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Register a new userOn the Statistics of Biased Tracers in the Effective Field Theory of Large Scale Structures
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With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial non-Gaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo three-point functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of $N$-body simulations. For the lowest mass bin, we find percent level agreement up to $ksimeq 0.3,h,{rm Mpc}^{-1}$ for the one-loop two-point functions, and up to $ksimeq 0.15,h,{rm Mpc}^{-1}$ for the tree-level three-point functions, with the $k$-reach decreasing with higher mass bins. This is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.
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We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper, focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.
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 $Lambda$CDM, a fixed value of the baryon/dark-matter ratio, $Omega_b/Omega_c$, 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, $Omega_m$, and the Hubble parameter, $H_0$, to about $13%$, $3.2%$ and $3.2%$ respectively, obtaining $ln(10^{10}As)=2.72pm 0.13$, $Omega_m=0.309pm 0.010$, $H_0=68.5pm 2.2$ 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.
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 $Lambda$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, $Omega_b h^2$, 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, $Omega_m$, 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 $ln ( 10^{10} A_s) =2.91pm 0.19$, $Omega_m=0.314pm 0.018$, $H_0=68.7pm 1.5$ km/(s Mpc) and $n_s=0.979pm 0.071$ at $68%$ confidence level. A public code is released with this preprint.
We investigate the application of Hybrid Effective Field Theory (HEFT) -- which combines a Lagrangian bias expansion with subsequent particle dynamics from $N$-body simulations -- to the modeling of $k$-Nearest Neighbor Cumulative Distribution Functions ($k{rm NN}$-${rm CDF}$s) of biased tracers of the cosmological matter field. The $k{rm NN}$-${rm CDF}$s are sensitive to all higher order connected $N$-point functions in the data, but are computationally cheap to compute. We develop the formalism to predict the $k{rm NN}$-${rm CDF}$s of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how $k{rm NN}$-${rm CDF}$ statistics of a set of biased tracers, such as halos or galaxies, of the cosmological matter field can be modeled given a set of low-redshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the two-point clustering. For a specific sample of halos, we show that both the two-point clustering textit{and} the $k{rm NN}$-${rm CDF}$s can be well-fit on quasi-linear scales ($gtrsim 20 h^{-1}{rm Mpc}$) by the second-order HEFT formalism with the textit{same values} of the bias parameters, implying that joint modeling of the two is possible. Finally, using a Fisher matrix analysis, we show that including $k{rm NN}$-${rm CDF}$ measurements over the range of allowed scales in the HEFT framework can improve the constraints on $sigma_8$ by roughly a factor of $3$, compared to the case where only two-point measurements are considered. Combining the statistical power of $k{rm NN}$ measurements with the modeling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.
Cosmological tensions can arise within $Lambda$CDM scenario amongst different observational windows, which may indicate new physics beyond the standard paradigm if confirmed by measurements. In this article, we report how to alleviate both the $H_0$ and $sigma_8$ tensions simultaneously within torsional gravity from the perspective of effective field theory (EFT). Following these observations, we construct concrete models of Lagrangians of torsional gravity. Specifically, we consider the parametrization $f(T)=-T-2Lambda/M_P^2+alpha T^beta$, where two out of the three parameters are independent. This model can efficiently fit observations solving the two tensions. To our knowledge, this is the first time where a modified gravity theory can alleviate both $H_0$ and $sigma_8$ tensions simultaneously, hence, offering an additional argument in favor of gravitational modification.
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