Assessment of the information content of the power spectrum and bispectrum

The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related line-of-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether nextgeneration spectroscopic surveys could make such a detection. For a Stage IV spectroscopic Hα survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is O(10). Long-mode relativistic effects couple to short-mode Newtonian effects in the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for detectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the power spectrum requires multiple galaxy surveys to detect the corresponding signal.

Section: Nonlinear Effectsmentioning

confidence: 87%

“…where we have introduced the complex conjugate B * g since the bispectrum has an imaginary correction. Here Var[B g ] is the variance of the bispectrum estimator [19]:…”

Section: Signal To Noisementioning

confidence: 99%

Detecting the relativistic galaxy bispectrum

Maartens

Jolicoeur

Umeh

et al. 2020

“…In addition to the primordial and gravitation contributions, the galaxy bispectrum receives a stochastic contribution due to the discreteness of galaxies. The Poisson prediction for the shot noise contribution is [61,62] B shot g (k 1 , k 2 , k 3 ) = 1 n g P g (k 1 ) + 2 perms + 1 n 2 g , (3.37)…”

Section: Shot Noisementioning

confidence: 99%

Capturing non-Gaussianity of the large-scale structure with weighted skew-spectra

Dizgah

Lee

Schmittfull

et al. 2020

The forthcoming generation of wide-field galaxy surveys will probe larger volumes and galaxy densities, thus allowing for a much larger signal-to-noise ratio for higher-order clustering statistics, in particular the galaxy bispectrum. Extracting this information, however, is more challenging than using the power spectrum due to more complex theoretical modeling, as well as significant computational cost of evaluating the bispectrum signal and the error budget. To overcome these challenges, several proxy statistics have been proposed in the literature, which partially or fully capture the information in the bispectrum, while being computationally less expensive than the bispectrum. One such statistics are weighted skew-spectra, which are cross-spectra of the density field and appropriately weighted quadratic fields. Using Fisher forecasts, we show that the information in these skew-spectra is equivalent to that in the bispectrum for parameters that appear as amplitudes in the bispectrum model, such as galaxy bias parameters or the amplitude of primordial non-Gaussianity. We consider three shapes of the primordial bispectrum: local, equilateral and that due to massive particles with spin two during inflation. To obtain constraints that match those from a measurement of the full bispectrum, we find that it is crucial to account for the full covariance matrix of the skew-spectra.

“…the bispectrum. In fact, the bispectrum has a comparable signal-to-noise ratio to the power spectrum on nonlinear scales (Sefusatti & Scoccimarro 2005;Chan & Blot 2017). Furthermore, although M ν is not included in their analyses, Sefusatti et al (2006) and Yankelevich & Porciani (2019) have shown that including the bispectrum significantly improves constraints on cosmological parameters.…”

mentioning

confidence: 99%

Constraining M_ν with the bispectrum. Part I. Breaking parameter degeneracies

Hahn

Villaescusa-Navarro

Castorina

et al. 2020

158

188

Massive neutrinos suppress the growth of structure below their free-streaming scale and leave an imprint on large-scale structure. Measuring this imprint allows us to constrain the sum of neutrino masses, M ν , a key parameter in particle physics beyond the Standard Model. However, degeneracies among cosmological parameters, especially between M ν and σ 8 , limit the constraining power of standard two-point clustering statistics. In this work, we investigate whether we can break these degeneracies and constrain M ν with the next higher-order correlation function -the bispectrum. We first examine the redshift-space halo bispectrum of 800 N -body simulations from the HADES suite and demonstrate that the bispectrum helps break the M ν -σ 8 degeneracy. Then using 22,000 N -body simulations of the Quijote suite, we quantify for the first time the full information content of the redshift-space halo bispectrum down to nonlinear scales using a Fisher matrix forecast of {Ω m , Ω b , h, n s , σ 8 , M ν }. For k max =0.5 h/Mpc, the bispectrum provides Ω m , Ω b , h, n s , and σ 8 constraints 1.9, 2.6, 3.1, 3.6, and 2.6 times tighter than the power spectrum. For M ν , the bispectrum improves the 1σ constraint from 0.2968 to 0.0572 eV -over 5 times tighter than the power spectrum. Even with priors from Planck, the bispectrum improves M ν constraints by a factor of 2.7. Although we reserve marginalizing over a more complete set of bias parameters to the next paper of the series, these constraints are derived for a (1 h −1 Gpc) 3 box, a substantially smaller volume than upcoming surveys. Thus, our results demonstrate that the bispectrum offers significant improvements over the power spectrum, especially for constraining M ν .