1,440 research outputs found
Maximal compression of the redshift space galaxy power spectrum and bispectrum
We explore two methods of compressing the redshift space galaxy power
spectrum and bispectrum with respect to a chosen set of cosmological
parameters. Both methods involve reducing the dimension of the original
data-vector ( e.g. 1000 elements ) to the number of cosmological parameters
considered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the first
case, we run MCMC sampling on the compressed data-vector in order to recover
the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The
second option, approximately 2000 times faster, works by orthogonalising the
parameter space through diagonalisation of the Fisher information matrix before
the compression, obtaining the posterior distributions without the need of MCMC
sampling. Using these methods for future spectroscopic redshift surveys like
DESI, EUCLID and PFS would drastically reduce the number of simulations needed
to compute accurate covariance matrices with minimal loss of constraining
power. We consider a redshift bin of a DESI-like experiment. Using the power
spectrum combined with the bispectrum as a data-vector, both compression
methods on average recover the 68% credible regions to within 0.7% and 2% of
those resulting from standard MCMC sampling respectively. These confidence
intervals are also smaller than the ones obtained using only the power spectrum
by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f
and the scalar amplitude parameter A_s.Comment: 27 pages, 8 figures, 1 table, Accepted 2018 January 28. Received 2018
January 25; in original form 2017 September 11. Added clarifications in the
text on the bias modelling and compression limits following referee's
comments. Removed tetraspectrum term from the pk-bk cross covariance +
correction in the appendi
A redshift distortion free correlation function at third order in the nonlinear regime
The zeroth-order component of the cosine expansion of the projected
three-point correlation function is proposed for clustering analysis of cosmic
large scale structure. These functions are third order statistics but can be
measured similarly to the projected two-point correlations. Numerical
experiments with N-body simulations indicate that the advocated statistics are
redshift distortion free within 10% in the non-linear regime on scales
~0.2-10Mpc/h. Halo model prediction of the zeroth-order component of the
projected three-point correlation function agrees with simulations within ~10%.
This lays the ground work for using these functions to perform joint analyses
with the projected two-point correlation functions, exploring galaxy clustering
properties in the framework of the halo model and relevant extensions.Comment: 10 pages, 6 figs; MNRAS accepte
CMB Bispectrum from Primordial Scalar, Vector and Tensor non-Gaussianities
We present an all-sky formalism for the Cosmic Microwave Background (CMB)
bispectrum induced by the primordial non-Gaussianities not only in scalar but
also in vector and tensor fluctuations. We find that the bispectrum can be
formed in an explicitly rationally invariant way by taking into account the
angular and polarization dependences of the vector and tensor modes. To
demonstrate this and present how to use our formalism, we consider a specific
example of the correlation between two scalars and a graviton as the source of
non-Gaussianity. As a result, we show that the CMB reduced bispectrum of the
intensity anisotropies is evaluated as a function of the multipole and the
coupling constant between two scalars and a graviton denoted by ;
. By
estimating the signal-to-noise ratio, we find that the constraint as will be expected from the PLANCK experiment.Comment: 19 pages, 4 figures. Accepted for publication in PT
Heterogeneous multireference alignment: a single pass approach
Multireference alignment (MRA) is the problem of estimating a signal from
many noisy and cyclically shifted copies of itself. In this paper, we consider
an extension called heterogeneous MRA, where signals must be estimated, and
each observation comes from one of those signals, unknown to us. This is a
simplified model for the heterogeneity problem notably arising in cryo-electron
microscopy. We propose an algorithm which estimates the signals without
estimating either the shifts or the classes of the observations. It requires
only one pass over the data and is based on low-order moments that are
invariant under cyclic shifts. Given sufficiently many measurements, one can
estimate these invariant features averaged over the signals. We then design
a smooth, non-convex optimization problem to compute a set of signals which are
consistent with the estimated averaged features. We find that, in many cases,
the proposed approach estimates the set of signals accurately despite
non-convexity, and conjecture the number of signals that can be resolved as
a function of the signal length is on the order of .Comment: 6 pages, 3 figure
The bispectrum of matter perturbations from cosmic strings
We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings
The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
This article presents the first computation of the complete bispectrum of the
cosmic microwave background temperature anisotropies arising from the evolution
of all cosmic fluids up to second order, including neutrinos. Gravitational
couplings, electron density fluctuations and the second order Boltzmann
equation are fully taken into account. Comparison to limiting cases that
appeared previously in the literature are provided. These are regimes for which
analytical insights can be given. The final results are expressed in terms of
equivalent fNL for different configurations. It is found that for moments up to
lmax=2000, the signal generated by non-linear effects is equivalent to fNL~5
for both local-type and equilateral-type primordial non-Gaussianity.Comment: 44 pages, 8 figure
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