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Here, we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed. Sometimes this leads to an unwanted doubling of the results. In this paper, we illustrate this issue with the example of two apparently different gravitational theories: (i) the (minimally coupled) Einstein-massless-scalar (EMS) system and (ii) the Sáez–Ballester theory (SBT). We demonstrate that the latter is not a scalar–tensor theory of gravity, as widely acknowledged. Moreover, SBT is identified with the EMS theory. As illustrations of this identification we show that several known solutions of SBT are also solutions of the EMS system and vice versa. Cosmological arguments are also considered. In particular, a dynamical systems-based demonstration of the dynamical equivalence between these theories is given. The study of the asymptotic dynamics of the Sáez–Ballester-based cosmological model shows that there are no equilibrium points which could be associated with accelerated expansion, unless one includes a cosmological constant term or a self-interacting scalar field. This is a well-known result for cosmological models which are based on the Einstein-self-interacting-scalar theory, also known as quintessence. [ABSTRACT FROM AUTHOR]

In this paper, we study a cosmological model governed by a generalized scalar field nonminimally coupled to scalar torsion in the framework of teleparallel gravity. By applying the Noether symmetry approach, we attempt to explore the explicit forms of the coupling function and the scalar field potential in the Friedmann–Lemaitre–Robertson–Walker (FLRW) flat spacetime. The existence of such symmetry permits the equations of motion to take a simpler form and provides an exponential form cosmological solution for both the scale factor and scalar field. It is shown that the tachyon field behaves as the origin of inflation and contributes significantly to the accelerating expansion of the universe in the early times. While, in the late times, gravitational sources are a pressureless matter field together with the tachyon field, which plays the essential role of dark energy and is the origin of deceleration-acceleration phase transition. Later on, it is also shown that the present model contains a cosmological degeneracy in the sense that different coupling parameters and tachyonic potentials can contribute to the same cosmological behaviors such as the cosmic acceleration, age, equation of state and mean Hubble of FLRW universe. [ABSTRACT FROM AUTHOR]

In this work, we propose a model of noncommutative cosmology through the deformation of minisuperspace. We focus on an exponentially potential with a homogeneous scalar field minimally coupled to gravity in the spatially flat universe. To process, we use a particular case of noncommutativity by making a deformation of space coordinates only. Then, we compare results in both the commutative model and the noncommutative one. [ABSTRACT FROM AUTHOR]

In this paper, the scalar–tensor theory is applied to the study of perturbations in a multifluid universe, using the 1 + 3 covariant approach. Both scalar and harmonic decompositions are instituted on the perturbation equations. In particular, as an application, we study perturbations on a background Friedmann-Robertson-Walker (FRW) cosmology consisting of both radiation and dust in the presence of a scalar field. We consider both radiation-dominated and dust-dominated epochs, respectively, and study the results. During the analysis, quasi-static approximation is instituted. It is observed that the fluctuations of the energy density decrease with increasing redshift, for different values of n of a power-law R n model. [ABSTRACT FROM AUTHOR]

We discuss nonminimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a nonminimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss–Bonnet scalars are considered. We show that couplings, potentials and kinetic terms are determined by the existence of Noether symmetries which, moreover, allows to reduce and solve dynamics. The main finding of the paper is that different nonminimally coupled theories, presenting the same Noether symmetries, are dynamically equivalent. In other words, Noether symmetries are a selection criterion to compare different theories of gravity. [ABSTRACT FROM AUTHOR]

The gravitational wave (GW) event GW170817 from a binary neutron star merger together with the electromagnetic counterpart showed that the speed of GWs c t is very close to that of light for the redshift z < 0. 0 0 9. This places tight constraints on dark energy models constructed in the framework of modified gravitational theories. We review models of the late-time cosmic acceleration in scalar–tensor theories with second-order equations of motion (dubbed Horndeski theories) by paying particular attention to the evolution of dark energy equation of state and observables relevant to the cosmic growth history. We provide a gauge-ready formulation of scalar perturbations in full Horndeski theories and estimate observables associated with the evolution of large-scale structures, cosmic microwave background and weak lensing by employing a so-called quasi-static approximation for the modes deep inside the sound horizon. In light of the recent observational bound of c t , we also classify surviving dark energy models into four classes depending on different structure-formation patterns and discuss how they can be observationally distinguished from each other. In particular, the nonminimally coupled theories in which the scalar field ϕ has a coupling with the Ricci scalar R of the form G 4 (ϕ) R , including f (R) gravity, can be tightly constrained not only from the cosmic expansion and growth histories but also from the variation of screened gravitational couplings. The cross-correlation of integrated Sachs–Wolfe signal with galaxy distributions can be a key observable for placing bounds on the relative ratio of cubic Galileon density to total dark energy density. The dawn of GW astronomy will open up a new window to constrain nonminimally coupled theories further by the modified luminosity distance of tensor perturbations. [ABSTRACT FROM AUTHOR]

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon. [ABSTRACT FROM AUTHOR]

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 deal with the duality symmetry of the dilaton field in cosmology and specifically with the so-called Gasperini–Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the dilaton field, and we show that under conformal transformations Gasperini–Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the dilaton field. Finally, we show that the Lagrangian of the dilaton field is equivalent with the two-dimensional “hyperbolic oscillator” in a Lorentzian space whose O(d, d) invariance is transformed into the Gasperini–Veneziano duality invariance in the original coordinates. [ABSTRACT FROM AUTHOR]

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke sub-class, and one that also takes note of the latter's equivalence with gravitation theories. A covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaître-Robertson-Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy-density perturbations is oscillatory, with growing amplitudes for , and with decaying amplitudes for . This is a new result. [ABSTRACT FROM AUTHOR]

The dynamical aspects of scaling solutions for the dark energy component in the theoretical framework of teleparallel gravity are considered, where dark energy is represented by a scalar field nonminimally coupled with the torsion and with a boundary term, where the boundary coupling term represents the divergence of the torsion vector. The behavior and stability of the scaling solutions are studied for scalar fields endowed with inverse power law potentials and with exponential potentials. It is shown that for scalar fields endowed with inverse power-law potentials, the stability conditions are not affected by the coupling coefficients. For the scalar fields endowed with exponential potentials, two cases are studied: at first, we have considered an infinitesimal deviation from the scaling solution in the corresponding Klein-Gordon equation, and the impact of distinct coupling coefficients on the stability of the solution are analyzed. Secondly, the potential-free case is considered where the dominance of the coupling terms over the potential term is analyzed, discussing the validity of the corresponding particular solution. [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]

In this paper, we review the effective field theory of modified gravity in which the Lagrangian involves three-dimensional geometric quantities appearing in the 3+1 decomposition of spacetime. On the flat isotropic cosmological background, we expand a general action up to second-order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories - including Horndeski theory/its recent generalizations and the projectable/nonprojectable versions of Hořava-Lifshitz gravity. We derive the equations of motion for linear cosmological perturbations and apply them to the calculations of inflationary power spectra as well as the dark energy dynamics in Galileon theories. We also show that our general results conveniently recover stability conditions of Hořava-Lifshitz gravity already derived in the literature. [ABSTRACT FROM AUTHOR]

We propose the holographic principle as a dynamical cutoff for any quantum theory of gravity, incorporating ideas of effective field theory. This is done by viewing the holographic bound as a limit on the number of degrees of freedom that can be turned on before the geometrical picture of gravity loses applicability. We illustrate the proposal by revisiting the problem of defining a measure for homogeneous and isotropic space-times coupled to a scalar field and conclude by discussing the implications to the single scalar field inflationary model. [ABSTRACT FROM AUTHOR]

We review cosmological solutions and their stability in nonlinear massive gravity. After constructing homogeneous and isotropic solutions, we show that they suffer from ghost instability. We then find new attractor solutions, in which the physical metric is of Friedmann-Robertson-Walker (FRW) type but anisotropy in the fiducial metric leads to statistical anisotropy of perturbations. [ABSTRACT FROM AUTHOR]

Using a new effective action predicted from quantum gravity where the sign of the Euclidean Einstein action is reversed, we discuss Wentzel-Kramers-Brillouin (WKB) solutions in quantum cosmology and predict that this sign change might explain the origin of phantom scalars. [ABSTRACT FROM AUTHOR]

We consider a nonlinear sigma-model-like theory of bulk scalar fields coupled to the five-dimensional Einstein gravity. In Robertson-Walker spacetimes, we find some power-law cosmological solutions for the scale factor when the expansion rate of an extra dimension is proportional to one of our (3+1)-dimensional universe. Among them, the solution with a decreasing warp factor could be related to the one-brane model of Randall and Sundrum. [ABSTRACT FROM AUTHOR]

In this paper we study the dynamics of the universe in Friedmann-Robertson-Walker models including perfect fluid and coupled scalar field with nonzero scalar potential in higher derivative theory of gravitation. We study the evolution of the universe by assuming the scalar potential and scale factor as functions of the scalar field. Exact cosmological solutions are obtained for flat, closed and open models, which are physically interesting for the description of the present-day universe. The properties of scalar field and other physical parameters are discussed in detail. Some special cases have been studied by imposing certain constraints on constants to discuss the decelerated and accelerated phases of the universe. [ABSTRACT FROM AUTHOR]

An action in which the Ricci scalar is non-minimally coupled with a scalar field and contains higher order curvature invariant terms carries a conserved current under certain conditions that decouples geometric part from the scalar field. The conserved current relates the pair of arbitrary coupling parameters f(ϕ) and ω(ϕ) with the gravitational field variable, where ω(ϕ) is the Brans-Dicke coupling parameter. The existence of such conserved current may be helpful to sketch the cosmological evolution from its early age till date in a single frame. [ABSTRACT FROM AUTHOR]

We have considered five-dimensional massive scalar field coupled to gravity and evaluated the one-loop effective potential in higher dimensions. It is demonstrated that nonminimally coupled φ4 theory can be regularized in five dimensions. Temperature dependent one-loop correction and critical temperature βc are computed. The phase transitions in the early universe depend on the space–time curvature R and scalar gravitational coupling ξ. A brief discussion of symmetry restoration is also presented and the nature of phase transitions in the early universe is found to be of second order. [ABSTRACT FROM AUTHOR]

Models where the accelerated expansion of our Universe is caused by a quintessence scalar field are reviewed. In the framework of high energy physics, the physical nature of this field is discussed and its interaction with ordinary matter is studied and explicitly calculated. It is shown that this coupling is generically too strong to be compatible with local tests of gravity. A possible way out, the chameleon effect, is also briefly investigated. [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]

The phenomena customarily described with the standard ΛCDM model are broadly reproduced by an extremely simple model in TeVeS, Bekenstein's1 modification of general relativity motivated by galaxy phenomenology. Our model can account for the acceleration of the Universe seen at SNeIa distances without a cosmological constant, and the accelerations seen in rotation curves of nearby spiral galaxies and gravitational lensing of high-redshift elliptical galaxies without cold dark matter. The model is consistent with BBN and the neutrino mass between 0.05 eV to 2 eV. The TeVeS scalar field is shown to play the effective dual roles of dark matter and dark energy, with the amplitudes of the effects controlled by a μ function of the scalar field, called the μ essence here. We also discuss outliers to the theory's predictions on multiimaged galaxy lenses and outliers on the subgalaxy scale. [ABSTRACT FROM AUTHOR]