887 research outputs found
Disantangling the effects of Doppler velocity and primordial non-Gaussianity in galaxy power spectra
We study the detectability of large-scale velocity effects on galaxy
clustering, by simulating galaxy surveys and combining the clustering of
different types of tracers of large-scale structure. We employ a set of
lognormal mocks that simulate a deg near-complete survey up to
, in which each galaxy mock traces the spatial distribution of dark
matter of that mock with a realistic bias prescription. We find that the ratios
of the monopoles of the power spectra of different types of tracers carry most
of the information that can be extracted from a multi-tracer analysis. In
particular, we show that with a multi-tracer technique it will be possible to
detect velocity effects with . Finally, we investigate the
degeneracy of these effects with the (local) non-Gaussianity parameter , and how large-scale velocity contributions could be mistaken for the
signatures of primordial non-Gaussianity.Comment: 17 pages, 25 figure
Testing gaussianity, homogeneity and isotropy with the cosmic microwave background
We review the basic hypotheses which motivate the statistical framework used
to analyze the cosmic microwave background, and how that framework can be
enlarged as we relax those hypotheses. In particular, we try to separate as
much as possible the questions of gaussianity, homogeneity and isotropy from
each other. We focus both on isotropic estimators of non-gaussianity as well as
statistically anisotropic estimators of gaussianity, giving particular emphasis
on their signatures and the enhanced "cosmic variances" that become
increasingly important as our putative Universe becomes less symmetric. After
reviewing the formalism behind some simple model-independent tests, we discuss
how these tests can be applied to CMB data when searching for large scale
"anomalies"Comment: 52 pages, 22 pdf figures. Revised version of the invited review for
the special issue "Testing the Gaussianity and Statistical Isotropy of the
Universe" for Advances in Astronomy
Why multi-tracer surveys beat cosmic variance
Galaxy surveys that map multiple species of tracers of large-scale structure
can improve the constraints on some cosmological parameters far beyond the
limits imposed by a simplistic interpretation of cosmic variance. This
enhancement derives from comparing the relative clustering between different
tracers of large-scale structure. We present a simple but fully generic
expression for the Fisher information matrix of surveys with any (discrete)
number of tracers, and show that the enhancement of the constraints on
bias-sensitive parameters are a straightforward consequence of this
multi-tracer Fisher matrix. In fact, the relative clustering amplitudes between
tracers are eigenvectors of this multi-tracer Fisher matrix. The diagonalized
multi-tracer Fisher matrix clearly shows that while the effective volume is
bounded by the physical volume of the survey, the relational information
between species is unbounded. As an application, we study the expected
enhancements in the constraints of realistic surveys that aim at mapping
several different types of tracers of large-scale structure. The gain obtained
by combining multiple tracers is highest at low redshifts, and in one
particular scenario we analyzed, the enhancement can be as large as a factor of
~3 for the accuracy in the determination of the redshift distortion parameter,
and a factor ~5 for the local non-Gaussianity parameter. Radial and angular
distance determinations from the baryonic features in the power spectrum may
also benefit from the multi-tracer approach.Comment: New references included; 9 pages, 9 figure
A completeness-like relation for Bessel functions
Completeness relations are associated through Mercer's theorem to complete
orthonormal basis of square integrable functions, and prescribe how a Dirac
delta function can be decomposed into basis of eigenfunctions of a
Sturm-Liouville problem. We use Gegenbauer's addition theorem to prove a
relation very close to a completeness relation, but for a set of Bessel
functions not known to form a complete basis in
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