Warm dark matter primordial spectra and the onset of structure formation at redshift z

Analytic formulas reproducing the warm dark matter (WDM) primordial spectra are obtained for WDM particles decoupling in and out of thermal equilibrium which provide the initial data for WDM non-linear structure formation. We compute and analyze the corresponding WDM overdensities and compare them to the CDM case. We consider the ratio of the WDM to CDM primordial spectrum and the WDM to CDM overdensities: they turn to be self-similar functions of k/k_{1/2} and R/R_{1/2} respectively, k_{1/2} and R_{1/2} being the wavenumber and length where the WDM spectrum and overdensity are 1/2 of the respective CDM magnitudes. Both k_{1/2} and R_{1/2} show scaling as powers of the WDM particle mass m while the self-similar functions are independent of m. The WDM primordial spectrum sharply decreases around k_{1/2} with respect to the CDM spectrum, while the WDM overdensity slowly decreases around R_{1/2}. The nonlinear regions where WDM structure formation takes place are shown and compared to those in CDM: the WDM non-linear structures start to form later than in CDM, and as a general trend, decreasing the DM particle mass delays the onset of the non-linear regime. The non-linear regime starts earlier for smaller objects than for larger ones; smaller objects can form earlier both in WDM and CDM. We compute and analyze the differential mass function dN/dM for WDM at redshift z in the Press-Schechter approach. The WDM suppression effect of small scale structure increases with the redshift z. Our results for dN/dM are useful to be contrasted with observations, in particular for 4 < z < 12. We perfom all these studies for the most popular WDM particle physics models. Contrasting them to observations should point out the precise value of the WDM particle mass in the keV scale, and help to single out the best WDM particle physics model (Abridged).Comment: 18 pages, 8 figures. To appear in Phys Rev

The pre-inflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles

We study the entire coupled evolution of the inflaton and the scale factor for general initial conditions at a given initial time. The generic early universe evolution has three stages: decelerated fast-roll followed by inflationary fast roll and then inflationary slow-roll. This evolution is valid for all regular inflaton potentials. In addition, we find a special (extreme) slow-roll solution starting at t = -infty in which the fast-roll stages are absent. At some time t = t_*, the generic evolution backwards in time reaches a mathematical singu- larity where a(t) vanishes and Hubble becomes singular. We find the general behaviour near the singularity. The classical inflaton description is valid for t-t_* > 10 t_{Planck} well before the beginning of inflation, quantum loop effects are negligible there. The singularity is never reached in the validity region of the classical treatment and therefore it is not a real physical phenomenon here. The whole evolution of the fluctuations is computed. The Bunch-Davies initial conditions (BDic) are generalized for the present case. The power spectrum gets dynamically modified by the effect of the fast-roll eras and the BDic choice at a finite time through the transfer function D(k) of initial conditions. D(0) = 0. D(k) presents a first peak for k ~ 2/eta_0 (eta_0 being the conformal initial time), then oscillates with decreasing amplitude and vanishes asymptotically for k -> infty. The transfer function D(k) affects the low CMB multipoles C_l: the change Delta C_l/C_l for l=1-5 is computed as a function of the starting instant of the fluctuations t_0. CMB quadrupole observations give large suppressions which are well reproduced here(Abridged)Comment: 31 pages, 10 figures. Version to appear in PR

Quantum WDM fermions and gravitation determine the observed galaxy structures

Quantum mechanics is necessary to compute galaxy structures at kpc scales and below. This is so because near the galaxy center, at scales below 10 - 100 pc, warm dark matter (WDM) quantum effects are important: observations show that the interparticle distance is of the order of, or smaller than the de Broglie wavelength for WDM. This explains why all classical (non-quantum) WDM N-body simulations fail to explain galactic cores and their sizes. We describe fermionic WDM galaxies in an analytic semiclassical framework based on the Thomas-Fermi approach, we resolve it numerically and find the main physical galaxy magnitudes: mass, halo radius, phase-space density, velocity dispersion, fully consistent with observations, including compact dwarf galaxies. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the observed galaxy DM cores and their sizes. [In addition, as is known, WDM simulations produce the right DM structures in agreement with observations for scales > kpc]. We show that compact dwarf galaxies are natural quantum macroscopic objects supported against gravity by the fermionic WDM quantum pressure (quantum degenerate fermions) with a minimal galaxy mass and minimal velocity dispersion. Interestingly enough, the minimal galaxy mass implies a minimal mass m_{min} for the WDM particle. The lightest known dwarf galaxy (Willman I) implies m > m_{min} = 1.91 keV. These results and the observed halo radius and mass of the compact galaxies provide further indication that the WDM particle mass m is approximately around 2 keV.Comment: 15 pages, 2 figures, expanded version to appear in Astroparticle Physics. admin note: substantial text overlap with arXiv:1204.309

Hemispherical power asymmetry: parameter estimation from CMB WMAP5 data

We reexamine the evidence of the hemispherical power asymmetry, detected in the CMB WMAP data using a new method. At first, we analyze the hemispherical variance ratios and compare these with simulated distributions. Secondly, working within a previously-proposed CMB bipolar modulation model, we constrain model parameters: the amplitude and the orientation of the modulation field as a function of various multipole bins. Finally, we select three ranges of multipoles leading to the most anomalous signals, and we process corresponding 100 Gaussian, random field (GRF) simulations, treated as observational data, to further test the statistical significance and robustness of the hemispherical power asymmetry. For our analysis we use the Internally-Linearly-Coadded (ILC) full sky map, and KQ75 cut-sky V channel, foregrounds reduced map of the WMAP five year data (V5). We constrain the modulation parameters using a generic maximum a posteriori method. In particular, we find differences in hemispherical power distribution, which when described in terms of a model with bipolar modulation field, exclude the field amplitude value of the isotropic model A=0 at confidence level of ~99.5% (~99.4%) in the multipole range l=[7,19] (l=[7,79]) in the V5 data, and at the confidence level ~99.9% in the multipole range l=[7,39] in the ILC5 data, with the best fit (modal PDF) values in these particular multipole ranges of A=0.21 (A=0.21) and A=0.15 respectively. However, we also point out that similar or larger significances (in terms of rejecting the isotropic model), and large best-fit modulation amplitudes are obtained in GRF simulations as well, which reduces the overall significance of the CMB power asymmetry down to only about 94% (95%) in the V5 data, in the range l=[7,19] (l=[7,79]).Comment: 24 pages, 10 figures; few typos corrected; published in JCA

Testing String Theory with CMB

Future detection/non-detection of tensor modes from inflation in CMB observations presents a unique way to test certain features of string theory. Current limit on the ratio of tensor to scalar perturbations, r=T/S, is r < 0.3, future detection may take place for r > 10^{-2}-10^{-3}. At present all known string theory inflation models predict tensor modes well below the level of detection. Therefore a possible experimental discovery of tensor modes may present a challenge to string cosmology. The strongest bound on r in string inflation follows from the observation that in most of the models based on the KKLT construction, the value of the Hubble constant H during inflation must be smaller than the gravitino mass. For the gravitino mass in the usual range, m_{3/2} < O(1) TeV, this leads to an extremely strong bound r < 10^{-24}. A discovery of tensor perturbations with r > 10^{-3} would imply that the gravitinos in this class of models are superheavy, m_{3/2} > 10^{13} GeV. This would have important implications for particle phenomenology based on string theory.Comment: 13 pages, 2 figure

Fermionic warm dark matter produces galaxy cores in the observed scales because of quantum mechanics

15 pages, no figuresInternational audienceThe fermionic dark matter (DM) phase-space density Q(r) = rho(r)/sigma^3(r) must be smaller than K m^4/\hbar^3 where m is the DM particle mass, sigma(r) is the DM velocity dispersion and K is a pure number of order one which we estimate. This bound follows from the Pauli principle which restricts the phase-space distribution function of fermionic spin-1/2 dark matter (DM) particles to be f(r,p) < 2. Cusped profiles from N-body galaxy simulations produce a divergent Q(r) at r = 0 violating this quantum bound. Combining this quantum bound with the behavior of Q(r) from simulations and with galaxy observational data on Q, implies that classical galaxy dynamics breaks down for fermionic DM at a distance from the centre of at least r_q. For keV scale WDM r_q turns to be in the parsec scale. For cold dark matter (CDM), r_q is between dozens of kilometers and a few meters, astronomically compatible with zero. For fermionic hot dark matter (HDM) r_q is from kpc to Mpc. This quantum bound rules out the presence of galaxy cusps for fermionic WDM. This is in agreement with astronomical observations which show that the DM halos are cored. The formation of cusps would be allowed for bosonic DM for which the Pauli principle does not apply. Hence, bosonic DM is strongly disfavored by the observation of galaxy cores. Quantum dynamical calculations become necessary to compute galaxy structures at kpc scales and below. N-body simulations can be used at scales larger than a kpc and matched with the quantum evolution.The Thomas-Fermi quantum approximation to self-gravitating fermions with masses in the keV scale yields galaxy properties as halo radius, mass and velocity dispersion consistent with the observations. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the observed DM cores of galaxies

The CMB Quadrupole depression produced by early fast-roll inflation: MCMC analysis of WMAP and SDSS data

23 pages, 11 figuresInternational audienceGenerically,the classical evolution of the inflaton has a brief fast roll stage that precedes the slow roll regime. The fast roll stage leads to a purely attractive potential for the curvature and tensor perturbations (this potential is purely repulsive in slowroll). This attractive potential depresses the CMB quadrupole moment for the curvature and B-mode spectra. A single new cosmological parameter emerges: the comoving wavenumber k_1 characteristic scale of this attractive potential.k_1 happens to exit the horizon precisely at the transition from fast to slowroll.The fastroll stage dynamically modifies the initial power spectrum by a transfer function D(k). We compute D(k) by solving the inflaton evolution equations. D(k) suppresses the primordial power for k < k_1 and enjoys the scaling property D(k) = Psi(k/k_1) where Psi(x) is an universal function. We perform a MCMC analysis of the WMAP/SDSS data including the fast-roll stage and find k_1 = 0.266/Gpc. The quadrupole mode k_Q = 0.145/Gpc exits the horizon 2/3 of an efold before k_1. We compare the fastroll fit with a fit with a sharp lower cutoff on the primordial power. Fastroll provides a slightly better fit than a sharp cutoff both for the TT and TE modes.Moreover, our fits provide non-zero lower bounds for r, while for the other cosmological parameters we essentially get those of the LCDM model. The fact that k_Q exits the horizon before the slowroll stage implies an upper bound in the total number of efolds N_{tot} during inflation.Combining this with estimates during the radiation dominated era we obtain N_{tot} \sim 66, with the bounds 62 < N_{tot} < 82.We repeated the analysis with the WMAP-5/ACBAR-2007/SDSS data confirming the overall picture

MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio

25 pages, 8 figures. Expanded and improved versionInternational audienceWe perform a MCMC (Monte Carlo Markov Chains) analysis of the available CMB and LSS data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the GinsburgLandau spirit with fourth degree trinomial potentials in the inflaton field phi.We derive explicit formu- lae and study in detail the spectral index ns of the adiabatic fluctuations the ratio r of tensor to scalar fluctuations and the running index dn_s/dln k. We use these analytic formulas as hard constraints on n_s and r in the MCMC analysis.Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follow: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the phi -> -phi symmetry of the inflaton potentials both for new and for chaotic inflation.(ii)Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data.(iii)Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space.(iv) The chaotic symmetric trinomial potential is almost certainly ruled out(at 95% CL).In tri- nomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which ressembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data.(vi) We find a lower bound for r within trinomial new inflation potentials r > 0.016 (95% CL) and r > 0.049 (68% CL). (vii) The preferred new inflation trinomial potential is a double well, even function of the field yielding as most probable values: n_s ~ 0.958, r ~ 0.055

The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis

Review article, 134 pages, 41 figuresInternational audienceInflation is part of the Standard Model of the Universe supported by CMB and large scale structure LSS datasets. This review presents new developments of inflation in three main chapters. (I): The effective theory of inflation a la Ginsburg-Landau (GL): the inflaton potential is a polynomial with universal form making explicit the inflation energy scale M, the Planck mass and the inflation e-folds number N ~ 60. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings are naturally small as powers of (M/M_{Pl})^2. The spectral index (n_s - 1) and the ratio of tensor/scalar fluctuations r are O(1/N), the running index is O(1/N^2). M ~ 0.7 10^{16} GeV is completely determined by the scalar adiabatic fluctuations amplitude. (II): A Monte Carlo Markov Chains (MCMC) analysis of the CMB+LSS data (including WMAP5) with our analytic theoretical results yields: a lower bound for r (new inflation): r > 0.023 (95%CL), r > 0.046 (68%CL); the preferred inflation potential is a double well, even function of the field yielding as most probable values n_s ~ 0.964, r ~ 0.051. This value for r is within reach of forthcoming CMB observations. Slow-roll inflation is generically preceded by a short fast-roll stage which leads to a suppression of the CMB quadrupoles. MCMC analysis of the WMAP+SDSS data shows that fast-roll fits the TT, TE and EE modes well reproducing the quadrupole suppression and fixes the total number of efolds of inflation to be N_{total} ~ 64. (III) Quantum loop corrections are very small and controlled by powers of (H /M_{Pl})^2 ~ 10^{-9} which validates the effective theory of inflation. We show how powerful is the GL theory of inflation in predicting observables

Forecast for the Planck precision on the tensor to scalar ratio and other cosmological parameters

The Planck satellite, successfully launched on 2009 May 14 to measure with unprecedented accuracy the primary cosmic microwave background (CMB) anisotropies, is operating as expected. The Standard Model of the Universe ("concordance" model) provides the current realistic context to analyze the CMB and other cosmological/astrophysical data, inflation in the early universe being part of it. The Planck performance for the crucial primordial parameter r, the tensor-to-scalar ratio related to primordial B-mode polarization, will depend on the quality of data analysis and interpretation. The Ginzburg-Landau (G-L) approach to inflation allows us to take high benefit of the CMB data. The fourth-degree double-well inflaton potential gives an excellent fit to the current CMB+LSS data. We evaluate the Planck precision to the recovery of cosmological parameters, taking into account a reasonable toy model for residuals of systematic effects of instrumental and astrophysical origin based on publicly available information. We use and test two relevant models: the ΛCDMr model, i.e., the standard ΛCDM model augmented by r, and the ΛCDMrT model, where the scalar spectral index, ns , and r are related through the theoretical "banana-shaped" curve r = r(ns ) coming from the G-L theory with a double-well inflaton potential. In the latter case, the analytical expressions for ns and r are imposed as a hard constraint in a Monte Carlo Markov Chain (MCMC) data analysis. We consider two C ℓ-likelihoods (with and without B modes) and take into account the white noise sensitivity of Planck (LFI and HFI) in the 70, 100, and 143 GHz channels as well as the residuals from systematic errors and foregrounds. We also consider a cumulative channel of the three mentioned. We produce the sky (mock data) for the CMB multipoles CTT l , CTE l , CEE l , and CBB l from the ΛCDMr and ΛCDMrT models and obtain the cosmological parameter marginalized likelihood distributions for the two models. Foreground residuals affect only the cosmological parameters sensitive to the B modes. As expected, the likelihood r distribution is more clearly peaked near the fiducial value (r = 0.0427) in the ΛCDMrT model than in the ΛCDMr model. The best value for r in the presence of residuals turns out to be about r 0.04 for both the ΛCDMr and the ΛCDMrT models. The ΛCDMrT model is very stable; its distributions do not change by including residuals and the B modes. For r we find 0.028 < r < 0.116 at a 95% confidence level (CL) with the best value r = 0.04. We also compute the B mode detection probability by the most sensitive HFI-143 channel. At the level of foreground residual equal to 30% of our toy model, only a 68% CL (1σ) detection is very likely. For a 95% CL detection (2σ), the level of foreground residual should be reduced to 10% or lower of the adopted toy model. The lower bounds (and most probable value) we infer for r support the searching of CMB B-mode polarization in the current data as well as the planned CMB missions oriented toward B polarization