# Generalized Brans-Dicke theories in light of evolving dark energy

## TL;DR

This paper reconstructs generalized Brans-Dicke scalar-tensor theories from recent dark energy data, analyzing their effects on cosmological observables and showing that certain signatures can rule out these theories as explanations for dark energy dynamics.

## Contribution

It introduces a method to reconstruct GBD Lagrangians from data and investigates their observable signatures, providing a way to test scalar-tensor theories against cosmological observations.

## Key findings

- Reconstructed GBD models can mimic observed dark energy behavior.
- The ISW effect can distinguish GBD theories from other dark energy models.
- Certain GBD models are ruled out by CMB and galaxy cross-correlation data.

## Abstract

The expansion history of the Universe reconstructed from a combination of recent data indicates a preference for a changing Dark Energy (DE) density. Moreover, the DE density appears to be increasing with cosmic time, with its equation of state being below -1 on average, and possibly crossing the so-called phantom divide. Scalar-tensor theories, in which the scalar field mediates a force between matter particles, offer a natural framework in which the effective DE equation of state can be less than -1 and cross the phantom barrier. We consider the generalized Brans-Dicke (GBD) class of scalar-tensor theories and reconstruct their Lagrangian given the effective DE density extracted from recent data. Then, given the reconstructed Lagrangian, we solve for the linear perturbations and investigate the characteristic signatures of these reconstructed GBD in the cosmological observables, such as the cosmic microwave background (CMB) anisotropy, the galaxy number counts, and their cross-correlations. In particular, we demonstrate that the Integrated Sachs-Wolfe (ISW) effect probed by the cross-correlation of CMB with the matter distribution can rule out scalar-tensor theories as the explanation of the observed DE dynamics independently from the laboratory and solar system fifth force constraints.