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

TL;DR

The paper demonstrates that the Effective Field Theory of Large-Scale Structure provides a robust perturbative framework to model mildly non-linear galaxy clustering in redshift space. By applying EFTofLSS to the DR12 BOSS data, the authors extract cosmological parameters ($A_s$, $\Omega_m$, $h$) with percent-level precision and show substantial improvements over previous analyses, especially when incorporating a Planck sound-horizon prior. They validate the approach with extensive simulations, quantify theory-systematic errors, and assess the impact of window functions, fiber collisions, and the bispectrum. The results indicate that LSS data can independently determine key cosmological parameters and even offer a window into galaxy formation physics via EFT parameters, while remaining consistent with Planck results within uncertainties. They also explore the potential to constrain neutrino masses with upcoming surveys, highlighting the promise of EFTofLSS for future cosmological inferences.

Abstract

The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a formalism that allows us to predict the clustering of Cosmological Large-Scale Structure in the mildly non-linear regime in an accurate and reliable way. After validating our technique against several sets of numerical simulations, we perform the analysis for the cosmological parameters of the DR12 BOSS data. We assume $Λ$CDM, a fixed value of the baryon/dark-matter ratio, $Ω_b/Ω_c$, and of the tilt of the primordial power spectrum, $n_s$, and no significant input from numerical simulations. By using the one-loop power spectrum multipoles, we measure the primordial amplitude of the power spectrum, $A_s$, the abundance of matter, $Ω_m$, and the Hubble parameter, $H_0$, to about $13\%$, $3.2\%$ and $3.2\%$ respectively, obtaining $\ln(10^{10}As)=2.72\pm 0.13$, $Ω_m=0.309\pm 0.010$, $H_0=68.5\pm 2.2$ km/(s Mpc) at 68\% confidence level. If we then add a CMB prior on the sound horizon, the error bar on $H_0$ is reduced to $1.6\%$. These results are a substantial qualitative and quantitative improvement with respect to former analyses, and suggest that the EFTofLSS is a powerful instrument to extract cosmological information from Large-Scale Structure.

Figures (27)

• Figure 1: Fourier-space window function $W(k,k')_{\ell,\ell'}$, for $k=0.1023h\,{\rm Mpc}^{-1}$. One easily sees that indeed, being the window function a multiplication in real space, it is a convolution in Fourier space. One can also see that the computation of $W(k,k')_{\ell,\ell'}$ does not seem to present ringing or other numerical issues.
• Figure 2: Typical power spectra before ( dashed) and after ( continous) the application of the window function, using the Fourier-space formula of (\ref{['eq:windowfourierr']}). Blue is monopole, green is quadrupole. As expected, the window function suppresses the power spectra at low wavenumbers. We also see that there seem not to appear any numerical artifacts, such as oscillations and ringing.
• Figure 3: Redshift distribution, up to a normalization factor, of the galaxies in the CMASS NGC sample.
• Figure 4: We plot the ratios $\frac{1}{D(z_{\rm eff})^2} \int dz\; n(z) \, D(z)^{2}\ , \frac{1}{f(z_{\rm eff}) D(z_{\rm eff})^2} \int dz\; n(z) \,f(z)\, D(z)^{2}$, $\frac{1}{f(z_{\rm eff}) ^2D(z_{\rm eff})^2} \int dz\; n(z) \,f(z)^2\, D(z)^{2}$ and $\frac{1}{D(z_{\rm eff})^4} \int dz\; n(z) \, D(z)^{4}$ as a function of $z_{\rm eff}$. We can see that the choice of $z_{\rm eff}=0.55$ for all the integral is very accurate, better than 0.5%. In particular, notice that the loop terms will contribute by a smaller amount to the final answer (about 10%), so one can afford a larger inaccuracy in those. Notice also that the contribution of the term in $f^2$ to the monopole, which is the better measured quantity, is suppressed by several numerical factors. We conclude that we can simply evaluate the EFTofLSS prediction directly at $z_{\rm eff}$.
• Figure 5: Residuals between the monopole ( dotted, blue) and quadrupole ( dotted, green) power spectra and the ones reconstructed using the NN&shot-noise method, measured by the mean of 30 BOSS-like Patchy mocks, together with the error bars of one box. The dashed lines represents the correction given by the 'Effective Window Method' of Hahn:2016kiy with $k_{\rm trust}=0.25h\,{\rm Mpc}^{-1}$. In the figure we use the nuisance parameters of Hahn:2016kiy equal to $-43$ for the monopole shot-noise and $-9$ for the quadrupole $k^2$ stochastic term (Notice that these values are much smaller than the natural ones we have for the stochastic EFT-parameters). We see that the signal is reconstructed with extreme accuracy, allowing us to neglect any residual systematic error from fiber collision effects.