Power-law cosmic expansion in f(R) gravity models

International Journal of Geometric Methods in Modern Physics

We show that an [Formula: see text]-dimensional generalized Robertson–Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress–energy tensor for any [Formula: see text] gravity model. Furthermore, we prove that a conformally flat GRW space-time is still a perfect fluid in both [Formula: see text] and quadratic gravity where other curvature invariants are considered.

The European Physical Journal C, 2020

We prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $${\mathcal {F}}(R, {\mathcal {G}})$$ F ( R , G ) theories are given as examples.

Arxiv preprint gr-qc/0508038, 2005

We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for a general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α − 1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the authors, there exists in principle a viscosity-driven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.

General Relativity and Gravitation

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, ..., k R) have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.

Physical Review D, 2015

We consider cosmological modelling in f (R) theories of gravity, using both top-down and bottomup constructions. The top-down models are based on Robertson-Walker geometries, and the bottomup constructions are built by patching together sub-horizon-sized regions of perturbed Minkowski space. Our results suggest that these theories do not provide a theoretically attractive alternative to the standard general relativistic cosmology. We find that the only f (R) theories that can admit an observationally viable weak-field limit have large-scale expansions that are observationally indistinguishable from the Friedmann solutions of General Relativity with Λ. Such theories do not alleviate any of the difficulties associated with Λ, and cannot produce any new behaviour in the cosmological expansion without simultaneously destroying the Newtonian approximation to gravity on small scales.

International Journal of Theoretical Physics, 2012

In this paper we study the evolution of a flat Friedmann-Robertson-Walker model filled with a perfect fluid and a scalar field minimally coupled to gravity in higher derivative theory of gravitation. Exact solution of the field equations are obtained by the assumption of power-law form of the scale factor. A number of evolutionary phases of the universe including the present accelerating phase are found to exist with scalar field in the higher derivative theory of gravitation. The properties of scalar field and other physical parameters are discussed in detail. We find that the equation of state parameter for matter and scalar field are same at late time in each case. We observe that a higher derivative term can hardly be a candidate to describe the presently observed accelerated expansion. It is only the hypothetical fluids, which provide the late time acceleration. It is also remarkable that the higher derivative theory does not effect the radiating model of scalar field cosmology.

AIP Conference Proceedings, 2010

The late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source is studied in the conformal frame of f (R) gravity. We assume that the corresponding scalar field, nonminimally coupled to matter, has an arbitrary non-negative potential function V (φ). We prove that equilibria corresponding to non-negative local minima for V are asymptotically stable. We investigate all cases where one of the matter components eventually dominates. The results are valid for a large class of non-negative potentials without any particular assumptions about the behavior of the potential at infinity. In particular for a nondegenerate minimum of the potential with zero critical value we show that if γ, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the later eventually dominates.

Physical Review D, 2006

Modified theories of gravity have recently been studied by several authors as possibly viable alternatives to the cosmological concordance model. Such theories attempt to explain the accelerating expansion of the universe by changing the theory of gravity, instead of introducing dark energy. In particular, a class of models based on higher order curvature invariants, so-called f (R) gravity models, has drawn attention. In this letter we show that within this framework, the expansion history of the universe does not uniquely determine the form of the gravitational action and it can be radically different from the standard Einstein-Hilbert action. We demonstrate that for any barotropic fluid, there always exists a class of f (R) models that will have exactly the same expansion history as that arising from the Einstein-Hilbert action. We explicitly show how one can extend the Einstein-Hilbert action by constructing a f (R) theory that is equivalent on the classical level. Due to the classical equivalence between f (R) theories and Einstein-Hilbert gravity with an extra scalar field, one can also hence construct equivalent scalar-tensor theories with standard expansion.

2021

It has shown that the accelerated expansion of the FRW Universe can be explained as the quest towards the holographic equipartition ($N_{sur} = N_{bulk}$), satisfies the expansion law $\frac{dV}{dt} = l_{P}^{2} \left( N_{sur} - \epsilon N_{bulk} \right)$, from which one can derive the Friedmann equation of the FRW Universe in Einstein gravity \cite{paddy2012jun}. We introduce a generic derivation of the expansion law from the generalized first law of thermodynamics $-dE=TdS$ and $dE=TdS + WdV$. The generic derivation provides an expression for $N_{sur}$ in terms of entropy $S$ and the expansion law consistent with gravity theories with different entropy $S$, like Gauss-Bonnet and more general Lovelock gravity. We extended the same idea to the non-equilibrium situation and obtained the expansion law in f(R) gravity as a specific case. For this, we used the first law of thermodynamics in non-equilibrium description having the extra entropy production term $Td_{i}S.$

arXiv (Cornell University), 2015

A complete analysis of the dynamics of the Hu-Sawicki modification to General Relativity is presented. In particular, the full phase-space is given for the case in which the model parameters are taken to be n = 1, c1 = 1 and several stable de Sitter equilibrium points together with an unstable "matter-like" point are identified. We find that if the cosmological parameters are chosen to take on their ΛCDM values today, this results in a universe which, until very low redshifts, is dominated by an equation of state parameter equal to 1 3 , leading to an expansion history very different from ΛCDM. We demonstrate that this problem can be resolved by choosing ΛCDM initial conditions at high redshift and integrating the equations to the present day.