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In this paper we will study the cosmological dynamical system of an f (R) gravity in the presence of a canonical scalar field ϕ with an exponential potential by constructing the dynamical system in a way that it is rendered autonomous. This feature is controlled by a single variable m , which when it is constant, the dynamical system is autonomous. We focus on the m = 0 case which, as we demonstrate by using a numerical analysis approach, leads to an unstable de Sitter attractor, which occurs after N ∼ 6 0 e -foldings. This instability can be viewed as a graceful exit from inflation, which is inherent to the dynamics of de Sitter attractors. [ABSTRACT FROM AUTHOR]

In this paper, we explore the equivalence between two theories, namely f (R) and scalar–tensor theories of gravity. We use this equivalence to explore several f (R) toy models focusing on the inflation epoch of the early universe. The study is done based on the definition of the scalar field in terms of the first derivative of f (R) model. We have applied the slow-roll approximations during inflationary parameters consideration. The comparison of the numerically computed inflationary parameters with the observations is done. We have inspected that some of the f (R) models produce numerical values of n s that are in the same range as the suggested values from observations. But for the case of the tensor-to-scalar ratio r , we realized that some of the considered f (R) models suffer to produce a value which is in agreement with the observed values for different considered space parameter. [ABSTRACT FROM AUTHOR]

In this paper, spatially homogeneous and anisotropic Bianchi type- VI 0 dark energy (DE) cosmological transit models with string fluid source in f (R , T) gravity [T. Harko et al., Phys. Rev. D84 (2011) 024020], where R is the Ricci scalar and T the trace of the stress energy–momentum tensor, have been studied in the context of early time decelerating and late-time accelerating expansion of the Universe as suggested by the recent observations. The exact solutions of the field equations are obtained first by using generalized hybrid expansion law (HEL) a = (t α e β t) 1 n which yields a time-dependent deceleration parameter q = − 1 + α n (α + β t) 2 and second by considering the metric coefficient A = a k . By using recent constraints from supernovae type-Ia union data [Cunha, arXiv:0811.2379[astro-ph]], we obtain α = 0. 8 and β = 0. 1 1 8 4 for transit model n = 2. The Universe has an initial singularity and is anisotropic closed and it tends to be flat at the late time, i.e. our Universe is in accelerating expansion. Our model shows a phase transition property from decelerating to accelerating. It is remarkable to mention here that our Universe is homogeneous and anisotropic in the early phase whereas it becomes homogeneous and isotropic for k = 1. We have also discussed the stability of the background solution with respect to perturbations of the metric along with the properties of future singularities in the Universe dominated by DE including the phantom-type fluid. Various physical and dynamical parameters are also calculated and investigated in terms of time and redshift both. [ABSTRACT FROM AUTHOR]

We study gravity models in the language of scalar-tensor (ST) theories. The correspondence between gravity and ST theories is revisited since gravity is a subclass of Brans-Dicke models, with a vanishing coupling constant (). In this treatment, four toy models are used to analyze the early-universe cosmology, when the scalar field dominates over standard matter. We have obtained solutions to the Klein-Gordon equation for those models. It is found that for the first model , as time increases the scalar field decreases and decays asymptotically. For the second model , it was found that the function crosses the -axis at different values for different values of . For the third model , when the value of is small, the potential behaves like the standard inflationary potential. For the fourth model , we show that there is a transition between . The behavior of the potentials with is totally different from those with . The slow-roll approximation is applied to each of the four models and we obtain the respective expressions for the spectral index and the tensor-to-scalar ratio . [ABSTRACT FROM AUTHOR]

We explore exact gravity solutions that mimic Chaplygin-gas inspired CDM cosmology. Starting with the original, generalized and modified Chaplygin-gas (MCG) equations of state (EoS), we reconstruct the forms of Lagrangians. The resulting solutions are generally quadratic in the Ricci scalar, but have appropriate CDM solutions in limiting cases. These solutions, given appropriate initial conditions, can be potential candidates for scalar field-driven early universe expansion (inflation) and dark energy-driven late-time cosmic acceleration. [ABSTRACT FROM AUTHOR]

We review thermodynamic properties of modified gravity theories, such as gravity and gravity, where is the scalar curvature and is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in gravity. We show both equilibrium and nonequilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met, when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it. [ABSTRACT FROM AUTHOR]

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling. [ABSTRACT FROM AUTHOR]