Narrow Results

We focus on the consequences of that the Event Horizon Telescope obtained images of the black hole shadow in the center of the M87 galaxy. We show that to test extended theories of gravity the improving of the resolution by 3 orders is necessary. In addition it is demonstrated that the rotation distorts the shape of the shadow and corrections from the extended gravity may affect on this distortion.

We obtain new exact solutions to the field equations in the Einstein–Gauss–Bonnet (EGB) modified theory of gravity for a five-dimensional spherically symmetric static matter distribution. By using a coordinate transformation, the study is reduced to the analysis of a single first-order nonlinear differential equation which is an Abel equation of the second kind. Three classes of exact models are generated. The first solution has a constant density and a nonlinear equation-of-state; it contains the familiar Einstein static universe as a special case. The second solution has variable energy density and is expressible in terms of elementary functions. The third solution has vanishing Gauss–Bonnet coupling constant and is a five-dimensional generalization of the Durgapal–Bannerji model. The solution is briefly examined for physical admissibility. In particular, a set of constants is found which ensures that a pressure-free hypersurface exists which in turn defines the boundary of the distribution. The matter distribution is well behaved and the adiabatic sound speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution.

In this paper, in a new approach, we study the stability of the dynamical system (DS) of $R^{1+ϵ}$ in terms of two significant cosmological parameters, deceleration parameter and jerk parameter $\{q,j\}$. Other cosmographic parameters such as $(l,s,\dots )$ have been obtained in terms of these two parameters. We have obtained critical points ($q_e,j_e$), the best fitted current values of cosmographic parameters ($q_0,j_0,l_0,s_0$), best value for model parameter $ϵ$ and best trajectory of dynamics of system in phase space by simultaneously solving the DS and best fitting the parameter by the SNIa data. By defining modified redshift in anisotropic cosmological model as $1+z(t,\widehat{p})=\frac{a(t_{0)}}{a(t)}(1-A(\widehat{n}\cdot \widehat{p}))$ (where $A$ is a magnitude of anisotropy, $\widehat{n}$ is direction of privileged axis and $\widehat{p}$ is the direction of each SNe Ia sample to galactic coordinates), the luminosity distance has been obtained in terms of modified redshift using cosmography method. Using union 2 data, we have found the direction of privileged axis in the galactic coordinate. The results show that the magnitude of anisotropy is about $\left|A\right|\simeq 10^{-3}$ and the direction of privileged axis is $(l,b)=(298_{+34}^{-34},2_{+23}^{-23})$. Also, our results are consistent with other studies in $1-\sigma$ confidence level.

Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\mathrm{\Lambda }$CDM model, based on General Relativity (GR) and standard model of particles, are discussed in view of the most recent observational constraints. The motivations for considering extensions and modifications of GR are taken into account, with particular attention to $f(R)$ and $f(T)$ theories of gravity where dynamics is represented by curvature or torsion field, respectively. The features of $f(R)$ models are explored in metric and Palatini formalisms. We discuss the connection between $f(R)$ gravity and scalar–tensor theories highlighting the role of conformal transformations in the Einstein and Jordan frames. Cosmological dynamics of $f(R)$ models is investigated through the corresponding viability criteria. Afterwards, the equivalent formulation of GR (Teleparallel Equivalent General Relativity (TEGR)) in terms of torsion and its extension to $f(T)$ gravity is considered. Finally, the cosmographic method is adopted to break the degeneracy among dark energy models. A novel approach, built upon rational Padé and Chebyshev polynomials, is proposed to overcome limits of standard cosmography based on Taylor expansion. The approach provides accurate model-independent approximations of the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain integration of cosmic data, are presented to bound coefficients of the cosmographic series. These techniques are thus applied to reconstruct $f(R)$ and $f(T)$ functions and to frame the late-time expansion history of the universe with no a priori assumptions on its equation-of-state. A comparison between the $\mathrm{\Lambda }$CDM cosmological model with $f(R)$ and $f(T)$ models is reported.

In this paper, we have derived the field equations in an extended theory of gravity in an anisotropic spacetime background and in the presence of magnetic field. The physical and geometrical parameters of the models are determined with respect to the Hubble parameter using some algebraic approaches. A time varying scale factor has been introduced to analyze the behavior of the model. From some diagnostic approach, we found that the model behaves as ${\mathrm{\Lambda }}_{\mathrm{\text{CDM}}}$ model at late time of cosmic evolution.

In this paper, we present some cosmological models with a hybrid scale factor (HSF) in the framework of general relativity (GR). The HSF fosters an early deceleration as well as a late-time acceleration and mimics the present Universe. The dynamical aspects of different cosmological models with HSF in the presence of different matter fields have been discussed.

Chae’s analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin of Einstein’s general relativity, the request of Mach on the structure of the theory has been the core of the foundational debate. This issue is strictly connected with the nature of the mass–energy equivalence. This was exactly the key point that Einstein used to derive the same general relativity. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories, which have recently been further strengthened by the analyses of GAIA observations, request a better understanding of the Equivalence Principle. By considering a direct coupling between the Ricci curvature scalar and the matter Lagrangian, a nongeodesic ratio between the inertial and gravitational masses can be fixed and MOND-like theories are retrieved at low energies.

The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.

We review the possible violation of the Equivalence Principle at finite temperature $T$ in the framework of curvature-based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at $T\ne 0$. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quantify the amount of Equivalence Principle violation. Specifically, Brans–Dicke Theory, Standard Model Extension and Conformal Gravity are considered in detail.

In this paper, in an extended theory of gravity, we have presented bouncing cosmological model at the backdrop of an isotropic, homogeneous space-time, in the presence of general relativistic hydrodynamics (GRH). The scale factor has been chosen in such a manner that with appropriate normalization, the quintom bouncing scenario can be assessed. Accordingly, the bounce occurs at $t=0$ and the corresponding Hubble parameter vanishes at the bounce epoch. The equation of state (EoS) parameter and the energy conditions of the model have been analyzed. The violation of strong energy condition further supports the behavior of extended gravity. As the bouncing cosmology suffers with instability, this model also shows the similar behavior.

We study gravitational particle production in the inflaton oscillation regime after inflation both in Einstein gravity and extended gravity models. In some extended models, the particle production rate is large enough to complete the reheating. We also find that there exists a gradient instability during the inflaton oscillation in some extended models.

We shall discuss equivalence of frames in Palatini f(ℛ)-theories at action level. A Palatini formulation of Brans-Dicke theories (equivalent to the purely metric ones) will also be discussed.

In this paper we show how in the most natural extension of gravity with torsion, fermion fields are endowed with running coupling in spinorial interaction that are eventually shown to reproduce the strength and structure of the leptonic weak forces.