Cosmology and the bispectrum

Abstract

The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 h −1 Mpc spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work we present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. We address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. We show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models we show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of two. Moreover, we demonstrate that the expected statistical uncertainties in σ8 of a few percent are robust to relaxing the dark energy beyond a cosmological constant.

Bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and nonlinear galaxy bias

“…(We do include covariance between b 1 , b 2 , and f N L .) Sefusatti et al (2006) have shown that, for the SDSS main sample, an analysis with the full covariance among all parameters with a prior from the WMAP 3-yr results yields an error on b 1 that is twice as large as that from a simpler analysis without covariance. On the other hand, an error on b 2 is not affected significantly.…”

“…On the other hand, an error on b 2 is not affected significantly. Note that the effect on b 1 that they observed was due mainly to degeneracy between b 1 and the amplitude of matter fluctuations, as Sefusatti et al (2006) did not use the reduced bispectrum. We expect that degeneracy would be lifted in our analysis, as we use the reduced bispectrum in which the overall amplitude of matter fluctuations cancels.…”

“…This method has been applied successfully to existing galaxy surveys such as the 2dFGRS and the SDSS, yielding constraints on non-linearities in galaxy bias (Verde et al 2002;Pan & Szapudi 2005;Gaztañaga et al 2005;Nishimichi et al 2006) as well as on the Halo Occupation Distribution (HOD) (Kulkarni et al 2007). Moreover, it has been shown that the galaxy bispectrum contains additional cosmological information that is not present in the power spectrum (Sefusatti & Scoccimarro 2005;Sefusatti et al 2006).…”

Probing cosmology with weak lensing Minkowski functionals

“…This is because gravity is non-linear, and it generates nonGaussianity on small scales. Perhaps the most natural way to proceed and characterize non-Gaussian statistical signatures is by using higher-order poly-spectra [1], or equivalently, three-point and higher-order correlation functions [2][3][4][5][6][7][8][9][10]. 1 An interesting, and less explored alternative, originally suggested in the context of the cosmic density field [12], is to utilize topological features.…”

Matter bispectrum in cubic Galileon cosmologies

“…It is well known that NG can be classified in primordial and late-time. The primordial ones come from non-linearities encoded in the inflationary perturbations [60]; these are imprinted in the CMB and in the Large-Scale Structure (LSS) of the universe [61][62][63][64][65][66][67], and should be constrained by present and future surveys [68,69]. The late-time non-Gaussianity in the LSS is generated classically by gravitational instability, when cosmological perturbations enter non-linear scales.…”