Ricci Scalar Research Articles

Evolution of Collisional Matter in Modified Teleparallel Theories

Here, we discuss the cosmic evolution in the presence of collisional matter (CM) with and without radiations within the framework of modified teleparallel theories. We opt f(T, B) theory (where T stands for torsion scalar and B represents the boundary term associated to the divergence of torsion 2∇ μ Tμ = B), which makes a good connection between f(R) (R for Ricci Scalar) and f(T) (T for torsion) theory under reasonable conditions. The power law and logarithmic f(T, B) models are selected to discuss the behavior of deceleration parameter q(z), Hubble parameter H(z), Equation of state (EoS) for dark energy (DE), and effective EoS. We found the great oscillations of EoS for DE across the phantom divide line. Effective EoS also crossed the phantom divide line without any oscillations. The graphs for H(z), q(z), effective EoS are alike for NCM with radiations, CM without radiaitons and CM with radiations.

On the Analyticity of Static Solutions of a Field Equation in Finsler Gravity

It is well-known that static vacuum solutions of Einstein equations are analytic in suitable coordinates. We ask here for an extension of this result in the context of Finsler gravity. We consider Finsler spacetimes that retain several properties of static Lorentzian spacetimes, are Berwald and have vanishing Ricci scalar.

Dynamical wormholes in Einstein\u2013Gauss\u2013Bonnet gravity

In the present work, we investigate evolving wormhole configurations in higher-dimensions, by adding a Gauss–Bonnet term to the standard Einstein–Hilbert action. Using a generalized Friedmann–Robertson–Walker spacetime, we derive evolving wormhole geometries by considering a constraint on Ricci scalar. In standard cosmological models, the Ricci scalar is independent of radial coordinate r and is only a function of time. We use this property to introduce a particular class of wormhole solutions for which microscopic wormholes may have been enlarged to macroscopic sizes in an expanding inflationary cosmological background. We find, for the first time, specific solutions that satisfy the weak energy condition (WEC) throughout the entire spacetime in four dimensions. In addition to this, we also present other wormhole solutions that satisfy the WEC throughout their respective evolution.

Generalized scalar\u2013tensor theory of gravity reconstruction from physical potentials of a scalar field

We describe how to reconstruct generalized scalar–tensor gravity (GSTG) theory, which admits exact solutions for a physical type of potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is an a priori specified relation between the Hubble parameter H and a function of a non-minimal coupling F=1+delta F, Hpropto sqrt{F}. Deviations from Einstein gravity delta F induce corresponding deviations of the potential delta V from a constant value and modify the dynamics from a pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such a consideration allows us to substitute the physical potential into the obtained equations and then to calculate the non-minimal coupling function and kinetic term that define the GSTG parameters. With this method, we reconstruct GSTG for the polynomial, exponential, Higgs, Higgs–Starobinsky and Coleman–Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove the correspondence of the obtained solutions to observational data from Planck.

Viability of the $$R+e^T$$ cosmology

We propose a new theoretical approach for a cosmological model, which starts from an exponential of the trace of the energy-momentum tensor-dependence on the gravitational action, to be summed to the Ricci scalar. We derive the referred field equations and Friedmann-like equations. We derive the scale factor, Hubble parameter and deceleration parameter, in terms of both time and redshift. In possession of those parameters in terms of the redshift, we confront their predictions with the observational Hubble dataset and the outcomes are pretty satisfactory so that the model can be seen as a new alternative to the cosmological constant problem. We also present the statefinder diagnostic and discuss profoundly the dynamical behaviour of the model.

Reconstruction of logamediate and exponential inflationary models using generalized induced gravity scenario

This manuscript explores the dynamics of an inflationary model using two known exact solutions, i.e., logamediate and exponential expansion. To achieve this, the framework of generalized induced gravity non-minimally coupled to Ricci scalar is taken under consideration. Using slow-roll approximation and a generalized form of coupling function, we find the possible forms of potential needed to produce inflation in the model and conduct the mathematical analysis of cosmological perturbations. In both of the eras, we constraint the involved model parameters by comparing the $r-n_{s}$ trajectories with Planck 2015 astrophysical data. Also, we reconstruct these inflationary models assuming as attractors the scalar spectral index and tensor-scalar ratio as a function of number of e-foldings.

Nonlinearly charged AdS black hole solutions in three-dimensional massive gravity's rainbow

Two new families of nonlinearly charged and asymptotically anti-de Sitter (AdS) rainbow black holes have been introduced, as the exact solutions to the coupled electromagnetic and gravitational field equations, in massive gravity theory and in the presence of power-law nonlinear electrodynamics. The conserved and thermodynamic quantities such as black hole mass, charge, temperature, entropy and electric potential have been calculated from geometric and thermodynamic approaches. Despite the fact that some of them receive corrections from rainbow functions and nonlinear electrodynamics, it has been proved that they fulfill the first law of black hole thermodynamics. Thermal stability of the black holes has been studied by use of the canonical ensemble and geometrical thermodynamics methods, separately. Regarding the black hole heat capacity and thermodynamic Ricci scalars, the points of type-one and type-two phase transitions and the conditions under which the black holes remain locally stable have been determined. Also, global stability of the novel rainbow black holes has been investigated from the viewpoint of the grand canonical ensemble. Through calculation of Gibbs free energy of the black holes, the points of Hawking-Page phase transition and the size of the black holes which are globally stable or in the radiative phase have been determined.

On complete Finsler spaces of constant negative Ricci curvature

Here, using the projectively invariant pseudo-distance and Schwarzian derivative, it is shown that every connected complete Finsler space of the constant negative Ricci scalar is reversible. In particular, every complete Randers metric of constant negative Ricci (or flag) curvature is Riemannian.

Existence of solutions with a horizon in pure scalar-Gauss-Bonnet theories

We consider the Einstein-scalar-Gauss-Bonnet theory and assume that, at regimes of large curvature, the Ricci scalar may be ignored compared to the quadratic Gauss-Bonnet term. We then look for static, spherically-symmetric, regular black-hole solutions with a non-trivial scalar field. Despite the use of a general form of the spacetime line-element, no black-hole solutions are found. In contrast, solutions that resemble irregular particle-like solutions or completely regular gravitational solutions with a finite energy-momentum tensor do emerge. In addition, in the presence of a cosmological constant, solutions with a horizon also emerge, however, the latter corresponds to a cosmological rather than to a black-hole horizon. It is found that, whereas the Ricci term works towards the formation of the positively-curved topology of a black-hole horizon, the Gauss-Bonnet term exerts a repulsive force that hinders the formation of the black hole. Therefore, a pure scalar-Gauss-Bonnet theory cannot sustain any black-hole solutions. However, it could give rise to interesting cosmological or particle-like solutions where the Ricci scalar plays a less fundamental role.

Disformal Transformations in Modified Teleparallel Gravity

In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for f ( T ) gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others.

Phantom cosmology in an extended theory of gravity

Some phantom cosmological models without big rip singularity have been constructed in a simple extended theory of gravity. In the geometrical part of the action, a minimally coupled linear function of the Ricci Scalar and the trace of the energy momentum tensor have been considered in place of the Ricci scalar. Four Little Rip and Pseudo Rip models have been investigated where the equation of state parameter evolves asymptotically and sufficiently rapidly to −1. The effect of the coupling constant of the extended gravity theory on the dynamics has been discussed. Possible wormhole solutions for the phantom models are obtained. The possibility of Big Trip in wormholes are discussed for the models.

Study on wormhole geometry with rho (R, R^{'}) matter in modified gravity

In this work, static traversable wormholes are investigated in R^2 gravity with logarithmic trace term T, where R denotes the Ricci scalar, and T=-rho +p_r+2p_t>0, the trace of the energy momentum tensor. The connection between energy density of the matter component and the Ricci scalar is taken into account. Exact wormhole solutions are determined for three different novel forms of energy density: rho =alpha _1 R+beta _1 R^{'}e^{xi _1 R}, rho =alpha _2 R e^{xi _2 R} and rho =alpha _3 R^2+beta _2 R^{'} e^{xi _3 R^{'}}, where prime denotes derivative with respect to r. The parameters alpha _1, beta _1, xi _1, alpha _2, xi _2, alpha _3, xi _3 and beta _2 play an important role for the absence of exotic matter inside the wormhole geometry. The parameter space is separated into numerous regions where the energy conditions are obeyed.

Non-Singular Model of Magnetized Black Hole Based on Nonlinear Electrodynamics

A new modified Hayward metric of magnetically charged non-singular black hole spacetime in the framework of nonlinear electrodynamics is constructed. When the fundamental length introduced, characterising quantum gravity effects, vanishes, one comes to the general relativity coupled with the Bronnikov model of nonlinear electrodynamics. The metric can have one (an extreme) horizon, two horizons of black holes, or no horizons corresponding to the particle-like solution. Corrections to the Reissner–Nordström solution are found as the radius approaches infinity. As r → 0 the metric has a de Sitter core showing the absence of singularities, the asymptotic of the Ricci and Kretschmann scalars are obtained and they are finite everywhere. The thermodynamics of black holes, by calculating the Hawking temperature and the heat capacity, is studied. It is demonstrated that phase transitions take place when the Hawking temperature possesses the maximum. Black holes are thermodynamically stable at some range of parameters.

Late-times asymptotic equation of state for a class of nonlocal theories of gravity

We investigate the behavior of the asymptotic late-times effective equation of state for a class of nonlocal theories of gravity. These theories modify the Einstein-Hilbert Lagrangian introducing terms containing negative powers of the d'Alembert operator acting on the Ricci scalar. We find that imposing vanishing initial conditions for the nonlocal content during the radiation-dominated epoch implies the same asymptotic late-times behavior for most of these models. In terms of the effective equation of state of the universe, we find that asymptotically $\omega_{ \rm eff} \rightarrow -1$, approaching the value given by a cosmological constant. On the other hand, unlike in the case of $\Lambda$CDM, the Hubble factor is a monotonic growing function that diverges asymptotically. We argue that this behavior is not a coincidence and discuss under which conditions this is to be expected in these nonlocal models.

Spherically symmetric gravitational collapse in Einstein Gauss–Bonnet theory

This paper deals with spherically symmetric gravitational collapse of inhomogeneous perfect fluid in Einstein Gauss–Bonnet gravity. The physical quantities have been plotted in the EGB gravity. The Ricci Scalar and Kretschmann scalar have been determined to study the curvature singularity. The shell focusing curvature singularities are generated at last stage of gravitational collapse of object. The formation of singularity and apparent horizon depends on the initial data. Also, the energy conditions have been discussed for the reasonable energy momentum tensor. The presence of GB coupling constant [Formula: see text] modifies the structure of singularity and formation of apparent horizon.

On modeling neutrinos oscillations by geometry methods in the frames of the theory for a fermion with three mass parameters

Starting from the general Gel’fand-Yaglom approach, we develop the theory of a new wave equation for a spin 1/2 fermion, which is characterized by three mass parameters. On the base of a 20-component wave function, three auxiliary bispinors are introduced, in absence of external fields these bispinors obey three separate Dirac-like equations with different masses. In presence of external electromagnetic fields or gravitational non-Euclidean background with a non-vanishing Ricci scalar curvature, the main equation is not split into separated three equations, instead a quite definite mixing of three Dirac-like equations arises. It is shown that for neutral Majorana particle, a generalized equation with three mass parameters exists as well. Such a generalized Majorana equation is not split into three separated equations in the curved space-time background, if the Ricci scalar of that space-time does not vanish. We have studied in detail the Majorana case, assuming approximation when an external cosmological background is taken into account by a constant Ricci parameter, R = const, and the Cartesian coordinates are used. With the help of a special linear transformation, the system of three linked Majorana equations transforms into three separate ones, with modified mass parameters, the last are solvable in the usual way. The spectrum of arising mass parameters is studied analytically and numerically.

Ricci subtraction for cosmological Coleman-Weinberg potentials

We reconsider the fine-tuning problem of scalar-driven inflation arising from the need to couple the inflaton to ordinary matter in order to make reheating efficient. Quantum fluctuations of this matter induce Coleman-Weinberg corrections to the inflaton potential, depending (for de Sitter background) in a complex way on the ratio of the inflaton to the Hubble parameter. These corrections are not Planck-suppressed and cannot be completely subtracted because they are not even local for a general geometry. A previous study showed that it is not satisfactory to subtract a local function of just the inflaton and the {\it initial} Hubble parameter. This paper examines the other allowed possibility of subtracting a local function of the inflaton and the Ricci scalar. The problem in this case is that the new, scalar degree of freedom induced by the subtraction causes inflation to end almost instantly.

The Spectrum of Quantum Gravity

In this paper we consider the degrees of freedom beyond the graviton present in the effective field theory for quantum gravity. We point out that the position of the poles due to $${{R}^{2}}$$ and $${{R}_{{\mu \nu }}}{{R}^{{\mu \nu }}}$$ cannot be affected by operators that are higher order in curvature. On the other hand, operators of the type $$R\square R$$ will lead to new poles while shifting the positions of the poles found at second order in curvature. New degrees of freedom can be identified either, as just described, by looking at the poles of the graviton propagator corrected by quantum gravity or by mapping the Jordan frame theory to the Einstein frame theory. While this procedure is very well defined for second order curvature terms in the effective action, we point out that higher order terms in curvature lead to a nonlinear and non-local relation between the propagating scalar degree of freedom and the Ricci scalar. We show how to resolve these ambiguities and how to obtain the correct action in the Einstein frame. We illustrate our results by looking at $$f(R)$$ gravity.

Spherically Symmetric Black Holes and Wormholes in Hybrid Metric-Palatini Gravity

The so-called hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. This paper gives a complete description of static, spherically vacuum solutions of HMPG in the simplest case where its scalar-tensor representation has a zero scalar field potential $V(\phi)$, and both Riemannian ($R$) and Palatini ($\cal R$) Ricci scalars are zero. Such a scalar-tensor theory coincides with general relativity with a phantom conformally coupled scalar field as a source of gravity. Generic asymptotically flat solutions either contain naked central singularities or describe traversable wormholes, and there is a special two-parameter family of globally regular black hole solutions with extremal horizons. In addition, there is a one-parameter family of solutions with an infinite number of extremal horizons between static regions and a spherical radius monotonically changing from region to region. It is argued that the obtained black hole and wormhole solutions are unstable under monopole perturbations. As a by-product, it is shown that a scalar-tensor theory with $V(\phi)=0$, in which there is at least one nontrivial ($\phi \ne \rm const$) vacuum solution with $R\equiv 0$, necessarily reduces to a theory with a conformal scalar field (the latter may be usual or phantom).

Conformally flat polytropes for anisotropic fluid in f (R) gravity

This paper provides a detailed analysis of conformally flat spherically symmetric fluid distributions governed by a polytropic equation of state utilizing the metric f (R) gravity, R being the Ricci scalar. The Lane-Emden equation is formulated using Bianchi identity and couple of polytropic equation of states. We discussed two families of relativistic polytropes and the constraints are evaluated for their necessary physical applications. The physical practicability of polytropes is scrutinized via energy conditions. An explicit relation of the Weyl tensor with material variables is explored. The condition of vanishing Weyl tensor is imposed on the Lane-Emden equation in the background of particular f (R) model in both cases to explore physical constraints on polytropes.