Gravity at the horizon: on relativistic effects, CMB-LSS correlations and ultra-large scales in Horndeski's theory

TL;DR

This paper investigates how modifications in gravity, within Horndeski theories, affect relativistic effects in large-scale structure and CMB correlations, revealing significant deviations from General Relativity that could be observed in future surveys.

Contribution

It provides a fully consistent linear-scale analysis of relativistic effects in Horndeski gravity, including scalar field dynamics, and assesses their impact on observable large-scale correlations.

Findings

Line-of-sight integrals like ISW can be significantly altered in Horndeski models.

Galileon models show up to 1000% deviation in ISW effect from GR.

Future surveys could detect ~50% deviations in LSS-CMB correlations.

Abstract

We address the impact of consistent modifications of gravity on the largest observable scales, focusing on relativistic effects in galaxy number counts and the cross-correlation between the matter large scale structure (LSS) distribution and the cosmic microwave background (CMB). Our analysis applies to a very broad class of general scalar-tensor theories encoded in the Horndeski Lagrangian and is fully consistent on linear scales, retaining the full dynamics of the scalar field and not assuming quasi-static evolution. As particular examples we consider self-accelerating Covariant Galileons, Brans-Dicke theory and parameterizations based on the effective field theory of dark energy, using the \hiclass\, code to address the impact of these models on relativistic corrections to LSS observables. We find that especially effects which involve integrals along the line of sight (lensing convergence, time delay and the integrated Sachs-Wolfe effect -- ISW) can be considerably modified, and even lead to $\mathcal{O}(1000\%)$ deviations from General Relativity in the case of the ISW effect for Galileon models, for which standard probes such as the growth function only vary by $\mathcal{O}(10\%)$. These effects become dominant when correlating galaxy number counts at different redshifts and can lead to $\sim 50\%$ deviations in the total signal that might be observable by future LSS surveys. Because of their integrated nature, these deep-redshift cross-correlations are sensitive to modifications of gravity even when probing eras much before dark energy domination. We further isolate the ISW effect using the cross-correlation between LSS and CMB temperature anisotropies and use current data to further constrain Horndeski models (abridged).