signatures of decay and annihilations of massive relics in cosmological observables 4 dark matter invisible decay 

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Recombination as a tool for new physics: a first comment

It is remarkable that such a high precision on recombination physics has been achieved during the last decade, while current cosmological data indicate an excellent agreement with standard physics ex-pectations. Interesting consequences of such hard work is the possibility of constraining non-standard scenario as we shall explore in this work, especially in the case of exotic electromagnetic energy injection, which can follow from particle decays or annihilations. Another nice repercussion is the possibility of testing variations of fundamental constants, as has been done extensively in the past [72], [88], [260], [292], [358], [424], [513], [530].
Recombination physics, as we have already argued, has a major impact on the studies of CMB anisotropies, and it is through modifications of the CMB TT, EE and TE power spectrum that most of the constraints come from. The impact of varying some cosmological parameters inside their current (roughly) 1 uncertainty as measured by Planck [19] is illustrated in Fig. 16. The degeneracy between parameters in CMB power spectra analysis degrade the possible sensitivity that one could
It is, however, important to recall that recombination physics is intrinsically linked to another ob-servables, namely the spectral distortions from a perfect blackbody of the CMB. Indeed, we have seen that solving the recombination problem in practice amounts to solving the coupled system of equations “recombination physics + radiative transfer”, which means that an accurate code is able to follow those distortions and predict the amount expected today due to both purely standard and non-standard physics. A recent review of all standard processes leading to spectral distortions can be found in Ref. [172]. Nowadays, simple analytical estimate as well as accurate numerical codes are available to compute spectral distortions, and we discuss those in more details in sec. 3.6. However, in the context of standard recombination physics, it is necessary to mention the most important ones, namely the cosmological recombination lines (CRR), created by the large emissions of photons in bound-bound and bound-free transitions. Many calculations have been carried out over the years [163], [167], [178], [179], [222], [223], [368], [516], [520], [522], and it is nowadays possible to get % level prediction in a few seconds runtime, thanks to the most recent one, namely the CosmoSpec code [173]. These tiny distortions, at the nK- K level, which should today be present at mm to dm wavelength, are sensitive to the finest details of the recombination history. They represent a fingerprint from the recombina-tion era, encoding very distinct spectral features of the recombination processes. Their amplitude typically depends on the number density of baryons in the Universe, while the detailed shapes of the CRR is affected by Helium recombination. Moreover, the positions and width of the line depends on both when and how fast recombination occurs, thereby giving a tremendous leverage on recombi-nation physics, while providing us with an independent way of measuring cosmological parameters [159]. Unfortunately, in its current proposal to NASA, the PIXIE experiment lacks sensitivity by a factor of a few [172], [209]. One needs to go for space experiments such as PRISM [48] and Millimetron [556], or ground-based experiment in the cm to dm wavelength range [501] to measure these distortions.


General considerations

Although the recombination era is well under control from both the theoretical and the observational point of view, the low-redshift evolution of the ionization fraction is affected by a major unknown: the onset of star formation, which triggers the beginning of the so-called Epoch of reionization (EoR). The EOR of the Universe, namely the era at which the cosmic gas mainly made of Hydrogen and Helium atoms goes from (almost) fully neutral to fully reionized, is still largely unknown nowadays. Currently, the best observation of this transition of the Universe is the so-called Gunn-Peterson trough: the observation of redshifted Lyman- absorption lines in quasar spectra is a very sensitive probe of the presence of neutral hydrogen along the line of sight. Even a small fraction of neutral hydrogen leads to a clear signature, and we expect quasars spectra to show a very small level of Lyman- absorption at redshift for which the Universe is reionized. Predicted in 1965 [286] and observed in Quasar spectra much more recently (Fig. 17 shows the historical first measurement of the GP trough) [92], [94], [238], [239], [585], it teaches us that the Hydrogen was almost fully reionized by z ’ 6. Hence, in the standard picture, Hydrogen reionization occurs across the entire Universe between z ’ 12 to z ’ 6, typically because of ionizing photons emmited by early star-forming galaxies. Quasars are then believed to be responsible for Helium reionization from z ’ 6 to z ’ 2 (see e.g. [425] for a recent review).
Details of the EoR are strongly connected to many fundamental questions in cosmology and astro-physics. It could teach us about many properties of the first galaxies and quasars, such as the time at which they form and how the formation of very metal-poor stars proceeded, but we could also learn about more exotic processes such as the nature of DM itself. It is usually accepted that a dominant source of reionization would be given by Lyman continuum photons from UV sources in pristine star-forming galaxies, but the fraction of photons produced by stellar populations that can escape to ionize the IGM, or the efficiency of the stellar population to produce Lyman continuum photons, two key quantities of our current reionization models, are still suffering orders of magnitude uncertainties.
Another question that has also puzzled the community is whether early galaxies were the only source of reionization in the Universe. A key quantity measured by CMB experiments is the so called optical depth to reionization reio, quantifying the amount of Thomson scattering between CMB photons and free electrons in the IGM. From eq. (1.3.56), one defines with zbeg; reio the redshift of the beginning of reionization3, ne(z) the number density of free elec-trons and T the Thomson cross-section. Measurements of the Gunn-Peterson trough seem to require reionization to be centered around z 6 7, thus hinting to rather small optical depth to reioniza-tion . However, this bound was in tension with the very high measurements of reio = 0:17 0:04 based on the temperature-polarization TE cross-power spectrum of WMAP after 1 year of data taking [373], requiring reionization to be centered somewhere in between 11 < zreio < 30 (95% CL). Several solutions to the problem have been invoked: i) One might need to reinterpret the Gunn-Peterson bound, since they are model-dependent. In practice, they rely on a modelling of the IGM density and temperature, the UV background from stars and some assumption about the homogeneity of the reionization. Release of the tension has been achieved by questioning these modelisations [93], [421].
This discrepancy could also indicate the need for a complexified star reionization picture (invoking e.g several population of stars [153], [598]). iii) Finally, it was suggested that this could be a hint for DM annihilations in halos or decay, since these processes would typically enhance the optical depth. One of the first proposals was, for instance, the presence of decaying massive sterile neutrinos [294]. Over the years, this discrepancy has systematically decreased, and finally disappeared with Planck measurements, but still improving our knowledge of this epoch could lead to unexpected discoveries, while at the same time helping us to constrain exotic reionization models, as we shall do in this work. In the near future, many experimental efforts will be devoted to measuring this era precisely, mostly through the 21 cm line created by the hyperfine transition of the Hydrogen atom. Tomographic sur-veys of the cosmological 21cm observable, sensitive both to xe(z) and TM(z), are certainly the most promising avenue to progress in the knowledge of these redshift epochs. Experiments such as PAPER In CAMB it is hardly coded at 50. In CLASS it can be set by the user. In our studies, we define it as the minimum of the visibility function g(z) since in the absence of reionization it is a decreasing function of redshift. We comment on this issue in appendix D.3.
On the other hand, CMB experiments are also sensitive to the EoR. Indeed, the increase of free elec-trons at low-z enhancing the Compton scattering rate of CMB photons off these free electrons will lead to very peculiar pattern in the power spectra. The most characteristic ones, which we shall describe in this section, are the step-like suppression of CMB TT modes inside hubble horizon at reionization, typically above ‘ 20, accompanied by the big regeneration of power in the same multipole range of the EE spectrum, the so-called reionization bump. Many studies in the past have tried to assess more carefully what amount of information could be extracted from CMB power spectra (see e.g. [326], [356], [403], [435] for more detailed studies). The CMB is mostly sensitive to the column density of electrons along each line-of-sight10 and therefore to the Thomson optical depth to reionization . There are well known degeneracies between and other cosmological parameters, e.g., when using temperature data alone, with the amplitude of the primordial scalar perturbations11 As and the spectral index ns. Moreover, in extensions of the CDM model, there exists a degeneracy between and the sum of neutrino masses P m , which gets strengthened by the addition of external datasets such as BAO measurements [42], [407]. Thus, an accurate measurement of through the reionization bump at large scales is essential for the determination of other cosmological parameters as well.
Let us also mention that different reionization histories do lead to differences in the low-‘ part of the
spectrum that can potentially give more insight on this epoch. Unfortunately, principal component analysis (PCA) have revealed that CMB experiments, limited by cosmic variance in this multipole range, would not be the best probe of this era although it can have some handle on the first five eigenmodes [435].

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Implementation in Boltzmann codes

In principle, in order to account for the reionization in our universe, one needs to modify the cou-pled recombination equations by adding a source term quantifying the impact of stars (typically UV photons background). This is, however, not the strategy that has been adopted until now by Boltz-mann codes, based on the fact that: i) There are order of magnitudes uncertainties on the paramaters quantifying the impact of stars; ii) The CMB is not so sensitive to the exact details of reionization, affecting multipoles that are cosmic variance limited; iii) Although stellar reionization is believed to have happened in “bubbles” embedded in neutral surroundings, and thus to be very inhomogenous, the CMB is sensitive to the average over all sky directions of xe(1 + b) and this complication only affects the determination of cosmological parameters at a negligeable level [15].

Table of contents :

i introduction to particle cosmology 
1 the standard cosmological model 
1.1 General Relativity in a homogeneous and isotropic Universe
1.1.1 Geometry of the expanding Universe
1.1.2 Dynamics of the expanding Universe
1.1.3 Distances in our Universe
1.2 Inflation in a nutshell
1.2.1 Original motivations for Inflation
1.2.2 Scalar field inflation and slow-roll conditions
1.3 Thermal history of the Universe
1.3.1 From equilibrium to freeze-out
1.3.2 Big Bang Nucleosynthesis
1.3.3 Recombination
1.3.4 Reionization
2 from perturbations to observables: cmb and matter power spectrum 
2.1 Cosmological perturbation theory at first order
2.1.1 Perturbed Einstein equations
2.1.2 Perturbed collisionless Boltzmann equations
2.1.3 Thomson scattering collision term and polarization anisotropies
2.1.4 Initial conditions from Inflation
2.2 The CMB and matter power spectrum
2.2.1 Cosmology as a stochastic theory
2.2.2 Primordial power spectrum from inflation
2.2.3 The CMB power spectra
2.2.4 The matter power spectrum
3 massive relics in the universe
3.1 The Standard Model of Particle Physics in a nutshell
3.1.1 The Standard Model and its main successes
3.1.2 Main issues with the Standard Model
3.2 Neutrino masses in Cosmology
3.2.1 Neutrino oscillations: evidence for neutrino masses
3.2.2 Sterile neutrinos and neutrino mass mechanisms
3.3 Evidence for Dark Matter
3.3.1 Galaxy rotation curves and density profiles
3.3.2 Clusters of galaxy : X-rays and weak lensing
3.3.3 The Dark Matter relic abundance and the WIMP miracle
3.4 Models predicting massive relics
3.4.1 WIMP Dark Matter candidates
3.4.2 Decaying massive relics
3.4.3 A word on detection strategies
3.5 Electromagnetic cascade: an overview
3.5.1 Electromagnetic cascade at high redshift (z 1000)
3.5.2 Electromagnetic cascade close to and after recombination
3.6 CMB spectral distortions
3.6.1 Basics of the thermalization problem
3.6.2 Usual analytical estimates: the and y parameters
3.6.3 Some sources of spectral distortions
ii signatures of decay and annihilations of massive relics in cosmological observables
4 dark matter invisible decay 
4.1 Introduction and models
4.2 Boltzmann equations for the decaying Dark Matter
4.2.1 Background equations
4.2.2 Perturbation equations in gauge invariant variables
4.3 Cosmological effects of a decaying Dark Matter fraction
4.3.1 Impact of Dark Matter decay on the CMB
4.3.2 Impact of the decaying Dark Matter on the matter power spectrum
4.3.3 Potential degeneracy with the neutrino mass
4.4 Application of the decaying Dark Matter model
4.4.1 Constraints from the CMB power spectra only
4.4.2 Adding low redshift astronomical data
4.5 Conclusions
5 non-thermal bbn from electromagnetically decaying particles
5.1 Introduction
5.2 E.m. cascades and breakdown of universal nonthermal spectrum
5.3 Nonthermal nucleosynthesis
5.3.1 Review of the formalism
5.3.2 Light element abundances
5.4 Constraints from the CMB
5.5 Non Universal constraints from BBN
5.5.1 Constraints from 4He
5.5.2 Constraints from 2H
5.5.3 Constraints from 3He
5.6 A solution to the cosmological lithium problem
5.6.1 Proof of principle
5.6.2 A concrete realisation with a sterile neutrino
5.7 Conclusions
6 cosmological constraints on exotic injection of electromagnetic energy
6.1 Introduction
6.2 CMB power spectra constraints
6.2.1 Standard equations
6.2.2 Effects of electromagnetic decays on the ionization history and the CMB power spectra
6.3 Results: Summary of constraints and comparison with other probes
6.3.1 Methodology
6.3.2 Results and comparison of various constraints
6.4 Applications and forecasts
6.4.1 Low mass primordial black holes
6.4.2 High mass primordial black holes
6.4.3 Sterile neutrinos
6.4.4 The 21 cm signal from the Dark Ages
6.5 Conclusion
7 dark matter annihilations in halos and high-redshift sources of reionization 
7.1 Introduction
7.2 Ionization and thermal evolution equations
7.2.1 Dark Matter annihilation in the smooth background
7.2.2 Dark Matter annihilation in halos
7.3 Impact of high redshift sources on the reionization history
7.4 Impact of reionization histories on the CMB spectra
7.5 Discussion and prospects
iii neutrino properties from current and future cosmological data 
8 robustness of cosmic neutrino background detection in the cmb 
8.1 Introduction
8.2 Modelling the properties of the (dark) radiation component
8.2.1 Massless neutrinos
8.2.2 Massive neutrinos
8.3 Impact of (c2 e ; c2 vis) on observables
8.3.1 Effect on neutrino perturbations
8.3.2 CMB temperature and polarisation
8.3.3 Matter power spectrum
8.4 Models and data set
8.4.1 Model descriptions
8.4.2 Data sets and parameter extraction
8.5 Results
8.6 Conclusions
9 physical effects of neutrino masses in future cosmological data
9.1 Introduction
9.2 Effect of a small neutrino mass on the CMB
9.2.1 General parameter degeneracies for CMB data
9.2.2 CMB data definition
9.2.3 Degeneracies between very small M’s and other parameters with CMB data only
9.3 Effect of neutrino mass on the BAO scale
9.4 Effect of neutrino mass on Large Scale Structure observables
9.4.1 Cosmic shear and galaxy clustering spectrum
9.4.2 Degeneracies between M and other parameters
9.5 Joint analysis results
9.5.1 Combination of CMB, BAO and galaxy shear/correlation data
9.5.2 Adding 21cm surveys
9.6 Conclusions


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