Abstract
Gravitational waves in the presence of a non-minimal curvature-matter coupling are analysed, both in the Newman–Penrose and perturbation theory formalisms. Considering a cosmological constant as a source, the non-minimally coupled matter-curvature model reduces to f(R) theories. This is in good agreement with the most recent data. Furthermore, a dark energy-like fluid is briefly considered, where the propagation equation for the tensor modes differs from the previous scenario, in that the scalar mode equation has an extra term, which can be interpreted as the longitudinal mode being the result of the mixture of two fundamental excitations delta R and delta rho .
Highlights
In order to test gravity with gravitational waves (GW) [16], it is important to note that modifications of General Relativity (GR) may imply anomalous deviations in the propagation of tensor modes
In this work we have analysed the effects of a non-minimal coupling between matter and curvature on gravitational waves
The perturbation of the trace of the field equations exhibits a behaviour that can be interpreted as the dynamics of the effective scalar field decoupled into two scalar modes: one that arises from perturbations on the Ricci scalar and the other from perturbations on the matter Lagrangian density
Summary
In order to test gravity with GWs [16], it is important to note that modifications of GR may imply anomalous deviations in the propagation of tensor modes. Some alternative theories of gravity rely on higher-order curvature terms in the action This is a relevant modification since it allows for a successful model of inflation, namely the Starobinsky’s one [36]. Another proposal of alternative theories of gravity extends the f (R) theories by including a non-minimal coupling (NMC) between curvature and matter [39] 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]. Extensions of f (R, Lm) gravity were explored by considering the presence of generalized scalar field and kinetic term dependences [58] and a NMC between the curvature scalar and the trace of the energy-momentum tensor, the so-called f (R, T ) gravity [59].
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