Cosmological perfect fluids in Gauss–Bonnet gravity

Abstract

In a [Formula: see text]-dimensional Friedmann–Robertson–Walker metric, it is rigorously shown that any analytical theory of gravity [Formula: see text], where [Formula: see text] is the curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant, can be associated to a perfect-fluid stress–energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.

FLRW-cosmology in generic gravity theories

“…Since the Ricci tensor R μν and Ricci scalar R are obtainable from the Riemann tensor we did not consider the function F depending on explicitly on the Ricci tensor and Ricci scalar. There are some works showed recently that the tensor E μν takes the perfect fluid form for the FLRW spacetimes when the function F depends only the Ricci and the Gauss-Bonnet scalars R and G respectively [18,19], as well as the Ricci scalar R and R of any order [20]. In the present work, we prove that the tensor E μν takes the perfect fluid form for any generic modified gravity theory in the FLRW spacetimes in arbitrary dimensions.…”

“…Amongst the latter, higher order curvature corrections to Einstein's field equations have been considered by several authors [14][15][16][17]. In the context of modified theories, some attempts for a geometric interpretation of the dark side of the universe as a perfect fluid have been done [18][19][20][21][22][23] but the picture is not complete yet. In this work, we put one step forward to prove that the perfect fluid from of the dark component of the Universe is true for any generic modified theory of gravity.…”

Cosmological perfect fluids in higher-order gravity

“…In a GRW space-time of dimension n = 4, the condition ∇ m C jklm = 0 is equivalent to C jklm = 0 and the space-time is Robertson-Walker (RW) (see Prop.4.1 in [11]). The result can be extended to F (R, G) theories [12] in RW space-times: the new terms have the perfect fluid form, i.e. they contribute to the energy-momentum tensor of matter T ij = (p + µ)u i u j + pg ij as terms that modify the total pressure and energy density or, in other words, can be dealt as a new effective fluid.…”

Stable exponential cosmological solutions with three factor spaces of dimensions m = 3, k1 = k and k2 = k in the Einstein–Gauss–Bonnet model with a Λ-term

“…It is of interest to generalize this trick to solutions with an anisotropic fluid in the theory of gravity f (R, G) which are considered by many authors. We note, that in the article [28] it was shown that, in the n-dimensional Friedmann-Robertson-Walker metric, it is rigorously shown that any analytical theory of Gauss-Bonnet gravity f (R, G) where R is the curvature scalar and G is the Gauss-Bonnet term, can be associated to a perfect-fluid stressenergy tensor. One may think, that in this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.…”