CMB Anisotropies at Second Order I

We present the computation of the full system of Boltzmann equations at second-order describing the evolution of the photon, baryon and cold dark matter fluids. These equations allow to follow the time evolution of the Cosmic Microwave Background (CMB) anisotropies at second-order at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present through the recombination era. This paper sets the stage for the computation of the full second-order radiation transfer function at all scales and for a a generic set of initial conditions specifying the level of primordial non-Gaussianity. In a companion paper, we will present the computation of the three-point correlation function at recombination which is so relevant for the issue of non-Gaussianity in the CMB anisotropies.Comment: 26 pages, LaTeX file, typos correcte

The bispectrum of redshifted 21-cm fluctuations from the dark ages

Brightness-temperature fluctuations in the redshifted 21-cm background from the cosmic dark ages are generated by irregularities in the gas-density distribution and can then be used to determine the statistical properties of density fluctuations in the early Universe. We first derive the most general expansion of brightness-temperature fluctuations up to second order in terms of all the possible sources of spatial fluctuations. We then focus on the three-point statistics and compute the angular bispectrum of brightness-temperature fluctuations generated prior to the epoch of hydrogen reionization. For simplicity, we neglect redshift-space distortions. We find that low-frequency radio experiments with arcmin angular resolution can easily detect non-Gaussianity produced by non-linear gravity with high signal-to-noise ratio. The bispectrum thus provides a unique test of the gravitational instability scenario for structure formation, and can be used to measure the cosmological parameters. Detecting the signature of primordial non-Gaussianity produced during or right after an inflationary period is more challenging but still possible. An ideal experiment limited by cosmic variance only and with an angular resolution of a few arcsec has the potential to detect primordial non-Gaussianity with a non-linearity parameter of f_NL ~ 1. Additional sources of error as weak lensing and an imperfect foreground subtraction could severely hamper the detection of primordial non-Gaussianity which will benefit from the use of optimal estimators combined with tomographic techniques.Comment: 15 pages, 4 figures, revised version accepted for publication in ApJ (contains an improved discussion of gas temperature fluctuations

On the Physical Significance of Infra-red Corrections to Inflationary Observables

Inflationary observables, like the power spectrum, computed at one- and higher-order loop level seem to be plagued by large infra-red corrections. In this short note, we point out that these large infra-red corrections appear only in quantities which are not directly observable. This is in agreement with general expectations concerning infra-red effects.Comment: 11 pages; LateX file; 5 figures. Some coefficients in Eq.(A6) corrected; References adde

Particle decay in inflationary cosmology

We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form eta^{Gamma1} with eta being conformal time and we give an explicit expression for Gamma1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the decaying field is << H then the decay rate during inflation is enhanced over the Minkowski spacetime result by a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find that the decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and alpha determined by the strength of the trilinear coupling. This result suggests a suppression of power for long wavelength modes upon horizon crossing. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-gaussianities.Comment: 19 pages, 1 .eps figure. Improved version to appear in Phys. Rev.

General Relativistic Dynamics of Irrotational Dust: Cosmological Implications

The non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in the two theories. Cosmological implications of relativistic effects, already present at second order in perturbation theory, are studied and the dynamical role of the magnetic part of the Weyl tensor is elucidated.Comment: 12 pages , DFPD 93/A/6

Observational evidence for stochastic biasing

We show that the galaxy density in the Las Campanas Redshift Survey (LCRS) cannot be perfectly correlated with the underlying mass distribution since various galaxy subpopulations are not perfectly correlated with each other, even taking shot noise into account. This rules out the hypothesis of simple linear biasing, and suggests that the recently proposed stochastic biasing framework is necessary for modeling actual data.Comment: 4 pages, with 2 figures included. Minor revisions to match accepted ApJL version. Links and color fig at http://www.sns.ias.edu/~max/r_frames.html or from [email protected]

Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum

The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus non-local in the density field, even if this term is absent in the initial conditions (Lagrangian space). Because the term is quadratic, it contributes as a loop correction to the power spectrum, so the standard linear bias picture still applies on large scales, however, it contributes at leading order to the bispectrum for which it is significant on all scales. Such a term could also be present in Lagrangian space if halo formation were influenced by the tidal field. We measure the corresponding coupling strengths from the matter-matter-halo bispectrum in numerical simulations and find a non-vanishing coefficient for the tidal tensor term. We find no scale dependence of the bias parameters up to k=0.1 h/Mpc and that the tidal effect is increasing with halo mass. While the Lagrangian bias picture is a better description of our results than the Eulerian bias picture, our results suggest that there might be a tidal tensor bias already in the initial conditions. We also find that the coefficients of the quadratic density term deviate quite strongly from the theoretical predictions based on the spherical collapse model and a universal mass function. Both quadratic density and tidal tensor bias terms must be included in the modeling of galaxy clustering of current and future surveys if one wants to achieve the high precision cosmology promise of these datasets.Comment: 14 pages, 4 figures, 1 tabl

Strip blowing from a wedge at hypersonic speeds

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76052/1/AIAA-12372-854.pd

Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations

Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order correlations, are obtained -- at any redshift and for any momentum scale -- by integrating a system of differential equations. The method is similar to the familiar BBGKY hierarchy. Truncating at the level of the trispectrum, the solution of the equations corresponds to the summation of an infinite class of perturbative corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than LambdaCDM, such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the Baryonic Acoustic Oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density-velocity and velocity-velocity power spectra are also computed, showing that they are much less contaminated by nonlinearities than the density-density one. The approach can be seen as a particular formulation of the renormalization group, in which time is the flow parameter.Comment: 20 pages, 7 figures. Matches version published on JCA

Primordial non-Gaussianity in the Bispectrum of the Halo Density Field

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on fNL and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.Comment: 34 pages, 15 figures, (v3): matches JCAP published versio