Cosmology in cubic and f(P) gravity

Abstract

We construct cubic gravity and its f (P ) extension and we investigate their early-and late-time cosmological applications. Cubic gravity is based on a particular invariant P , constructed from cubic contractions of the Riemann tensor, under three requirements: (i) the resulting theory possesses a spectrum identical to that of general relativity, (ii) it is neither topological nor trivial in four dimensions, and (iii) it is defined such that it is independent of the dimensions. Relaxing the last condition and restricting the parameters of cubic gravity we can obtain second-order field equations in a cosmological background. We show that at early times one can obtain inflationary, de Sitter solutions, which are driven by an effective cosmological constant constructed purely from the cubic terms of the simple cubic or f (P ) gravity. Concerning late-time evolution, the new terms constitute an effective dark-energy sector and we show that the Universe experiences the usual thermal history and the onset of late-time acceleration. In the case of f (P ) gravity, depending on the choice of parameters, we find that the dark-energy equation-of-state parameter can be quintessencelike, phantomlike or it can experience the phantom-divide crossing during the evolution, even if an explicit cosmological constant is absent. PACS numbers: 98.80.-k, 95.36.+x, 04.50.Kd I. INTRODUCTIONHigher-order gravities have been introduced in the general framework of modified theories of gravity, with the aim to describe in a uniform way the history of the Universe; to account for the early-time inflation, the late-time acceleration, and the presence of dark matter; and to be consistent with observations [1][2][3][4][5]. A more theoretical motivation in studying higher-order corrections to the Einstein-Hilbert term is that these theories arise naturally in the gravitational effective action of a complete string theory [6] and they result in a renormalizable and thus quantizable gravitational theory [7]. Additionally, in such considerations one can construct theories which possess general relativity as a particular limit [8]. Moreover, certain higher-order gravities are equivalent to Einstein gravity at the linearized level in the vacuum, and the only physical mode propagated by the metric perturbation is a transverse and massless graviton. Such theories are certain f(Lovelock) theories [9].Higher-order gravities and more generally modified theories of gravity provide a deeper understanding of Einstein gravity theory itself. The construction of modified theories of gravity starts from the Einstein-Hilbert Lagrangian and includes extra terms, such as in f (R) gravity [3,[10][11][12], f (G) gravity [13,14], Lovelock gravity [9,15], Weyl gravity [16,17], Galileon theory [18][19][20][21][22][23][24], etc. More radical modifications of Einstein gravity theory are provided by the introduction of torsion terms in f (T ) gravity [25][26][27][28] or f (T, T G ) gravity [29,30]. These modified theories of gravity allow us to unveil what features of a grav...

No-go theorem for inflation in Ricci-inverse gravity

“…It should be noted that the instabilities, found in this section for both isotropic and anisotropic solutions, are purely classical and therefore could not be related to the Ostrogradsky ghost [62]. Other classical instabilities of the Bianchi type I solutions of higher order gravity models, e.g., the Einsteinian cubic gravity [66][67][68][69], can been seen in Refs. [70].…”

Small free field inflation in higher curvature gravity

“…Interestingly enough, the inclusion of radiation -actually, any barotropic fluid for that matter -triggers a novel mechanism of cosmological accelerated expansion of the universe called Geometric Inflation, without the need to invoke a scalar field (see, also, [13]). Several features of this scenario were considered in [14][15][16][17].…”

Dark effects in $$\tilde{f}(R,P)$$ gravity

“…The extended cubic gravity based on the third order contractions of the Riemann tensor has been proposed recently [51], a theory which further corrects the Einstein-Hilbert action with a generic functional f (P) which encodes specific effects due to the topological invariant P. In this case the topological invariant P is based on some specific contractions of the Riemann tensor [51]. The dynamical features for the generalized extended cubic gravity have been addressed in [52], by taking into account two possible configurations for the cubic term which corrects the Einstein-Hilbert action.…”

“…In the present paper we shall further generalise the cubic extension of the Einstein-Hilbert action [51] by including viable effects from the curvature. Hence, in this approach we shall add to the Einstein-Hilbert action the functional f (R, P), a generalization which takes into account possible geometrical effects due to the curvature and the inclusion of the cubic invariant.…”