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Register a new userConstraining Early Dark Energy with Large-Scale Structure
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An axion-like field comprising $sim 10%$ of the energy density of the universe near matter-radiation equality is a candidate to resolve the Hubble tension; this is the early dark energy (EDE) model. However, as shown in Hill et al. (2020), the model fails to simultaneously resolve the Hubble tension and maintain a good fit to both cosmic microwave background (CMB) and large-scale structure (LSS) data. Here, we use redshift-space galaxy clustering data to sharpen constraints on the EDE model. We perform the first EDE analysis using the full-shape power spectrum likelihood from the Baryon Oscillation Spectroscopic Survey (BOSS), based on the effective field theory (EFT) of LSS. The inclusion of this likelihood in the EDE analysis yields a $25%$ tighter error bar on $H_0$ compared to primary CMB data alone, yielding $H_0 = 68.54^{+0.52}_{-0.95}$ km/s/Mpc ($68%$ CL). In addition, we constrain the maximum fractional energy density contribution of the EDE to $f_{rm EDE} < 0.072$ ($95%$ CL). We explicitly demonstrate that the EFT BOSS likelihood yields much stronger constraints on EDE than the standard BOSS likelihood. Including further information from photometric LSS surveys,the constraints narrow by an additional $20%$, yielding $H_0 = 68.73^{+0.42}_{-0.69}$ km/s/Mpc ($68%$ CL) and $f_{rm EDE}<0.053$ ($95%$ CL). These bounds are obtained without including local-universe $H_0$ data, which is in strong tension with the CMB and LSS, even in the EDE model. We also refute claims that MCMC analyses of EDE that omit SH0ES from the combined dataset yield misleading posteriors. Finally, we demonstrate that upcoming Euclid/DESI-like spectroscopic galaxy surveys can greatly improve the EDE constraints. We conclude that current data preclude the EDE model as a resolution of the Hubble tension, and that future LSS surveys can close the remaining parameter space of this model.
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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.
We study the imprints of an effective dark energy fluid in the large scale structure of the universe through the observed angular power spectrum of galaxies in the relativistic regime. We adopt the phenomenological approach that introduces two parameters ${Q,eta}$ at the level of linear perturbations and allow to take into account the modified clustering (or effective gravitational constant) and anisotropic stress appearing in models beyond $Lambda$CDM. We characterize the effective dark energy fluid by an equation of state parameter $w=-0.95$ and various sound speed cases in the range $10^{-6}leq c^2_sleq 1$, thus covering K-essence and quintessence cosmologies. We calculate the angular power spectra of standard and relativistic effects for these scenarios under the ${Q,eta}$ parametrization, and we compare these relative to a fiducial $Lambda$CDM cosmology. We find that, overall, deviations relative to $Lambda$CDM are stronger at low redshift since the behavior of the dark energy fluid can mimic the cosmological constant during matter domination era but departs during dark energy domination. In particular, at $z=0.1$ the matter density fluctuations are suppressed by up to $sim3%$ for the quintessence-like case, while redshift-space distortions and Doppler effect can be enhanced by $sim15%$ at large scales for the lowest sound speed scenario. On the other hand, at $z=2$ we find deviations of up to $sim5%$ in gravitational lensing, whereas the Integrated Sachs-Wolfe effect can deviate up to $sim17%$. Furthermore, when considering an imperfect dark energy fluid scenario, we find that all effects are insensitive to the presence of anisotropic stress at low redshift, and only the Integrated Sachs-Wolfe effect can detect this feature at $z=2$ and very large scales.
We study infrared effects in perturbation theory for large-scale structure coupled to the effective field theory of dark energy, focusing on, in particular, Degenerate Higher-Order Scalar-Tensor (DHOST) theories. In the subhorizon, Newtonian limit, DHOST theories introduce an extra large-scale velocity $v^i_pi$ which is in general different from the matter velocity $v^i$. Contrary to the case in Horndeski theories, the presence of this extra large-scale velocity means that one cannot eliminate the long-wavelength effects of both $v^i$ and $v^i_pi$ with a single coordinate transformation, and thus the standard $Lambda$CDM consistency relations for large-scale structure are violated by terms proportional to the relative velocity $v^i - v^i_pi$. We show, however, that in non-linear quantities this violation is determined by the linear equations and the symmetries of the fluid system. We find that the size of the baryon acoustic oscillations in the squeezed limit of the bispectrum is modified, that the bias expansion contains extra terms which contribute to the squeezed limit of the galaxy bispectrum, that infrared modes in the one-loop power spectrum no longer cancel, and that the equal-time double soft limit of the tree-level trispectrum is non-vanishing. In addition, we give explicit expressions for how these violations depend on the relative velocity. Many of our computations are also relevant for perturbation theory in $Lambda$CDM with exact time dependence.
We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $Lambda$CDM at intermediate redshifts ($0.5 lesssim z lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $Lambda$CDM. (3) The gravitational slip parameter $eta$ - the ratio of the space part of the metric perturbation to the time part - is bounded from above. For Brans-Dicke-type theories $eta$ is at most unity. For more general theories, $eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.
We study a class of early dark energy models which has substantial amount of dark energy in the early epoch of the universe. We examine the impact of the early dark energy fluctuations on the growth of structure and the CMB power spectrum in the linear approximation. Furthermore we investigate the influence of the interaction between the early dark energy and the dark matter and its effect on the structure growth and CMB. We finally constrain the early dark energy model parameters and the coupling between dark sectors by confronting to different observations.
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