Local primordial non-Gaussianity in the relativistic galaxy bispectrum

Abstract

Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primordial non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark matter density, due to redshift-space effects. The standard redshift-space distortions at first and second order produce a well-known primordial non-Gaussian imprint on the bispectrum. Relativistic corrections to redshift-space distortions generate new contributions to this primordial non-Gaussian signal, arising from: (1) a coupling of first-order scale-dependent bias with first-order relativistic observational effects, and (2) linearly evolved non-Gaussianity in the second-order velocity and metric potentials which appear in relativistic observational effects. Our analysis allows for a consistent separation of the relativistic `contamination' from the primordial signal, in order to avoid biasing the measurements by using an incorrect theoretical model. We show that the bias from using a Newtonian analysis of the squeezed bispectrum could be Δ fNL∼ 5 for a Stage IV Hα survey.

Including relativistic and primordial Non-Gaussianity contributions in cosmological simulations by modifying the initial condition

“…One of the intrinsically non-linear observables is the matter bispectrum: the Fourier space equivalent of the three-point correlation in the matter distribution. Due to its non-linear character, this observable is expected to show the effects of primordial Non-Gaussianity [5,12,13], complementing the effects expected in the power spectrum [14][15][16][17]. When computed in an evolved matter distribution, the bispectrum also shows the non-linearities of the clustering process, as has been shown in the perturbative regime of the Newtonian [18,19] and relativistic theories [20][21][22][23].…”

Predictions for local PNG bias in the galaxy power spectrum and bispectrum and the consequences for $f_{\rm NL}$ constraints

“…In our analysis, we consider k max = 0.2h/Mpc, on which corrections to our tree-level theory model do become important, but since the data vector is obtained from the theory model this does not impact our main conclusions on the impact of galaxy bias uncertainties. For simplicity, we also skip modeling the effects of redshift space distortions [96], so-called projection/relativistic effects [28,30,35,[97][98][99][100][101], and observational systematics [102]. Any reduction in constraining power from taking these complications into account reduces the overall importance of the uncertainties on galaxy bias, but only in the sense that there are more sources of uncertainty worsening the constraints on f nl .…”

“…In this way, the contribution scales as ∝ (b 1 − 1) f nl /k 2 , and since b 1 can in principle be constrained using the smaller-scale part of the power spectrum (where f nl contributes weakly), it then becomes possible to constrain f nl . The universality relation is adopted by almost all existing galaxy data constraints on f nl [16,[18][19][20][21][22][23][24][25] (the current tightest bound is f nl = −12 ± 21 (1σ) [25]), as well as in forecast studies [7,[26][27][28][29][30][31][32][33][34][35][36] for next-generation surveys. Despite its widespread adoption, there is however no reason to expect the universality relation to hold for real-life galaxy samples, and in fact, studies using N -body simulations have been indicating this to be the case already.…”

Multi-wavelength spectroscopic probes: biases from neglecting light-cone effects

“…Since the Doppler and potential contributions mimic the effect of f NL , it follows that neglecting these contributions could bias future measurements of f NL [8][9][10][11][12][13] (see also [14][15][16][17] for the galaxy bispectrum). Neglecting the lensing contribution can also lead to a biased measurement of f NL -by biasing the estimate of clustering bias that affects the amplitude of the f NL contribution [12,18].…”