Scalar-tensor gravity in an accelerating universe

TL;DR

This paper analyzes scalar-tensor theories of gravity in an accelerating universe, showing how observational data on luminosity distance constrains these theories and reconstructs their Lagrangians.

Contribution

It provides a general formulation of background and perturbation equations in scalar-tensor theories and links observational data to theoretical constraints and model reconstruction.

Findings

Luminosity distance data constrains scalar-tensor theories.

Positive energy conditions restrict viable models.

Closed universe models are favored in reconstructed theories.

Abstract

We consider scalar-tensor theories of gravity in an accelerating universe. The equations for the background evolution and the perturbations are given in full generality for any parametrization of the Lagrangian, and we stress that apparent singularities are sometimes artifacts of a pathological choice of variables. Adopting a phenomenological viewpoint, i.e., from the observations back to the theory, we show that the knowledge of the luminosity distance as a function of redshift up to z ~ (1-2), which is expected in the near future, severely constrains the viable subclasses of scalar-tensor theories. This is due to the requirement of positive energy for both the graviton and the scalar partner. Assuming a particular form for the Hubble diagram, consistent with present experimental data, we reconstruct the microscopic Lagrangian for various scalar-tensor models, and find that the most natural ones are obtained if the universe is (marginally) closed.