Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling

TL;DR

This paper explores a class of spatially covariant modified gravity theories with only two tensorial degrees of freedom, similar to general relativity, and examines their observational distinctions, black hole solutions, and cosmological behavior.

Contribution

It introduces a modified gravity framework with non-dynamical scalar mode, analyzes its observational signatures, black hole solutions, and cosmological perturbations, highlighting its similarities and differences with general relativity.

Findings

Same predictions as GR for weak fields and gravitational wave speed

No modifications to asymptotically flat black holes

Cosmological dynamics can mimic ΛCDM

Abstract

We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for weak gravitational fields and the propagation speed of gravitational waves. We also find that there is no modification to asymptotically flat black hole solutions. Due to a large degree of freedom to choose the time-dependent functions in the theory, the homogeneous and isotropic cosmological dynamics can be made close to or even identical to that of the $\Lambda$CDM model. We investigate the behavior of cosmological perturbations in the long and short wavelength limits and show that in both limits the effects of modified gravity appear only through the modification of the background evolution. Finally, it is remarked that in the presence of a galileon field in the matter sector, the scalar degree of freedom is revived, ruining the essential feature of the theory.