Lorentzian geometrical structures with global time, Gravity and Electrodynamics

We investigate Lorentzian structures in the four-dimensionalspace-time, supplemented either by a covector field of thetime-direction or by a scalar field of the global time. Furthermore,we propose a new metrizable model of the gravity. In contrast to theusual Theory of General Relativity where all ten components of thesymmetric pseudo-metrics are independent variables, the presentedhere model of the gravity essentially depend only on singlefour-covector field, restricted to have only three-independentcomponents. However, we prove that the Gravitational field, ruled bythe proposed model and generated by some massive body, resting andspherically symmetric in some coordinate system, is given by apseudo-metrics, which coincides with thewell known Schwarzschild metric from the General Relativity. TheMaxwell equations and Electrodynamics are also investigated in theframes of the proposed model. In particular, we derive the covariantformulation of Electrodynamics of moving dielectrics andpara/diamagnetic mediums.

Late time cosmology in f(R,G)- gravity with interacting fluids

Cosmological models are obtained in a $f(R)$ modified gravity with a coupled Gauss-Bonnet (GB) terms in the gravitational action. The dynamical role of the GB terms is explored with a coupled dilaton field in two different cases (I) $f(R)= R + \gamma R^2- \lambda \left( \frac{R}{3m_s^2} \right)^{\delta}$ where $\gamma$, $\lambda$ and $\delta$ are arbitrary constants and (II) $f(R)=R$ and estimate the constraints on the model parameters. In the first case we choose GB terms coupled with a free scalar field in the presence of interacting fluid and in the second case GB terms coupled with scalar field in a self interacting potential to compare the observed universe. The evolutionary scenario of the universe is obtained adopting a numerical technique as the field equations are highly non-linear. Defining a new density parameter $\Omega_{H}$, a ratio of the dark energy density to the present energy density of the non-relativistic matter, we look for a late accelerating universe. The state finder parameters $\Omega_{H}$, deceleration parameter ($q$), jerk parameter ($j$) are plotted. It is noted that a non-singular universe with oscillating cosmological parameters for a given strength of interactions is admitted in Model-I. The gravitational coupling constant $\lambda$ is playing an important role. The Lagrangian density of $f(R)$ is found to dominate over the GB terms when oscillating phase of dark energy arises. In Model-II, we do not find oscillation of the cosmological parameters as the universe evolves. In the presence of interaction the energy from radiation sector of matter cannot flow to the other two sectors of fluid. The range of values of the strengths of interaction of the fluids are estimated for a stable universe assuming the primordial gravitational wave speed equal to unity.

Scalar Perturbations of Black Holes in the f(R)=R−2αR Model

In this paper, we study the perturbations of the charged static spherically symmetric black holes in the f(R)=R−2αR model by a scalar field. We analyze the quasinormal modes spectrum, superradiant modes, and superradiant instability of the black holes. The frequency of the quasinormal modes is calculated in the frequency domain by the third-order WKB method, and in the time domain by the finite difference method. The results by the two methods are consistent and show that the black hole stabilizes quicker for larger α satisfying the horizon condition. We then analyze the superradiant modes when the massive charged scalar field is scattered by the black hole. The frequency of the superradiant wave satisfies ω∈(μ2,ωc), where μ is the mass of the scalar field, and ωc is the critical frequency of the superradiance. The amplification factor is also calculated by numerical method. Furthermore, the superradiant instability of the black hole is studied analytically, and the results show that there is no superradiant instability for such a system.

Generalized tachyonic dark energy

In this paper, a generalized tachyonic dark energy scenario is presented in the framework of a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) flat universe, in which a noncanonical scalar field is coupled to gravity nonminimally. By utilizing the Noether symmetry method, we found the explicit form of both potential density and coupling function, as a function of the scalar field. It is found that the tachyon field acts as the source of inflation and accelerates the evolution of the universe in the early times considerably. While, in the late times, gravitational sources are a pressureless matter field together with the tachyon field, which is the nature of dark energy and plays an essential role in the deceleration-acceleration phase transition of the universe. Further, the role of the coefficient function of tachyon potential, alongside the potential, is considered in the evolution of the universe. It is shown that this model involves a cosmological degeneracy in the sense that different coupling parameters and tachyonic potentials may be equivalent to the same cosmological standards such as the cosmic acceleration, age, equation of state and mean Hubble of the FLRW universe. The physical characteristics of the main cosmological observables are studied in detail, which suggests that the generalized tachyon field is a remarkable dark energy candidate.

Effective potential of scalar-tensor gravity with quartic self-interaction of scalar field

One-loop effective potential of scalar-tensor gravity with a quartic scalar field self-interaction is evaluated up to first post-Minkowskian order. The potential develops an instability in the strong field regime which is expected from an effective theory. Depending on model parameters the instability region can be exponentially far in a strong field region. Possible applications of the model for inflationary scenarios are highlighted. It is shown that the model can enter the slow-roll regime with a certain set of parameters.