Cosmology of hybrid metric-Palatini f(X)-gravity

TL;DR

This paper explores a new hybrid gravity theory combining metric and Palatini approaches, analyzing its cosmological solutions, perturbations, and potential to explain cosmic acceleration while satisfying local tests.

Contribution

It introduces a novel formulation of hybrid metric-Palatini gravity in terms of the variable X and investigates its cosmological implications and perturbation signatures.

Findings

The theory can produce both accelerating and decelerating cosmological solutions.

It passes Solar System tests despite a light scalar field.

The model predicts distinctive large-scale structure signatures.

Abstract

A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini was proposed recently. The dynamically equivalent scalar-tensor representation of the model was also formulated, and it was shown that even if the scalar field is very light, the theory passes the Solar System observational constraints. Therefore the model predicts the existence of a long-range scalar field, modifying the cosmological and galactic dynamics. An explicit model that passes the local tests and leads to cosmic acceleration was also obtained. In the present work, it is shown that the theory can be also formulated in terms of the quantity $X\equiv \kappa^2 T+R$, where T and R are the traces of the stress-energy and Ricci tensors, respectively. The variable X represents the deviation with respect to the field equation trace of general relativity. The cosmological applications of this hybrid metric-Palatini gravitational theory are also explored, and cosmological solutions coming from the scalar-tensor representation of f(X)-gravity are presented. Criteria to obtain cosmic acceleration are discussed and the field equations are analyzed as a dynamical system. Several classes of dynamical cosmological solutions, depending on the functional form of the effective scalar field potential, describing both accelerating and decelerating Universes are explicitly obtained. Furthermore, the cosmological perturbation equations are derived and applied to uncover the nature of the propagating scalar degree of freedom and the signatures these models predict in the large-scale structure.