In this paper we show that the on-shell Lagrangian of a perfect fluid depends on microscopic properties of the fluid, giving specific examples of perfect fluids with different on-shell Lagrangians but with the same energy-momentum tensor. We demonstrate that if the fluid is constituted by localized concentrations of energy with fixed rest mass and structure (solitons) then the average on-shell Lagrangian of a perfect fluid is given by Lm = T , where T is the trace of the energymomentum tensor. We show that our results have profound implications for theories of gravity where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, potentially leading to observable deviations from a nearly perfect cosmic microwave background black body spectrum: n-type spectral distortions, affecting the normalization of the spectral energy density. Finally, we put stringent constraints on f (R, Lm) theories of gravity using the COBE-FIRAS measurement of the spectral radiance of the cosmic microwave background.
In this work, we use a dynamical system approach to analyse the viability of f (R, L) candidates for dark energy. We compare these with nonminimal coupled f (R) theories and study the solutions for exponential and power-law forms in order to constraint the allowed range of model parameters.
In extended models of gravity a nonminimal coupling to matter has been assumed to lead to irreversible particle creation. In this paper we challenge this assumption. We argue that a nonminimal coupling of the matter and gravitational sectors results in a change in particle-momentum on a cosmological timescale, irrespective of particle creation or decay. We further argue that particle creation or decay associated with a non-minimal coupling to gravity could only happen as a result of significant deviations from a homogeneous Friedmann-Lemaître-Robertson-Walker geometry on microscopic scales, and provide a phenomenological description of the impact of particle creation or decay on the cosmological evolution of the density of the matter fields.
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