturbations in the early Universe. Sects. 6 and 7 discuss two importanttopics in dark matter studies, respectively the bounds on neutrinos masses andparameters and on thermal axion mass from cosmological data while Sec. 8 sum-marizes the state of the art on the neutron lifetime, τn, a fundamental quantity in
aPlanck is a project of the European Space Agency - ESA - with instruments provided by twoscientific Consortia funded by ESA member states (in particular the lead countries: France andItaly) with contributions from NASA (USA), and telescope reflectors provided in a collaborationbetween ESA and a scientific Consortium led and funded by Denmark.

bThis paper is based largely on the products available at the ESA Planck Legacy Archive andpublicly available publications by ESA and the Planck Collaboration, for what concerns the relatedaspects. Any material presented here that is not already described in Planck Collaboration papersrepresents the views of the authors and not necessarily those of the Planck Collaboration.

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nuclear physics. Attention is given to the comparison with laboratory experimentresults. Sec. 9 is devoted to the test of the Einstein equivalence principle (EEP),at the basis of general relativity (GR), through the analysis of the cosmic polariza-tion rotation (CPR) and to the comparison of results from astronomical and CMBbased analyses. Finally, Sec. 10 discusses the main cosmological and fundamentalphysics information contained in the CMB spectral distortions in the light of thecontribution expected from the Square Kilometre Array (SKA).

2. Integrated Sachs-Wolfe effect
The late integrated Sachs-Wolfe (ISW) effect 6–8 is a secondary anisotropy in thecosmic microwave background (CMB), which is caused by the interaction of CMBphotons with the time-dependent gravitational potential of the evolving cosmiclarge-scale structure (LSS). The ISW effect can be generated under several scenariosaffecting the late evolution of the structures: a cosmological constant, dark energy(DE), 9 modified gravity, 10 or spatial curvature. 11
The early ISW is generated after recombination (since the energy density of
relativistic matter is still considerable at that time): it adds in phase with theSachs-Wolfe primary anisotropy, increasing the height of the first acoustic peaks.

Besides, the effect on the APS, C (being the multipole of the spherical harmonicexpansion), is suppressed by the factor ρ2 (η
rec): increasing the radiation
energy density with respect to that of matter near recombination will give a largerearly ISW effect. The late ISW effect is active at more recent times: focusing onscales corresponding to galaxy clusters, the CMB photons get redshifted by thetime-dependent gravitational potentials. The potentials causing the late ISW alsogive rise to the weak lensing distortions: the interplay between these two effectsresults in a non-Gaussian correlation between small and large angular scales, whichis encoded in the lensing-induced bispectrum.

The optimal detection 9 of the ISW effect is made by the cross-correlation of
the CMB temperature anisotropies with tracers of the gravitational potential, like,for instance, galaxy catalogues. The first detection 12 was made using WilkinsonMicrowave Anisotropy Probe (WMAP) data and radio and X-ray galaxy catalogues.

The ISW signal is very weak (an ideal LSS tracer could provide a detection of upto ≈ 8 σ), and, therefore, its capability to constrain cosmological parameters, isvery limited. Nevertheless, using the ISW signal alone it is possible to constrainsome cosmological parameters, by fixing the remaining ones to their standard value(see e.g. the estimation of the DE density parameter 13 ΩΛ ≈ 0.67, with an errorof about 20%; the compatibility of the DE equation of state parameter with theexpected value for a ΛCDM scenario; 14 or the setting of upper limits on spatialflatness of a few per cent 15).

We will focus here on the main results of the ISW effect derived by Planck (see
Refs. [16] and [13] for a complete description).

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2.1. The ISW probed through the CMB-LSS cross-correlation
The four CMB maps 17 produced by Planck (COMMANDER, NILC, SEVEM, SMICA) havebeen cross-correlated with several tracers of the LSS. In the first release, the NRAOVLA Sky Survey (NVSS) radio-galaxy catalogue, the photometric luminous galaxy(SDSS-CMASS/LOWZ), and the photometrically-selected galaxies (SDSS-MphG)from the Sloan Digital Sky Survey (SDSS) were considered. Two additional cat-alogues from the Wide-Field Infrared Survey Explorer (WISE) were added to theanalysis of the second release: one based on star-forming galaxies (WISE-GAL),and another one based on active galactic nuclei (WISE-AGN). Considering the fullcross-correlations of the CMB with all the LSS tracers, the latest results provideda total ISW detection of around 3 σ, as expected for the standard ΛCDM model.

The NVSS catalogue already provides by itself a similar detection level.

The most novel result provided by Planck was its capability to provide a detec-
tion of the ISW without relying on external tracers of the LSS, thanks to its reliableestimation of the gravitational potential through the lensing suffered by the CMBphotons. 18 The cross-correlation of this map with the CMB one, or, equivalently,the specific shape of the ISW-lensing bispectrum, reported a detection of the ISWat around ≈ 3 σ. When all the LSS tracers are combined, the total ISW detectionis ≈ 4 σ, also in good agreement with the ΛCDM model.

Assuming the standard ΛCDM model, the statistical ISW captured in the CMB-
LSS cross-correlation can be used to estimate a map of the ISW anisotropies causedby the gravitational potential traced by each of the LSS probes. 19 Fig. 1 shows theISW fluctuation maps obtained from the full cross-correlation of the Planck SEVEMCMB map with NVSS, WISE-AGN, WISE-GAL, SDSS-CMASS/LOWZ, SDSS-MphG, and the Planck lensing LSS tracers.

Map (thermodynamic temperature in K) of the recovered ISW anisotropies (left) and its
corresponding estimated error per pixel (right), from the combination of the Planck SEVEM CMBmap and all the LSS tracers. The error map structure is determined by the sky coverage of thedifferent surveys. The total signal-to-noise of the ISW map cannot exceed, obviously, a value of≈ 4. The signal-to-noise is higher near the Galactic poles, with values of ≈ 2.

All these results were obtained without using CMB polarization information
(except for the estimation of the Planck lensing map). In principle, including po-
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larization could increase the ISW detection 20 around a 15%, however, the currentCMB polarization data from Planck is high-pass filtered at the largest angularscales (& 5◦), which are the most important ones in this context. Including thelarge scale polarization is, perhaps, the most important remaining aspect withinthe context of the ISW study, at least, from the CMB side. On the other side,future galaxy surveys like Euclid, 21 J-PAS 22 or LSST, 23 among others, will provideaccurate galaxy catalogues, probing very large volumes, allowing to perform, forinstance, a tomographic ISW detection.

A complementary approach consists in stacking the CMB fluctuations in the
position of known structures, such as voids and clusters, as done initially on WMAPdata 24 using a catalogue (GR08) of super-structures from SDSS. An anomalous ISWsignal, incompatible with the standard ΛCDM model was found, confirmed in thePlanck analyses, showing that the intensity of the detected signal (≈ −11 µK forvoids, and ≈ +8.5 µK for clusters) and the scale at which that signal is maximum(≈ 3.5◦ for voids, and ≈ 4.5◦ for clusters) are, indeed, unexpected.

At these scales, the current CMB Planck polarization map still retains certain
signal, despite the high-pass filtering and, therefore, it can be used to test furtherthe nature of this anomalous signal. The key point is that, if this signal is causedby the ISW effect, and, therefore, originated by a gravitational secondary CMBanisotropy, a negligible contribution of the CMB polarization is expected. In fact,no associated polarization is found in Planck data, although the diminishing of thesignal caused by the high-pass filtering limits any strong conclusion. Anyway, thecurrent polarization data are not in contradiction with assuming that the emissioncoming from these GR08 structures provides an anomalous ISW signal. Studyingthe stacked fluctuations of the Planck lensing map on the GR08 positions alsosupports this hypothesis. In fact, at least for the voids, a clear correlation betweenthe lensing gravitational potential and the position of the super-structures is found.

This kind of studies could be further extended once Planck provides its next and
final release, which will include polarization information at all the angular scales.

2.2. Parametrization of early and late ISW and data analysis
The ISW amplitude can be parametrized in terms of AeISW and AlISW, which rescalethe contribution of the ISW to the temperature anisotropies.

Monte-Carlo (MCMC) analysis was performed with a baseline standard ΛCDMmodel and flat priors on the parameters. 25 We also check the impact of a Gaussianprior AlISW = 1.00±0.25, consistent with the 68% confidence level (C.L.) bounds onthe same parameter from the estimation of the ISW-lensing bispectrum, which hasbeen obtained by cross-correlating the Planck CMB maps with the Planck map ofthe lensing potential. Various datasets were tested: the high- Planck temperatureand temperature+polarization APS in the range 30 ≤ < 2500 (hereafter T T andT T, T E, EE, respectively) in combination with the low- Planck temperature andpolarization APS in the range 2 ≤ < 30 (lowP). We also tested the WMAP APS
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including both temperature and polarization up to = 1200.

Planck T T + lowP data provide tighter constraints than WMAP on the early
ISW (AeISW = 1.064+0.042
at 68% C.L.), and present a 1σ
eISW = 1.007+0.056
evidence of AeISW 6= 1 that is stable when considering the extensions of the ΛCDMmodel shown in Fig. 2. Regarding the late ISW, Planck data place a constraintAlISW < 1.14 at 95% C.L.: Planck alone does not improve significantly the con-straint on AlISW with respect to WMAP data (which give AlISW = 0.958+0.391
68% C.L.). In fact, the late ISW affects angular scales that are dominated by cos-mic variance, rather than by instrumental noise. Adding the prior on AlISW comingfrom CMB temperature anisotropies-weak lensing correlations, we find a ∼ 4σ de-tection AlISW = 0.85 ± 0.21. When we consider the recent Planck polarization dataat high , the evidences for a non-standard value of AeISW disappear. Using alsothe small scale polarization APS does not change the results obtained for AlISW:their effect is to tighten the upper bounds obtained considering only the T T + lowPAPS.

*Planck *TT+lowP
+

*TCMB *+

*BAO*
+

*TCMB *+

*BAO*
+

*A ISW *prior

* ISW *prior

*Planck *TT+lowP
+

*A ISW *prior
+

*A ISW *prior
One-dimensional posteriors for AeISW and AlISW. In the left column, only Planck tem-
perature and low multipole polarization APS (Planck T T +lowP) were used. The plots in the rightcolumn use also the Planck polarization APS at high multipoles (Planck T T, T E, EE + lowP).

From Ref. [25].

3. CMB low multipoles anomalies
It is usually stated that the six parameters of the ΛCDM model 1,26,27 are enough todescribe the large scale Universe. However, some features are not well captured, and
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anomalies occur for instance at the largest CMB angular scales (see e.g. Ref. [28]),although they are often regarded as mere curiosities. We focus here on the lack ofcorrelation 29–37 and explain why it deserves attention. The low variance anomaly 38is a closely related observation, 36 so that the terms "lack of power" and "lack ofcorrelation" are used as synonymous.

There is a lack of power, with respect to ΛCDM, in the two-point correlation
function of CMB temperature anisotropies for angles >
∼ 60◦, as originally noted
with COBEc data 29 and then confirmed by the WMAP team already in their firstyear release. 30 In Ref. [31] this feature was associated to missing power in thequadrupole. WMAP-3yrs and WMAP-5yrs data were then used to show 32,33 thata lack of correlation occurs only in 0.03% of the ΛCDM realizations. A subse-quent analysis 34 confirmed the anomaly using WMAP-5yrs data, and, at the sametime, found, with a Bayesian approach, that the ΛCDM model cannot be excluded.

WMAP-7yrs data were taken into account in Ref. [35], while WMAP-9yrs data wereconsidered in Ref. [36], where the lack of correlation was studied against the Galac-tic masking. Planck 2013 and WMAP-9yrs data were analyzed in Ref. [37], whichconfirmed for this anomaly a significance at the level of 99.97%. Similar resultswere obtained in Ref. [39] where Planck 2015 data were taken into account. Oneintriguing feature of this anomaly is that it is more significant at high Galactic lat-itude. 36,39 Is this a simple statistical fluke or it is caused by a physical mechanism?
We now elaborate on a possible fundamental origin for this effect. 40,41 Lack of
power at large angular scales is a typical manifestation of early departures fromslow–roll, which follow naturally the emergence from an initial singularity. As ex-plained in Refs. [42, 43], when this occurs the PS approaches in the infrared thelimiting behavior
(k2 + ∆2)2−ns/2
which brings along a new physical scale ∆. An infrared depression of the PS presentsitself naturally in string theory, in orientifold vacua with high–scale supersymmetrybreaking (see e.g. references in Refs. [40, 41]). In these models a scalar field emergesat high speed from an initial singularity, to then bounce against a steep exponentialpotential before attaining an eventual slow–roll regime. The key ingredient is thesteep exponential, whose logarithmic slope is predicted by string theory, 44 and anumber of exactly solvable systems provide explicit realizations of this peculiardynamics. The results of a Bayesian analysis extended to all standard cosmologicalparameters and based on Planck 2013 data are shown in Fig. 3, where posteriors for∆ are given for two choices of the Galactic mask (even if equivalent, for an updatedand complete analysis see Ref. [41]). For the latter choice, the estimated value is
∆ = (0.340 ± 0.115) × 10−3 Mpc−1 .

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Posterior probabilities of ∆ (solid line for the standard mask with fsky ' 90%,
and dashed line for an extended mask with fsky ' 40%).

Interestingly, ∆ in eq. (2) is found to differ from 0 at 99% C.L. and its magnitudeappears reasonable. 40,41 Moreover, in analogy with the lack of power anomaly, Fig. 3shows that the significance of this result increases sizably for a larger Galactic mask.

In conclusion, the considerations in Refs. [42, 43], inspired by string theory,
and in particular by the supersymmetry breaking mechanism 45 and the relatedcosmological dynamics, 44 provided the original motivation for the present analysis.

The resulting scenario would associate ∆ to the onset of the inflationary phase.

Collecting more information on low multipoles of CMB APS might tell us somethingmore definite about how an inflationary regime was originally attained.

4. Features in the primordial fluctuations
The most recent CMB data by the Planck satellite 1 are in excellent agreementwith the assumption of adiabatic primordial scalar perturbation with nearly scale-invariant PS, described by a simple power law with spectral index ns very closeto (albeit different from) unity. 46 It would be produced in the simplest inflationaryscenario, in which a single minimally-coupled scalar field slowly rolls down a smoothpotential. In spite of this, models that account for localized ‘features' in the PPScould provide a better fit to data with respect to a smooth power-law spectrum.

These features could be produced in inflationary models with departures from thenear-scale-invariant-power-law spectrum of the standard simplest scenario, and ob-servable signatures would be in the CMB anisotropy temperature APS and in thematter PS from galaxy surveys. We analyze here three classes of models, and Fig.

4 displays the corresponding PPS shapes.

(i) Log-spaced oscillations model assumes an oscillation in proper time affecting
the amplitude of curvature perturbation during the inflationary expansion (pro-ducing features periodic in ln k). It is the case of models with no-Bunch-Daviesinitial condition, 47 or in the bouncing inflationary scenario 48 or also in the axionmonodromy inflation. 49 (ii) Linear oscillation model includes effects from a possibleboundary on effective field theory (where we assume new physics which occurs atone moment in time, such as a discontinuity in single-field inflation 50 or a sharpturn in multi-field inflation 51). (iii) Step oscillation model assumes a briefly inter-
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PPS simulated for various oscillatory models parametrized with an amplitude, a frequency
and a phase (for the Linear oscillation models we have the scale-dependence index as furtherparameter). Left: Log-spaced oscillations models for different values of the frequency oscillationparameter. Middle: Linear oscillation models for different values of the scale-dependence index.

Right: Step oscillation models for different values of the frequency and phase parameters.

ruption of the slow-roll. For instance it can happen by a phase transition, a burst ofresonant particle production, a sudden turn in field space or a step in the inflationpotential. 52 It is found to be essentially a power-law with superimposed oscillationslocalized only in a limited range of wavenumbers. It is noteworthy that this kindof models is able to produce oscillation at very high- , and it is very interestinglooking to the CMB temperature anisotropies glitches in correspondence of = 22and = 40, first observed by the WMAP experiment and later confirmed by thePlanck satellite.

We used here the Planck 2013 data release and a combined CMB and SDSS
(DR-11) 53 dataset. Our results show that using the CMB data alone we have no-evidence of improving the concordance with data and agree with the more recentresults of the Planck Collaboration. 46 Instead, using the combined dataset of CMBSDSS-DR11 data, we can see a positive Bayesian evidence for the inflationary log-spaced oscillation and step oscillation models. Updating this analysis with finalPlanck data will be very interesting to confirm or discard these kinds of models.

5. Primordial non-Gaussianity
The study of primordial non-Gaussianity (PNG) provides a powerful tool to shedlight on early Universe mechanisms for the generation of primordial perturbations(see e.g. Refs. [54, 55] and references therein). Different inflationary models predictdifferent amplitudes, shapes, and scale dependence of PNG. As a result, PNG allowsto discriminate between models that can show degeneracies considering only theAPS.

One of the main goals of these analyses is to constrain the amplitude and shape of
PNG using the angular bispectrum of CMB anisotropies, related via linear radiationtransfer to the primordial bispectrum, BΦ(k1, k2, k3), defined by
hΦ( k1)Φ( k2)Φ( k3)i = (2π)3δ(3)( k1 + k2 + k3)BΦ(k1, k2, k3) ;
here Φ is the primordial potential defined in terms of the comoving curvature per-turbation ζ on super-horizon scales by Φ ≡ (3/5)ζ. The bispectrum measures the
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correlation among three perturbation modes, and it is expected to be zero for Gaus-sian perturbations. In general, the bispectrum can be written as
BΦ(k1, k2, k3) = fNLF (k1, k2, k3) ,
where fNL is the so-called "nonlinearity parameter", a dimensionless parame-ter measuring the amplitude of non-Gaussianity. The functional dependence ofF (k1, k2, k3) on the type of triangle formed by k1, k2, k3 defines the shape of thebispectrum. 56 Even in the simplest models of inflation, consisting of a single slowly-rolling scalar field, some level of PNG is predicted, 57,58 but this is too small to bedetectable in CMB and LSS surveys. Large level of PNG can be produced howeverin multi-field scenarios, or in single-field models with non-standard Lagrangiansand deviations from Bunch-Davies vacuum, and in many other cases. Each of thescenarios outlined above predicts different shapes, the main of which are brieflydescribed below.

Local shape, where the signal peaks in "squeezed" triangles (k1 k2 ' k3). Thisshape is typically generated in multi-field models of inflation. Equilateral shape,peaking on equilateral bispectrum triangles(k1 ≈ k2 ≈ k3). Examples of thisclass include single-field models with non-canonical kinetic term, 59 such as e.g.

Dirac-Born-Infeld (DBI) inflation, 60 models characterized by more general higher-derivative interactions of the inflaton field, and models arising from effective fieldtheories. 61 Folded (flattened) shape, peaking on isosceles, nearly degenerate trian-gles. Examples of this class include e.g. single-field models with non-Bunch-Daviesvacuum. Orthogonal shape, which is generated, e.g., in single-field models of in-flation with a non-canonical kinetic term, or with general higher-derivative inter-actions. Notably, the folded shape described above can be obtained as a linearcombination of equilateral and orthogonal shapes. In light of this, actual measure-ments of PNG generally focus on local, equilateral and orthogonal templates.

It must be noted that many but not all models are included in the previous clas-
sification. For example, models with a temporary breaking of slow-roll conditionsgenerate strongly scale-dependent, oscillatory shapes that cannot be approximatedby a combination of local, equilateral and orthogonal templates. Given the limitedscope of this review, the focus here will be however only on the above main shapes.

Having computed the CMB angular bispectrum templates arising from the var-
ious primordial shapes, non-Gaussianity estimation consists then essentially in fit-ting such templates to the 3-point function of the data in order to measure thebest-fit amplitude parameters fNL. This apparently straightforward approach ac-tually presents many statistical and numerical complications. These arise mainlyfrom the huge number of modes (triangles) which contribute to the signal for highresolution experiments like Planck and WMAP, and from spurious mode couplingsfrom sky-cut and anisotropic instrumental noise. Several numerical techniques havebeen successfully tested in the literature and implemented by the Planck team inorder to address these issues. This gave rise to several independent, but ultimatelyequivalent, Planck bispectrum analysis pipelines, the so called modal, binned and
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separable template-fitting estimators, that were separately applied to the data. 62–66We refer the reader to Planck papers on PNG, 67,68 for all details of the analysis, in-cluding validation tests carried on data and simulations, descriptions of the variouspipelines, and constraints on a much larger set of shapes than the three discussedhere.

The final Planck results for the local, equilateral and orthogonal shapes, from
the 2015 combined analysis of temperature and polarization data, are as follows:
f local = +0.8 ± 5.0 ; f equil. = −4 ± 43 ; f ortho. = −26 ± 21 .

The main conclusion from Planck is that consistency with Gaussianity is found in
all cases (including shapes not considered here). Planck bispectrum constraints leadto important implications for inflationary model building, such as a lower bound onthe sound speed in effective single field inflation theory, or limits on the curvatondecay fraction, and so on. In light of the current results, the simplest slow-rollsingle field inflationary paradigm has passed its most stringent and accurate test todate (although alternative, more complex, possibilities, while constrained, are byno means ruled out yet). Planck has extracted nearly all the possible PNG informa-tion from CMB data. Even an ideal, noiseless temperature+polarization experimentwould improve on current error bars by at most a factor 2. For substantial improve-ments it will be necessary to look at different observables and wait for future ex-periments. LSS could be in principle promising, since it contains more modes thanthe CMB. Precise primordial bispectrum estimation from LSS surveys is howeververy hard due to non-linearities from gravitational evolution, galaxy-bias and othereffects; whether we will be able to achieve improvements from the LSS bispectrumwill strongly depend on how well we can keep all these systematics under control,and it is at present an open question. Two-point function based measurements oflarge scale signatures arising from scale-dependent halo bias look on the other handquite promising, and have the potential of achieving fNL ∼ 1 sensitivity for the localshape. 69 It has been pointed out that the study of the bispectrum of 21 cm radiationor measurements of cross-correlations between CMB spectral distortions and tem-perature anisotropies can in principle improve over current bounds by more thanone order of magnitude. These are fascinating but futuristic prospects, since high-sensitivity fNL measurements with these techniques will require either full-sky 21cm surveys with redshift tomography in the 30 . z . 100 range, or high-resolutionmaps of angular anisotropies of the CMB µ-distortion parameter. 70,71
6. Limits on neutrino masses from cosmology and particle physics
The absolute scale of neutrino masses is one of the main open issues both in cosmol-ogy and particle physics. Current experimental strategies involve i) measurementsexploiting kinematics effects in beta decay: 72, ii) searches for neutrinoless doublebeta decay ('0ν2β'), 73 and iii) cosmological observations. 74 The three approachesare complementary, each of them presenting its own advantages and disadvantages
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and being sensitive to slightly different quantities related to the neutrino masses. 75In this work, we derive joint constraints on neutrino mass parameters from the mostrecent observations from both laboratory and cosmological experiments, and fore-casts, combining them in the framework of Bayesian statistics. In particular, for'0ν2β' experiments, we take into account the uncertainty related to nuclear matrixelements, in order to account its impact on the neutrino mass estimates.

6.1. Neutrino parameters, method and data
We denote the masses of the neutrino mass eigenstates νi with mi (i = 1, 2, 3).

∆m2 represents the difference between the two eigenstates closest in mass, while
the sign of ∆m2 discriminates between the normal (NH, ∆m2 > 0) and inverted
< 0) hierarchies.

The neutrino mass eigenstates are related to the
flavour eigenstates να (α = e, µ, τ ) through να = P U
αiνi, where Uαi are the
elements of the neutrino mixing matrix U , parameterized by the three mixing an-gles (θ12, θ23, θ13), one Dirac (δ) and two Majorana (α21, α31) CP-violating phases.

Oscillation phenomena are insensitive to the Majorana phases, that however affect0ν2β decay. The different combinations of the mass eigenvalues and of the elementsof the mixing matrix probed by the experimental avenues are: the squared effec-tive electron neutrino mass m2 ≡ P U
(β decay experiments), the effective
i (0ν 2β searches), the sum of neutrino masses
i (cosmological observations). We perform a Bayesian analysis based
on a MCMC method, using cosmoMC 76 as a generic sampler. We consider the fol-lowing vector of base parameters:
Mν, ∆m2 , ∆m2 , sin2 θ
12, sin2 θ13, φ2, φ3, ξ
where φ2 ≡ α21, φ3 ≡ α31 − 2δ and ξ is a "nuisance" parameter related to thenuclear modeling uncertainty. We assume uniform prior distributions for all pa-rameters and neglect the mixing angle θ23, irrelevant for mass parameters.

Our baseline dataset is the global fit of the updated neutrino oscillation param-
eters. 77 We model the likelihood as a the product of individual Gaussians (corre-lations can be neglected 77,78).d KATRIN 79 and HOLMES 80 represent our forth-coming and next-generation direct measurement datasets, respectively. We take thelikelihood for kinematic measurements to be a Gaussian in m2 > 0, with a width
given by the expected sensitivity of the experiment, i.e. σ(m2 ) = 0.025, 0.006 eV2
for KATRIN and HOLMES, respectively. For 0ν2β searches, we consider the currentdata from the GERDA experiment 81 as the present dataset, its upgrade (GERDA-II) for the near-future, and the nEXO experimente as a next-generation dataset.

0ν2β experiments are sensitive to the half-life of 0ν2β decay T 0ν . If neutrinos
are Majorana particles, T 0ν is related to the Majorana effective mass through
e is the electron mass, G0ν is a phase space factor
dSee http://www.nu-fit.org/ for results updated after the Neutrino 2014 conference.

ehttps://www-project.slac.stanford.edu/exo/
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and M 0ν is the nuclear matrix element.

We model the likelihood of 0ν2β experiments as a Poisson distribution in the
number of observed events, with an expected value λ = λS + λB given by the sumof signal (S) and background (B) contributions. For a given value of T 0ν , the
expected number of signal events observed in a time Tobs for a detector mass M isλS = ln 2NAE where N
A is Avogadro's number, E ≡ M Tobs is the exposure, is
the detector efficiency, menr is the molar mass of the enriched element involved inthe decay. The level of background is given by the "background index", i.e. thenumber of expected background events per unit mass and time within an energybin of unit width. For GERDA-I, we use the parameters reported in Tab. I ofRef. [81] for the case with pulse-shape discrimination. For GERDA-II, we considera reduction of the background index down to 10−3 counts keV−1kg−1yr−1, a totalexposure of 120 kg yr, and the same efficiency as GERDA-I. 82 For nEXO, we assumea background index corresponding to 3.7 events ton−1yr−1 in the region of interestand an exposure of 25 ton yr, 83 and the same efficiency as EXO. 84
In order to account for the uncertainty related to nuclear modeling, 85 we com-
pute T 0ν for a given m
ββ using fiducial values of nuclear matrix elements (NME)
and axial coupling constant, and then rescale it by a factor ξ2 (see Ref. [86] for asimilar approach). For what concerns the cosmological dataset, we use the posteriordistribution of Mν from the combination of Planck temperature and polarizationdata with baryon acoustic oscillations (BAO), 1 as both our current and forthcomingreference dataset. Finally, we consider the Euclid mission (weak lensing tomography,galaxy clustering and ISW) in combination with data from Planck 21 as our referencenext-generation experiment. We model the likelihood as Gaussian in Mν = 0.1 eV,with σ(Mν) = 0.06 eV and the addition of the physical prior Mν > 0.

We present our results for Mν, mβ and mββ in Fig. 5, both in the case whereξ is fixed to 1 and when ξ is marginalized over, in order to show the impact ofuncertainties in nuclear modeling. Notice that the low mass region is excluded bythe oscillation data, with the only exception of mββ in the case of NH; the reasonis that in this case the phases can arrange in order to yield mββ = 0 even for finitevalues of the mass differences. Similar limits are provided by the "present" datasetindependently of whether nuclear uncertainties are marginalized over: present con-straints are dominated by the cosmological limit on Mν, that translates directly tobounds on mβ and mββ once oscillation data are taken into account. Forthcomingdatasets yield similar constraints for the mass parameters: the upgraded sensitivityof GERDA-II and the inclusion of KATRIN provide a marginal improvement tothe Planck +BAO plus oscillations data combination. Substantial differences arisefor next-generation experiments. In this case, cosmological observations and 0ν2βsearches have comparable constraining power, and the nuclear uncertainties havea dramatic impact in deriving parameter constraints. Marginal evidence for non-
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*Mν*[

*eV *]

*mββ*[

*eV *]

*mβ*[

*eV *]

*Mν*[

*eV *]

*mββ*[

*eV *]

*mβ*[

*eV *]
Posterior distributions for the neutrino mass parameters, for NH (top row) and IH (bottom
row). Solid (dashed) curves correspond to marginalization over nuclear uncertainties (fixed fiducialvalues for nuclear parameters). Black, blue and red curves refer to present, forthcoming and next-generation datasets, respectively.

minimal mass parameters can be highlighted in the case of normal hierarchy, evenwhen nuclear uncertainties are taken into account.

The combination of current and forthcoming data from oscillation, kinematic,
0ν2β and cosmological experiments allows to put upper bounds on the neutrino massparameters. Since these limits are dominated by the combination of oscillations andcosmological data, they are not affected by uncertainties in nuclear modeling. ForMν = 0.1 eV and a factor 2 uncertainty in nuclear modeling, future experimentswill ideally allow to measure non-minimal mass parameters with a 95% accuracy.

6.3. Limits on neutrino masses in a non-standard PPS scenario
In order to study how the cosmological constraints on the parameters change in moregeneral inflationary scenarios, we assume a non-parametric form for the PPS. Inparticular, we decide to parametrize the scalar PPS with a piecewise cubic Hermiteinterpolating polinomial 87 (PCHIP) to avoid some unwanted oscillating behaviourrelated to the natural cubic spline function (see Appendix A of Ref. [88]). Weconsider a ΛCDM model with three degenerate active massive neutrinos togetherwith the PPS approach. We also explore a scenario with three active light massiveneutrinos plus one massive sterile neutrino species characterized by an effective massmeff.

Our baseline data set consists of the Planck 2015 satellite CMB temperature
and polarization APS. 1,89 We also consider a prior on the Hubble constant, H0,estimated from a reanalysis of Cepheids data 90 and include measurements of theLSS in the form of BAO. In particular, we use the 6dFGS, SDSS-MGS and BOSSDR11 measurements. 91–93
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Planck TT,TE,EE+lowP
k2 k3 k4 k5 k6 k7 k8 k9 k10k11
10-1 10-5 10-4 10-3 10-2 10-1 100 101
Left: 95% CL on the active (sterile) neutrinos masses and on the total massive neutrino
species, Neff, from the combination of considered data sets. Right: 68%, 95% and 99% CL allowedregions for the PCHIP PPS scale dependence in the ΛCDM+Pmν model, using CMB data only.

The results are shown in table in the left panel of Fig. 6. In the first scenario,
concerning only CMB measurements, the bound on the sum of massive neutrinosis largely relaxed with respect to the the power-law model (Pmν < 0.49 eV at95% CL). 1 In the second scenario, there is no evidence for neutrino masses nor fornon-zero sterile neutrino mass. Concerning only CMB measurements, the bound onthe sum of massive neutrinos is more stringent with respect to previous scenario.

The reason for that is due to the degeneracy between Pmν and meff. Notice that
in both scenarios the addition of a prior on the Hubble constant and of the BAOdata displaces the bounds on Pmν to lower values in agreement with the standardpower-law PPS case. 1 An example of the reconstructed PPS is given in Fig. 6 (rightpanel). Note that both Ps,1 and Ps,12 are poorly constrained because of the absenceof measurements at their corresponding wavenumbers. All the remaining Ps,j, withj = 2, . . , 11 are well-constrained. In particular, in the range between k5 and k10the PPS can be perfectly described by a power-law parametrization. Moreover wecan notice that there is a significant dip at wavenumbers around k = 0.002 Mpc−1,that comes from the dip at = 20 − 30 in the CMB temperature APS and a smallbump around k = 0.0035 Mpc−1, corresponding to the increase at ' 40.

7. Robustness of cosmological thermal axion mass bounds
Relativistic axions contribute to the dark radiation content of the Universe, in-creasing the effective number of relativistic degrees of freedom Neff (see Ref. [94]for details), while massive thermal axions, when become non-relativistic, affect theLSS formation suppressing the small scale power, clustering only at scales largerthan their free-streaming scale. Massive axions affect also the CMB temperatureanisotropies via the early ISW effect. All the cosmological axion mass limitsf as-sumed the usual simple power-law description for the primordial perturbations,
fSee e.g. Refs. [95, 96] for recent cosmological constraints on thermal and non-thermal axions.

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defined by an amplitude and a scalar spectral index. In Ref. [94] the thermal axionmass is constrained using a non-parametric description of the scalar perturbationPPS, to test the robustness of its bounds. We adopted a function, the PCHIP 97 inthe same modified version 88 as in Sec. 6.3, to interpolate the PPS values in a seriesof nodes at fixed position.

We discuss here the ΛCDM model, extended with the axions hot thermal relics,
together with the PPS approach (see Ref. [94] for a similar analysis with two coex-isting hot dark matter species, thermal axion and massive neutrinos). We considervarious CMB measurements: the temperature data from the Planck satellite, 98,99the WMAP-9yrs polarization measurements, 100 the SPT 101 and ACT 2 datasets.

Concerning CMB datasets only, the bounds on the thermal axion mass are un-
constrained in the case in which the PPS is not described by a simple power-law(see Tab. III in Ref. [94]), while in this last case ma < 1.83 eV (see Tab. IV inRef. [94]). Including the Hubble Space Telescope (HST) prior on the Hubble con-stant, 90 H0 = 70.6 ± 3.3 km/s/Mpc, provides a 95% CL upper limit on the thermalaxion mass of 1.31 eV. The further addition of the BAO measurements 91,93,102–105brings this constraint down to 0.91 eV, being these last data sets directly sensitiveto the thermal axion free-streaming nature. These upper bounds are very simi-lar to the ones obtained considering the standard power-law PPS (see Tab. IV inRef. [94]). Adding the CFHTLenS 106 bounds on the σ8-Ωm relationship, the ther-mal axion mass bounds become weaker ma < 1.29 eV, since this dataset prefersa lower σ8 value. Finally, considering the Planck Sunyaev-Zeldovich (PSZ) 2013catalogue 107 dataset with fixed cluster mass bias, σ8(Ωm/0.27)0.3 = 0.78 ± 0.01,together with the CMB, BAO and HST measurements, a non-zero thermal axionmass of ∼ 1 eV is favored at ∼ 4σ level. Using more realistic approaches for thecluster mass bias, 107 σ8(Ωm/0.27)0.3 = 0.764 ± 0.025, the errors on the so-calledcluster normalization condition are larger, and, consequently, the preference for anon-zero axion mass is reduced.

Our results are summarized in Fig. 7. In conclusion, using a non-parametric
description 88 of the scalar perturbation PPS that relaxes the power-law assumptionin Ref. [94], we tested the robustness of the cosmological axion mass bounds, foundto be only mildly sensitive to the PPS choice and therefore not strongly dependenton the particular details of the underlying inflationary model.

8. Cosmological constraints on the neutron lifetime
The study of the neutron lifetime, τn, a fundamental quantity in nuclear physics,is fascinating since the current status of particle physics experiments is still puz-zling and unclear. The current used value is the one quoted by the Particle DataGroup 108 τn = (880.3 ± 1.1) s and it is obtained as an average between the sevenmost recent experiments, bottle-method and beam-method like (for further detailssee [109]). Combining the five most recent bottle-method measurements one obtainthe tight constraint τn = (879.6 ± 0.8) s while from the two most recent beam-
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ΛCDM+m (PCHIP) - CMB
ΛCDM+m (PCHIP) - CMB
ΛCDM+m (PCHIP) - CMB+BAO+HST
ΛCDM+m (PCHIP) - CMB+BAO+HST
ΛCDM+m (PCHIP) - CMB+BAO+HST+PSZ
ΛCDM+m (PCHIP) - CMB+BAO+HST+PSZ
ΛCDM+m (PCHIP) - CMB+BAO+HST+PSZ(fixed bias)
ΛCDM+m (PCHIP) - CMB+BAO+HST+PSZ(fixed bias)
68% and 95% CL allowed regions in the (ma, Ωch2) plane (left panel) and in the (ma,
σ8) plane (right panel) for different data combinations, when a PCHIP PPS is assumed. FromRef. [94].

method measurements one obtain τn = (888.0 ± 2.1) s. Given this tension, it isinteresting to investigate if cosmological measurements can constrain the neutronlifetime in an independent way with respect to particle physics experiments, thustesting them, and, moreover, to address the implications for cosmology of a a moreprecise determination of the neutron lifetime.

We start discussing constraints on τn from current cosmological data. Assum-
ing Standard Big Bang Nucleosynthesis it is possible to evaluate primordial abun-dances of light elements from CMB as functions of few parameters: 110 the baryonicabundance, the relativistic degrees of freedom, the chemical potential of electronneutrinos and the neutron lifetime. Neglecting the chemical potential, consideringthe high precision achieved in the determination of baryonic abundance and fixingNeff to its standard value of 3.046, from primordial abundances (in particular He-lium abundance) we can infer the value of the neutron lifetime. We start analyzingPlanck 2015 results as CMB dataset with the publicly available MCMC package
cosmoMC. Table 1 reports the most interesting results (for complete analysis seeRef. [111]).

The next step is to combine CMB observations with direct astrophysical mea-
surements of Helium. We consider eight primordial Helium measurements collectedin the last ten years and combine them with Planck data and select two possibleindependent combinations of these astrophysical datasets (referred to as M12-P forRefs. [112, 113] and M12-I14 for Refs. [112, 114]). As shown in Table 1, combin-ing the constraining power of CMB data, sensitive to the baryon density, with theHelium astrophysical measurements we obtain more stringent limits on the neutronlifetime, with respect to cosmological data only.

We extend the analysis performing some forecasts on future cosmological experi-
ments. Considering that CMB sensitivity on τn is encoded in the small-scale region,we expect tighter constraints from next CMB projects planned to measure the high range. As reported in Table 1, the most stringent constraint is obtained by the
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combination of future experiments COrEg and Euclid, giving τn = (880.3 ± 6.7) s.

Values of τn with 1σ erros for cos-
mological and astrophysical datasets.

Planck + BAO + Lensing
In conclusion, the combination of CMB anisotropies and astrophysical observa-
tions allows to obtain stringent limits and shed light on the present experimentaldiscrepancies, while future cosmological missions, such as COrE and Euclid, couldreach a sensitivity comparable with that of current experiments.

9. Testing general relativity with cosmic polarization rotation
The CPR provides a test of the EEP, which is the foundation of any metric theoryof gravity, including GR. Almost all the information about the Universe outside thesolar system is carried to us by photons, with their direction, energy and polariza-tion. The latter consists essentially in the position angle (PA) of the polarizationellipse, i.e. photons carry throughout the Universe an important geometrical infor-mation. To properly use this information, it is important to know if and how it ischanged while photons travel to us. The directions of photons can be modified bygravitational fields and their energies are modified by the Universe expansion, whilethe polarization PA is modified while photons travel in a plasma with a magneticfield, the so called Faraday rotation, proportional to the wavelength squared. Isthe polarization PA also modified while photons travel large distances in vacuum?Searches for CPR deal with this important question.

Clearly, if the CPR angle α is not zero, it should be either positive for a counter-
clockwise rotation, or negative for a clockwise rotation (we adopt the IAU conven-tion 115 for PA, which increases counter-clockwise facing the source, from Norththrough East). Therefore symmetry must be broken at some level, leading to theviolation of fundamental physical principles (see Ref. [116] for a recent review).

Indeed CPR is linked also to a possible violation of the EEP. The reasons for thelink are due to the unique counterexample to Schiff's conjecture 117 that any consis-tent Lorentz-invariant theory of gravity which obeys the weak equivalence principle
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(WEP) would also obey the EEP, which involves a pseudoscalar field, producingCPR. 118 Therefore, if we could show that α = 0◦, the EEP would be tested withthe same high accuracy of the WEP, greatly increasing our confidence in the EEPand then in GR. See Ref. [119] for a recent review of CPR tests.

CPR tests are simple in principle: they require a distant source of polarized
radiation with established polarization orientation at the emission, P Aem. By mea-suring the observed orientation P Aobs, the CPR angle can be calculated:
α = P Aobs − P Aem.

The problem is the estimate of P Aem. Fortunately it can be solved using the factthat scattered radiation is polarized perpendicularly to the plane containing theincident and scattered rays. This simple physical law has been applied to CPRtests, using both the ultraviolet (UV) radiation of radio galaxies (RG) and the tinyanisotropies of the CMB. The first CPR tests 25 years ago used instead a statisticalanalysis of the radio polarization in RG. 120 The most accurate CPR tests obtainedwith the various methods are summarized in Fig. 8, based on data in Ref. [119].

In summary, the results so far are consistent with a null CPR with upper limits
of the order of one degree.

CPR angle measurements by the various experiments, displayed in chronological order.

Blue error bars: statistical errors; red error bars: including also systematics, if present/available.

A systematic error should be added to the ATCPol measurement, equal to the unknown differenceof the Crab Nebula polarization PA between 146 GHz and 89 GHz.

9.1. Current problems and future prospects
Searches for CPR using the UV polarization of RG have reached the limits allowedby current instrumentation, for the lack of RG suitable for the test and brightenough so that their polarization can be measured with the available instruments.

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The most accurate results are now obtained with the CMB polarization, aver-
aging over large sky areas, i.e. assuming uniform CPR over these areas. A currentproblem with CPR searches using the CMB is the calibration of the polarizationPA for the lack of sources with precisely known PA at CMB frequencies. This in-troduces a systematic error, similar to the statistical measurement error, of about1◦ (see Fig. 8). Recently, the polarization PA of the Crab Nebula (Tau α) has beenmeasured with an accuracy of 0.2◦ at 89.2 GHz. 121 However, most CMB polariza-tion measurements are made at 100-150 GHz and the Crab Nebula is not visiblefrom the South Pole, the site of several CMB experiments. In order to overcomethe PA calibration problem, some CMB polarization experiments have used a T Band EB nulling procedure, 122 but this would eliminate together the PA systematicerror and any CPR angle α, so it cannot be used for CPR tests.

Furthermore, we note that, unfortunately, in the pixelization tool 123 widely
adopted in CMB experimentsh the polarization PA is assumed to increase clock-wisely (looking at the source), which is opposite to the standard IAU convention,adopted in other bands, thus calling for caution when comparing measures withdifferent methods, like for CPR tests.

The different methods are complementary in many ways. They cover different
wavelength ranges and the methods at shorter wavelength have an advantage, ifCPR effects grow with photon energy, as foreseen in some cases. 125,126 They alsoreach different distances, and the CMB method obviously reaches furthest. Howeverthe relative difference in light travel time between z = 3 and z = 1100 is only 16%.

Improvements are expected by better targeted high resolution radio polariza-
tion measurements of RGs and quasars, by more accurate UV polarization mea-surements of RGs with the coming generation of giant optical telescopes, 127–129and by future CMB polarization measurements such as those from Planck 27 andBICEP3. 130 Indeed, the Planck satellite has a very low statistical error (∼ 0.06◦)for CPR measurements, but to exploit its great accuracy a significant reduction inthe systematic error in the calibration of the polarization angle (currently of ∼ 1◦for CMB polarization experiments) is needed (see also Ref. [131]). Great opportu-nities will come from more precise polarization measurements of celestial sources atCMB frequencies with ATCA 132 and ALMA, 133 and by a calibration source on asatellite. 134
10. SKA contribution to future CMB spectrum experiments
Recent limits on CMB spectral distortions and constraints on energy dissipationprocesses in the plasma 135 are mainly set by COBE/FIRAS experiment. 136 Highaccuracy CMB spectrum space experiments, such DIMES (λ >
∼ 1 cm) and FIRAS II
∼ 1 cm), were proposed to constrain energy exchanges up to 100 times better
than FIRAS. Dissipation processes at early times (z >
∼ 105) result in Bose-Einstein
hSee Ref. [124] for a pixelization software adopting IAU convention.

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(BE)-like distortions, 137 while late epochs mechanisms (z <
∼ 104) before or after
the recombination era generate Comptonization and free-free (FF) distortions. 138New space missions were proposed to probe cosmic origin and evolution observ-ing CMB temperature and polarization anisotropies with ∼ degree resolution, asin PIXIE 139 and LiteBird,i or with arcmin resolution, as in COrE, PRISMj andCOrE+, in combination with spectrum measurements in the case of PIXIE andPRISM. SKA extremely high sensitivity and resolution can contribute to set newconstraints on CMB spectral distortions beyond current limits. Improved absolutetemperature measures will strengthen the constraints on CMB spectrum affectedby (pre-recombination) decaying and annihilating particles, by superconducting cos-mic strings electromagnetic radiation, by energy injection of evaporating primor-dial black holes (BH). Spectral distortions could constrain non evaporating BHspin, small scale magnetic fields, vacuum energy density decay, axions. In gen-eral, departure of CMB spectrum from a perfect blackbody is theoretically pre-dicted by: 140 (i) cosmological reionization, producing electron heating and physi-cally correlated Comptonization distortion (with typical Comptonization parametery ' (1/4)∆ε/εi ≈ 10−7 − 10−6 proportional to the fractional energy exchanged inthe interaction), and free-free (FF) distortion; (ii) dissipation of primordial per-turbations at small scales, damped by photon diffusion and thus invisible in CMBanisotropies, produces BE-like distorted spectra characterized by a positive chemicalpotential µ0 ' 1.4∆ε/εi ≈ 10−9 − 10−7; (iii) BE condensation of CMB photons bycolder electrons associated with the matter temperature decrease in the expandingUniverse relatively faster than that of radiation gives µ0 ≈ −3 × 10−9. The aboveFF signal is the most relevant type of low-frequency global spectral distortion (seeFig. 9). Indeed, the FF term is proportional to the square of baryon density andthe structure formation process implies a rate amplification by a factor ' 1 + σ2(being σ2 the matter distribution variance) with respect to the case of homogeneousplasma. 142 SKA high sensitivity and resolution can also be used to model the con-tribution from Galactic emissions and extragalactic foreground, a fundamental stepto accurately observe these kinds of distortions. Extragalactic source contributionis small compared to Galactic radio emission, currently the major astrophysicalproblem in CMB spectrum experiments, but, unlike the Galactic emission, it can-not be subtracted from the CMB monopole temperature by exploiting its angularcorrelation properties. A direct radio background estimate from precise numbercounts will certainly improve the robustness of this kind of analyses. Exploiting therecent differential number counts at 0.153 GHz, 0.325 GHz, 1.4 GHz,and 1.75 GHzit is possible to evaluate the contribution, Tb, to the radio background from extra-galactic sources in various ranges of flux densities. These signals can be significantat the accuracy level potentially achievable with future experiments. Subtracting
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sources brighter than several tens of nJy, T <
b ∼ 1 mK at ν >
∼ 1 GHz, but Tb ∼ 10 mK
below 0.3 GHz. The minimum source detection threshold is given by the sourceconfusion noise. The finite angular extension of faint galaxies, θ ∼ 100, impliesa "natural confusion limit" ∼ 10 nJy at ν ∼ 1.4 GHz, not a relevant limitationfor deep surveys. 143 At 1 GHz <
∼ some GHz (λ ≈ 1 dm) the signal amplitudes
found for CMB distorted spectra well below FIRAS constraints are significantlylarger than the estimates of the background from extragalactic sources fainter thansome tens of nJy. At decreasing frequencies FF distortion amplitude increases but,at the same time, source confusion noise may represent a serious problem, possi-bly preventing the achievement of the faint detection threshold necessary to havea source contribution to the background significantly less than the CMB distortionamplitude.

Left panel: distorted spectra in equivalent thermodynamic temperature vs. λ (cm) with
late energy injection ∆ε/εi = 5 × 10−6 plus an early/intermediate energy injection ∆ε/εi =5 × 10−6 (∼ 20 times smaller than current upper limits) at the "time" Comptonization parameteryh = 5, 1, 0.01 (bottom to top; the cases at yh = 5 and 1 are very similar at short λ; solid lines) plusa FF distortion with yB = 10−6 (dashes). yh = y with Te = TCMB when the integral is computedfrom the energy injection time to the current time. Right panel: FF distortion in SKA2 frequencyrange by two astrophysical reionization histories (a late phenomenological model is also displayedfor comparison). Inset: models absolute differences; vertical lines: ranges of SKA1 configurations.

From Ref. [141].

SKA will trace the neutral hydrogen distribution and the neutral-to-ionized
transition state at the reionization epoch through the 21-cm line. It could trace thedevelopment of ionized material directly by looking for FF emission from ionizedhalos. The expected signal can be derived by reionization models through both semi-analytical methods 144 and numerical simulations. 145 Dedicated high resolution skyareas observations allow to distinguish FF distortion by ionized halos rather thanby diffuse ionized IGM. SKA should be able to detect up to ∼ 104 individual FFemission sources with z > 5 in 1 , discerning ionized halos or diffuse ionizedIGM FF distortions. Thus, the precise mapping of individual halos represents an
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interesting goal for the excellent imaging capabilities of SKA.

Acknowledgements – The authors that are members Planck Collaboration warmly
thank the Planck Collaboration for numberless and constructive conversations on the
subjects discussed here. Some of the results in this paper have been derived using the
HEALPix 123 package. We acknowledge the use of the NASA Legacy Archive for Mi-
crowave Background Data Analysis (LAMBDA) and of the ESA Planck Legacy Archive.

CB, AG, ML and TT acknowledge partial support by ASI/INAF Agreement 2014-024-R.0
for the Planck LFI Activity of Phase E2.

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