Cosmological Parameters Degeneracies and Non-Gaussian Halo Bias

TL;DR

This work addresses how uncertainties in cosmological parameters affect constraints on local primordial non-Gaussianity $f_{\rm NL}$ obtained from the large-scale non-Gaussian halo bias. Using Fisher forecasts for Euclid- and LSST-like surveys, both with and without Planck priors, and within two neutrino frameworks, it quantifies degeneracies with parameters such as $\alpha_s$, $w$, $c_s^2$, and $M_\nu$, emphasizing the role of $N_\nu^{\rm rel}$. The main finding is that $f_{\rm NL}$ constraints are robust to most cosmological-model uncertainties, increasing only modestly (10–30%) when $N_\nu^{\rm rel}$ is fixed, but degrading by about 80% if $N_\nu^{\rm rel}$ is left free; with Planck priors, the marginalized error can reach $\Delta f_{\rm NL} \sim 2-5$, competitive with ideal CMB bispectrum limits. This indicates that upcoming large-volume LSS surveys can provide powerful, largely model-insensitive tests of local primordial non-Gaussianity, guiding survey design and joint analyses with CMB data.

Abstract

We study the impact of the cosmological parameters uncertainties on the measurements of primordial non-Gaussianity through the large-scale non-Gaussian halo bias effect. While this is not expected to be an issue for the standard LCDM model, it may not be the case for more general models that modify the large-scale shape of the power spectrum. We consider the so-called local non-Gaussianity model and forecasts from planned surveys, alone and combined with a Planck CMB prior. In particular, we consider EUCLID- and LSST-like surveys and forecast the correlations among $f_{\rm NL}$ and the running of the spectral index $α_s$, the dark energy equation of state $w$, the effective sound speed of dark energy perturbations $c^2_s$, the total mass of massive neutrinos $M_ν=\sum m_ν$, and the number of extra relativistic degrees of freedom $N_ν^{rel}$. Neglecting CMB information on $f_{\rm NL}$ and scales $k > 0.03 h$/Mpc, we find that, if $N_ν^{\rm rel}$ is assumed to be known, the uncertainty on cosmological parameters increases the error on $f_{\rm NL}$ by 10 to 30% depending on the survey. Thus the $f_{\rm NL}$ constraint is remarkable robust to cosmological model uncertainties. On the other hand, if $N_ν^{\rm rel}$ is simultaneously constrained from the data, the $f_{\rm NL}$ error increases by $\sim 80%$. Finally, future surveys which provide a large sample of galaxies or galaxy clusters over a volume comparable to the Hubble volume can measure primordial non-Gaussianity of the local form with a marginalized 1--$σ$ error of the order $Δf_{\rm NL} \sim 2-5$, after combination with CMB priors for the remaining cosmological parameters. These results are competitive with CMB bispectrum constraints achievable with an ideal CMB experiment.

Figures (3)

• Figure 1: The solid blue line represents the NG halo power spectrum for $f_{\rm NL}=100$ and halo mass $M=10^{13} M_\odot$, while the dotted blue line is the corresponding Gaussian halo power spectrum ($f_{\rm NL}=0$), at redshift $z=0$. The dashed red line represents the matter power spectrum calculated for $w=-0.9$, while the red three-dot-dashed line is the matter power spectrum for $w=-0.2$. The matter power spectra are evaluated at $z=0$ and normalized to the same amplitude at $k=0.002$. Note that $\Delta (\ln P_h(k))/\Delta w$ and $\Delta (\ln P_h(k))/\Delta f_{\rm NL}$ have opposite sign in the range of $k$ of interest here: it is clear from Eq. (3.3) that the two parameters can compensate each other, i.e. they are correlated
• Figure 2: 2-parameter $f_{\rm NL}$-$p_\alpha$ joint contours for the fiducial model with extra relativistic degrees of freedom $N_\nu^{\rm rel}$ as described in the text, obtained after combining LSST (upper panels) and EUCLID (lower panels) data with Planck priors. The blue dotted line, the red dashed line and the orange dot-dashed line represent the 68$\%$ C.L., 95.4$\%$ C.L. and 99.73$\%$ C.L., respectively. The black solid line shows the 1-parameter confidence level at 1--$\sigma$.
• Figure 3: The same as in Fig. 2, for the fiducial model with massive neutrinos of total mass $M_\nu|_{\rm fid}=0.3$ eV, as described in the text.