We prove that in Robertson–Walker space-times (and in generalized Robertson–Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert–Einstein Lagrangian density F(R, □ R, … , □ kR) have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.
Cosmological perfect fluids in higher-order gravity / S. Capozziello, C.A. Mantica, L.G. Molinari. - In: GENERAL RELATIVITY AND GRAVITATION. - ISSN 0001-7701. - 52:4(2020 Apr), pp. 36.1-36.9.
Cosmological perfect fluids in higher-order gravity
L.G. Molinari
2020
Abstract
We prove that in Robertson–Walker space-times (and in generalized Robertson–Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert–Einstein Lagrangian density F(R, □ R, … , □ kR) have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.
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