Bi-scalar modified gravity and cosmology with conformal invariance

TL;DR

This paper explores a bi-scalar modified gravity theory with conformal invariance, demonstrating its potential to mimic dark matter, dark radiation, and produce realistic cosmological evolution including late-time acceleration.

Contribution

It introduces a novel bi-scalar conformally invariant gravity model capable of explaining various cosmological phenomena without explicit matter sectors.

Findings

Analytical solutions exhibit matter and radiation era behaviors.

Model can produce late-time cosmic acceleration.

Effective dark-energy equation of state can become phantom.

Abstract

We investigate the cosmological applications of a bi-scalar modified gravity that exhibits partial conformal invariance, which could become full conformal invariance in the absence of the usual Einstein-Hilbert term and introducing additionally either the Weyl derivative or properly rescaled fields. Such a theory is constructed by considering the action of a non-minimally conformally-coupled scalar field, and adding a second scalar allowing for a nonminimal derivative coupling with the Einstein tensor and the energy-momentum tensor of the first field. At a cosmological framework we obtain an effective dark-energy sector constituted from both scalars. In the absence of an explicit matter sector we extract analytical solutions, which for some parameter regions correspond to an effective matter era and/or to an effective radiation era, thus the two scalars give rise to "mimetic dark matter" or to "dark radiation" respectively. In the case where an explicit matter sector is included we obtain a cosmological evolution in agreement with observations, that is a transition from matter to dark energy era, with the onset of cosmic acceleration. Furthermore, for particular parameter regions, the effective dark-energy equation of state can transit to the phantom regime at late times. These behaviours reveal the capabilities of the theory, since they arise purely from the novel, bi-scalar construction and the involved couplings between the two fields.