Cosmology and the Bispectrum

TL;DR

The paper analyzes how the galaxy bispectrum, in conjunction with the power spectrum and CMB data, can tighten cosmological parameter constraints beyond what the power spectrum alone offers. It develops a detailed covariance framework, validated with extensive 2LPT and PTHalos mocks, and demonstrates that the bispectrum primarily improves constraints on the amplitude $A_s$, spectral index $n_s$, and $\sigma_8$, while remaining robust to a non-$\Lambda$CDM equation of state $w$. Beat-coupling arising from the survey window is shown to enhance mixed covariances and must be included for accurate likelihoods; the bispectrum is found to be complementary to BAO information and to provide additional leverage in both $\Lambda$CDM and $w$CDM contexts (including a WMAP3 update in the Appendix). Overall, non-Gaussian statistics from the bispectrum are shown to meaningfully improve cosmological inferences and will inform analyses of future galaxy surveys.

Abstract

The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 Mpc/h 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 sigma8 of a few percent are robust to relaxing the dark energy beyond a cosmological constant.

Figures (2)

• Figure 1: An example showing the constraining power of the bispectrum compared to the power spectrum. The panels show marginalized likelihood functions corresponding to a hypothetical joint analysis of WMAP (first year) and SDSS North (by the end of the survey) where only the galaxy power spectrum is used (blue, dashed line), or only the galaxy bispectrum is used (red, solid line). Assumes a flat cosmology and scales up to $k_{\hbox{\tiny{max}}}=0.3\, h \, {\rm Mpc}^{-1}$.
• Figure 2: Power spectrum cross-correlation coefficients $r_{ij}^P$ between different scales for the main (left) and LRG sample (right) as measured from the SDSS mock catalogs. Black indicates maximum cross-correlation ($r_{ij}^P=1$), white no cross-correlation ($r_{ij}^P=0$). The wavenumbers are given in units of $\Delta k\simeq 0.015\, h \, {\rm Mpc}^{-1}$ for the main sample power spectrum, while $\Delta k\simeq 0.0075\, h \, {\rm Mpc}^{-1}$ for the LRG power spectrum. Note that bin 27 in the LRG case corresponds to bin 13 in the main sample case: the lower left region in the main sample plot encloses the scales corresponding to the LRG plot.