Abstract
We forecast constraints on primordial non-Gaussianity (PNG) and bias parameters from measurements of galaxy power spectrum and bispectrum in future radio continuum and optical surveys. In the galaxy bispectrum, we consider a comprehensive list of effects, including the bias expansion for non-Gaussian initial conditions up to second order, redshift space distortions, redshift uncertainties and theoretical errors. These effects are all combined in a single PNG forecast for the first time. Moreover, we improve the bispectrum modelling over previous forecasts, by accounting for trispectrum contributions. All effects have an impact on final predicted bounds, which varies with the type of survey. We find that the bispectrum can lead to improvements up to a factor $\sim 5$ over bounds based on the power spectrum alone, leading to significantly better constraints for local-type PNG, with respect to current limits from \textit{Planck}. Future radio and photometric surveys could obtain a measurement error of $\sigma(f_{\mathrm{NL}}^{\mathrm{loc}}) \approx 0.2$. In the case of equilateral PNG, galaxy bispectrum can improve upon present bounds only if significant improvements in the redshift determinations of future, large volume, photometric or radio surveys could be achieved. For orthogonal non-Gaussianity, expected constraints are generally comparable to current ones.
Highlights
Cosmological analyses of Large Scale Structure (LSS) surveys have relied nearly exclusively on matter and galaxy power spectrum estimation
It is wellknown that important extra-information can be extracted via higher-order correlation functions, such as the matter and galaxy bispectrum, which allow both probing the non-linear regime of structure growth and setting constraints on primordial non-Gaussianity (PNG)
The paper is structured as follows: In Sec. 2.1, we provide a brief review of the theory behind matter clustering and PNG; in Sec. 2.2 we discuss in more detail the relationship between matter and galaxy statistics; in Sec. 2.3 we present the expressions for galaxy power spectra and bispectra considering all the relevant effects; in Sec. 3 we describe the survey specifications that we have used for our analysis; in Sec. 4.1 we describe the Fisher matrix forecast method; in Sec. 4.2 we explain how to account for theoretical errors in the forecast
Summary
Cosmological analyses of Large Scale Structure (LSS) surveys have relied nearly exclusively on matter and galaxy power spectrum estimation. Bispectrum estimates of fNL with future LSS data do have in principle great potential to improve over CMB bounds, at least for specific shapes. This is because 3D LSS surveys, covering large volumes and probing a wide range of scales, have access to a much larger amount of modes, with respect to 2D CMB maps. LSS measurements will be very challenging, due to late-time non-linearities, expected to produce much larger non-Gaussian signatures than the primordial component. These contributions need to be understood and subtracted with exquisite accuracy. Note that an interesting probe for the local PNG consist of the asymmetric two-point cross-correlation between two different galaxy populations, which is enhanced by non-Gaussian initial conditions (see Dai et al 2016, for details)
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