1,082 research outputs found
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
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