Gravastar in the framework of symmetric teleparallel gravity

We present a novel gravastar model based on the Mazur-Mottola (2004) method with an isotropic matter distribution in \begin{document}$ f(Q) $\end{document} gravity. The gravastar, which is a hypothesized substitute for a black hole, is built using the Mazur-Mottola mechanism. This approach allows us to define the gravastar as having three stages. The first one is an inner region with negative pressure; the next region is a thin shell that is made up of ultrarelativistic stiff fluid, and we studied the proper length, energy, entropy, and surface energy density for this region. Additionally, we demonstrated the possible stability of our suggested thin shell gravastar model through the graphical study of the surface redshift. The exterior Schwarzschild geometry describes the outer region of the gravastar. In the context of \begin{document}$ f(Q) $\end{document} gravity, we discovered analytical solutions for the interior of gravastars that are free of any type of singularity and the event horizon.     

Explosive phenomena in modified gravity

Observational manifestations of some models of modified gravity, which have been suggested to explain the accelerated cosmological expansion, are analyzed for gravitating systems with time dependent mass density. It is shown that if the mass density rises with time, the system evolves to the singular state with infinite curvature scalar. The corresponding characteristic time is typically much shorter than the cosmological time.     

Gravitational leptogenesis in teleparallel and symmetric teleparallel gravities

In this study, we investigate the possibilities of generating baryon number asymmetry under thermal equilibrium within the frameworks of teleparallel and symmetric teleparallel gravities. Through the derivative couplings of the torsion scalar and the non-metricity scalar to baryons, baryon number asymmetry is produced in the radiation dominated epoch. For gravitational baryogenesis mechanisms in these two frameworks, the produced baryon-to-entropy ratio is too small to be consistent with observations. However, the gravitational leptogenesis models within both frameworks have the potential to explain the observed baryon-antibaryon asymmetry.     

Holographic renormalization in teleparallel gravity

We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analog of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed.     

Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity

We calculate energy and momentum of a spherically symmetric dilaton frame using the gravitational energy‐momentum 3‐form within the tetrad formulation of general relativity (GR). The frame we use is characterized by an arbitrary function ? with the help of which all the previously found solutions can be reproduced. We show how the effect of inertia (which is mainly reproduced from ?) makes the total energy and momentum always different from the well known result when we use the Riemannian connection . On the other hand, when use is made of the covariant formulation of teleparallel gravity, which implies to take into account the pure gauge connection, teleparallel gravity always yields the physically relevant result for the energy and momentum.     

Gravitational energy-momentum density in teleparallel gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Moller's canonical energy-momentum density of the gravitational field.     

Accelerating cosmology in modified gravity with scalar field

The modified gravity with 1/R term (R being the scalar curvature) and the Einstein-Hilbert term is studied by incorporating the phantom scalar field. A number of cosmological solutions are derived in the presence of the phantom field in the perfect fluid background. It is shown: the current inflation obtained in the modified gravity is affected by the existence of the phantom field.     

Energy conditions in generalized teleparallel gravity models

In this paper, we investigate the energy conditions (including null, weak, strong, dominant) in generalized teleparallel gravities including pure $F(T)$ , teleparallel gravity with non-minimally coupled scalar field and $F(T)$ with non-minimally coupled scalar field models. In particular, we apply them to Friedmann–Robertson–Walker cosmology and obtain some corresponding results. Using two specific phenomenological forms of $F(T)$ , we show that some of the energy conditions are violated.     

Palatini formulation of modified gravity with squared scalar curvature

In this comment we indicate that in the Palatini formulation of R² gravity, there will be no gravity-driven inflation and under some particular assumptions there will be a mild power-law inflation a t².     

Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

Quantum gravity and matter: counting graphs on causal dynamical triangulations

An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate technical tools, one is interested in measuring and classifying how the quantum fluctuations of geometry alter the behaviour of matter, compared with that on a fixed background geometry. In the simplified context of two dimensions, we show how a method invented to analyze the critical behaviour of spin systems on flat lattices can be adapted to the fluctuating ensemble of curved spacetimes underlying the causal dynamical triangulations (CDT) approach to quantum gravity. We develop a systematic counting of embedded graphs to evaluate the thermodynamic functions of the gravity-matter models in a high- and low-temperature expansion. For the case of the Ising model, we compute the series expansions for the magnetic susceptibility on CDT lattices and their duals up to orders 6 and 12, and analyze them by ratio method, Dlog Padé and differential approximants. Apart from providing evidence for a simplification of the model’s analytic structure due to the dynamical nature of the geometry, the technique introduced can shed further light on criteria à la Harris and Luck for the influence of random geometry on the critical properties of matter systems.     

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

We present a new Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like $3+1$ decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.     

Dark energy cosmology with tachyon field in teleparallel gravity

We construct a tachyon teleparallel dark energy model for a homogeneous and isotropic flat universe in which a tachyon as a non-canonical scalar field is non-minimally coupled to gravity in the framework of teleparallel gravity. The explicit form of potential and coupling functions are obtained under the assumption that the Lagrangian admits the Noether symmetry approach. The dynamical behavior of the basic cosmological observables is compared to recent observational data, which implies that the tachyon field may serve as a candidate for dark energy.     

Dark energy from modified gravity with Lagrange multipliers

We study scalar–tensor theory, k-essence and modified gravity with Lagrange multiplier constraint which role is to reduce the number of degrees of freedom. Dark Energy cosmology of different types (ΛCDM, unified inflation with DE, smooth non-phantom/phantom transition epoch) is reconstructed in such models. It is demonstrated that presence of Lagrange multiplier simplifies the reconstruction scenario. It is shown that mathematical equivalence between scalar theory and F(R)$F(R)$ gravity is broken due to presence of constraint. The cosmological evolution is defined by the second F₂(R)$F_2(R)$ function dictated by the constraint. The convenient F(R)$F(R)$ gravity sector is relevant for local tests. This opens the possibility to make originally non-realistic theory to be viable by adding the corresponding constraint. A general discussion on the role of Lagrange multipliers to make higher-derivative gravity canonical is developed.     

Dual gravity and matter

We consider the problem of finding a dual formulation of gravity in the presence of non-trivial matter couplings. In the absence of matter a dual graviton can be introduced only for linearised gravitational interactions. We show that the coupling of linearised gravity to matter poses obstructions to the usual construction and comment on possible resolutions of this difficulty.     

Energy Distributions of the Szekeres Universes in Teleparallel Gravity

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of Szekeres class I and II metrics, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy definitions in the teleparallel gravity (the tetrad theory of gravitation (TG)). We have found that Einstein and Bergmann–Thomson energy distributions give the same results, Landau–Lifshitz distribution is disagree in TG with these definitions. These results are the same as a previous works of Aygün et al., they investigated the same problem by using Einstein, Bergmann–Thomson, Landau–Lifshitz (LL) and Møller energy-momentum complexes in GR. However, both GR and TG are equivalent theories that is the energy densities are the same using different energy-momentum complexes in both theories. Also, our results are support the Cooperstock’s hypothesis.     

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f(T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.     

Nonlinear electrodynamics coupled to teleparallel theory of gravity

Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy--momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy--momentum we obtain the value of energy.     

String inspired quintom model with non-minimally coupled modified gravity

In this Letter we consider a quintom model of dark energy with non-minimal coupling between scalar field and modified gravity which is known f(R)$f(R)$ gravity. The Lagrangian for scalar field has been inspired by tachyonic Lagrangian in string theory. Then we obtain the equation of state (EoS), and the condition required for the model parameters when ω crosses over −1. This model shows that for having ω across over −1, one doesn't need to add some higher derivative operator in the tachyonic part of action (the way that usually used to obtain crossing of the phantom divide line for EoS parameter).