Perfect fluid Lagrangian and its cosmological implications in theories of gravity with nonminimally coupled matter fields

Abstract

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 ${\mathcal{L}}_m=T$, where $T$ is the trace of the energy-momentum 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 $f(R,{\mathcal{L}}_m)$ theories of gravity using the COBE-FIRAS measurement of the spectral radiance of the cosmic microwave background.

6 pages, no figures, matches published version

References in corpus (9)

• f(R,T) gravity
• Extra force in $f(R)$ modified theories of gravity
• f(R,L_m) gravity
• Nonminimal coupling of perfect fluids to curvature
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state
• p-brane dynamics in (N+1)-dimensional FRW universes: a unified framework
• Localized D-dimensional global k-defects
• Dynamical analysis of nonminimal coupled theories

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