Efficient Cosmological Analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure

TL;DR

This paper extends EFTofLSS analysis of BOSS DR12 by enabling a full νΛCDM parameter exploration through a low-order Taylor expansion of the EFTofLSS predictions around a reference cosmology, drastically accelerating likelihood evaluations. Analyzing the CMASS and LOWZ NGC data with the redshift-space one-loop power spectrum, the authors test multiple priors (Planck2018 on $f_{bc}$ and $n_s$, Planck2018 on $\omega_b$ and $n_s$, and a BBN prior on $\omega_b$) and examine scenarios with fixed or varying total neutrino mass $\sum_i m_{\nu_i}$. They find that, with a broad $\Omega_b h^2$ prior and a permissive neutrino-mass range, key parameters $A_s$, $\Omega_m$, $H_0$, and $n_s$ are constrained with percent-level precision, while neutrino masses are bounded (e.g., $\sum_i m_{\nu_i} < 0.83$ eV at 95% C.L.). The approach yields results consistent with prior analyses and demonstrates the EFTofLSS framework’s ability to extract robust cosmological information from large-scale structure data, aided by release of a public code implementing the Taylor-expansion pipeline.

Abstract

The precision of the cosmological data allows us to accurately approximate the predictions for cosmological observables by Taylor expanding up to a low order the dependence on the cosmological parameters around a reference cosmology. By applying this observation to the redshift-space one-loop galaxy power spectrum of the Effective Field Theory of Large-Scale Structure, we analyze the BOSS DR12 data by scanning over all the parameters of $Λ$CDM cosmology with massive neutrinos. We impose several sets of priors, the widest of which is just a Big Bang Nucleosynthesis prior on the current fractional energy density of baryons, $Ω_b h^2$, and a bound on the sum of neutrino masses to be less than 0.9 eV. In this case we measure the primordial amplitude of the power spectrum, $A_s$, the abundance of matter, $Ω_m$, the Hubble parameter, $H_0$, and the tilt of the primordial power spectrum, $n_s$, to about $19\%$, $5.7\%$, $2.2\%$ and $7.3\%$ respectively, obtaining $\ln ( 10^{10} A_s) =2.91\pm 0.19$, $Ω_m=0.314\pm 0.018$, $H_0=68.7\pm 1.5$ km/(s Mpc) and $n_s=0.979\pm 0.071$ at $68\%$ confidence level. A public code is released with this preprint.

Figures (15)

• Figure 1: Top: Relative difference between the computation of an EFTofLSS power spectrum by the direct evaluation or by approximation with the Taylor expansion, for cosmologies that lie on a hyper-ellipsoid with orthogonal semi-axes of length $2 \sigma_{\rm stat}$ centered on the reference cosmology, where the $2\sigma_{\rm stat}$'s are, for each cosmological parameter, the largest 95% confidence intervals obtained amongst the analyses with various priors performed here. Explicitly, we choose the following $2\sigma_{\rm stat}$ for the parameters: $30\%$ for $A_s$, $9.4\%$ for $\Omega_m$, $8.4\%$ for $h$, $12\%$ for $n_s$, for $\omega_b$, we choose $5.3\%$, which is motivated by BBN. For the neutrinos, we take $\sum_i m_{\nu_i} \in [0.1, 0.8]$eV. On the left we plot the monopole, on the right the quadrupole. In solid blue, we plot the $1\sigma$ error bars of the CMASS data, and in dashed and dotted blue the $\sigma/2$ and $\sigma/4$ error bars of the data, respectively. Bottom: Same as the top figure, but with the $2\sigma_{\rm stat}$ interval for $\omega_b$ equal to 20%. In both plots, we see that the disagreement is very small when confronted to the error bars of the data, and indeed it has negligible consequences on the inferred cosmological parameters.
• Figure 2: Left: Posterior distributions of $\ln (10^{10}A_s)$, $\Omega_m$ and $h$ obtained from the analysis of the CMASS NGC sample when fixing $f_{bc},\, n_s$ and $\sum_i m_{\nu_i}$ as in DAmico:2019fhj, up to $k_{\rm max }=0.20h\,{\rm Mpc}^{-1}$ using the Taylor expansion approximation for the EFT power spectrum. This figure should reproduce exactly Fig. 14 DAmico:2019fhj, where the same data were analyzed using a grid (see also Table 4 there). In vertical dashed we plot the expectation value from DAmico:2019fhj. We find that the disagreement is negligible for all 3 parameters, showing the great accuracy of the Taylor expansion for this dataset. Right: Same but for the CMASS sample combined with LOWZ NGC sample up to $k_{\rm max }=0.20h\,{\rm Mpc}^{-1}$ for CMASS and up to $k_{\rm max }=0.18h\,{\rm Mpc}^{-1}$ for LOWZ NGC. Now one should compare with Fig. 17 DAmico:2019fhj. The agreement is again remarkably good, though one should keep in mind that here we used $\sum_i m_{\nu_i} = 0.06$eV with NH instead of a single massive neutrino.
• Figure 3: Posterior distributions for the cosmological parameters obtained from the analysis of the CMASS and LOWZ NGC samples using the Taylor expansion approximation for the EFT power spectrum up to $k_{\rm max }=0.20h\,{\rm Mpc}^{-1}$ for CMASS and $k_{\rm max }=0.18h\,{\rm Mpc}^{-1}$ for LOWZ NGC. We put a Planck2018 prior on $f_{bc}$ and on $n_s$ and we fix the neutrino spectrum to $\sum_i m_{\nu_i} = 0.06$eV with NH. In vertical dashed we plot the expectation value from DAmico:2019fhj.
• Figure 4: Left: Posterior distributions for the cosmological parameters obtained from the analysis of the CMASSxLOWZ NGC sample using the Taylor expansion approximation for the EFT power spectrum up to $k_{\rm max }=0.20h\,{\rm Mpc}^{-1}$ for CMASS and $k_{\rm max }=0.18h\,{\rm Mpc}^{-1}$ for LOWZ NGC. We put a Planck2018 prior on $f_{bc}=\Omega_b/\Omega_c$ and $n_s$. Right: Same as the left plot, but with an additional flat prior for the neutrino masses: $0.06\, {\rm eV}\leq \sum_{i} m_{\nu_i}\leq 0.25\,{\rm eV}$.
• Figure 5: Posterior distributions for the cosmological parameters obtained from the analysis of the CMASS sample combined with the LOWZ NGC sample, using the Taylor expansion approximation for the EFT power spectrum up to $k_{\rm max }=0.20h\,{\rm Mpc}^{-1}$ for CMASS and $k_{\rm max }=0.18h\,{\rm Mpc}^{-1}$ for LOWZ NGC. We put a Planck2018 prior on $\omega_b=\Omega_b h^2$ and $n_s$.