Cosmological perturbations in theories with non-minimal coupling between curvature and matter

Abstract

In this work, we examine how the presence of a non-minimal coupling between spacetime curvature and matter affects the evolution of cosmological perturbations on a homogeneous and isotropic Universe, and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modified growth of matter density perturbations. We derive approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and discuss the compatibility of the obtained results with the hypothesis that the late time acceleration of the Universe is driven by a non-minimal coupling.

Inflation in non-minimal matter-curvature coupling theories

“…We can also determine several quantities which are related to CMB observational data, such as the amplitude of the dimensionless scalar curvature power spectrum: 27) where one can clearly see that the amplitude of curvature perturbations is suppressed for V H 2 M 2 P . The associated scalar spectral index is then given by:…”

Modified Friedmann equation from nonminimally coupled theories of gravity

“…Indeed, these can be coupled, for instance, in a nonminimal way [3] (see also Refs. [4][5][6] for early proposals in cosmology), a fact that can have a bearing on the dark matter [7,8] and dark energy [9,10] problems, as well as inflation [11,12] and structure formation [13]. This putative nonminimal coupling modifies the well-known energy conditions [14] and can give rise to several implications, from Solar System [15] and stellar dynamics [16][17][18][19] to close time-like curves [20] and wormholes [21].…”

Gravitational waves in theories with a non-minimal curvature-matter coupling

“…These theories can mimic dark matter profiles at galaxies [40,41] and clusters [42], modify the Layzer-Irvine and virial theorem [43] and are stable under cosmological perturbations [44]. They can also account for the late-time acceleration of the Universe [45,46] and have some consequences for black hole solutions [47].…”