Narrow Results

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.

In this paper, we investigate the cosmological dynamics in a spatially flat Friedmann–Lemaître–Robertson–Walker geometry in scalar-tensor and scalar-torsion theories where the nonminimally coupled scalar field is a complex field. We derive the cosmological field equations and we make use of dimensionless variables in order to determine the stationary points and determine their stability properties. The physical properties of the stationary points are discussed while we find that the two-different theories, scalar-tensor and scalar-torsion theories, share many common features in terms of the evolution of the physical variables in the background space.

In this paper, we implement the Einsenhart–Duval lift in scalar–tensor gravity as a means to construct integrable cosmological models and analytic cosmological solutions. Specifically, we employ a geometric criterion to constrain the free functions of the scalar–tensor theory such that the field equations can be written in the equivalent form of linear equations. This geometric linearization is achieved by the introduction of an extended minisuperspace description. The results are applied to construct analytic solutions in modified theories of gravity such as the $f(R)$-theory and the hybrid metric-Palatini $f({ℛ})$-gravity.

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 $f(R)$ gravitation theories. A $1+3$ 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 $R^n$ 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 $n>1$, and with decaying amplitudes for $0<n<1$. This is a new result.

A scalar-tensor model with Gauss–Bonnet and nonminimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is devised for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi-de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with the most accurate values of the observational indices.

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.

We study $f(R)$ gravity models in the language of scalar–tensor (ST) theories. The correspondence between $f(R)$ gravity and ST theories is revisited since $f(R)$ gravity is a subclass of Brans–Dicke models, with a vanishing coupling constant ($\omega =0$). In this treatment, four $f(R)$ toy models are used to analyze the early-universe cosmology, when the scalar field $\varphi$ dominates over standard matter. We have obtained solutions to the Klein–Gordon equation for those models. It is found that for the first model $(f(R)=\beta R^n)$, as time increases the scalar field decreases and decays asymptotically. For the second model $(f(R)=\alpha R+\beta R^n)$, it was found that the function $\varphi (t)$ crosses the $t$-axis at different values for different values of $\beta$. For the third model $\left(\right.f(R)=R-\frac{{\nu }^4}{R}\left)\right.$, when the value of $\nu$ is small, the potential $V(\varphi )$ behaves like the standard inflationary potential. For the fourth model $(f(R)=R-(1-m){\nu }^2\left(\right.\frac{R}{{\nu }^2}{\left)\right.}^m-2\mathrm{\Lambda })$, we show that there is a transition between $1.5<m<1.55$. The behavior of the potentials with $m<1.5$ is totally different from those with $m>1.55$. The slow-roll approximation is applied to each of the four $f(R)$ models and we obtain the respective expressions for the spectral index $n_s$ and the tensor-to-scalar ratio $r$.

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.