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 $20.000$ deg$^2$ near-complete survey up to $z=0.8$, 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 $\gtrsim 3 \sigma$. Finally, we investigate the degeneracy of these effects with the (local) non-Gaussianity parameter $f_{\rm NL}$, 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 $L^2[0, 1]$

Non singular bounce in modified gravity

We investigate bouncing solutions in the framework of the non-singular gravity model of Brandenberger, Mukhanov and Sornborger. We show that a spatially flat universe filled with ordinary matter undergoing a phase of contraction reaches a stage of minimal expansion factor before bouncing in a regular way to reach the expanding phase. The expansion can be connected to the usual radiation- and matter-dominated epochs before reaching a final expanding de Sitter phase. In general relativity (GR), a bounce can only take place provided that the spatial sections are positively curved, a fact that has been shown to translate into a constraint on the characteristic duration of the bounce. In our model, on the other hand, a bounce can occur also in the absence of spatial curvature, which means that the timescale for the bounce can be made arbitrarily short or long. The implication is that constraints on the bounce characteristic time obtained in GR rely heavily on the assumed theory of gravity. Although the model we investigate is fourth order in the derivatives of the metric (and therefore unstable vis-a-vis the perturbations), this generic bounce dynamics should extend to string-motivated non singular models which can accommodate a spatially flat bounce.Comment: 9 pages, 10 figure