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In this paper, we studied the bouncing behavior of the cosmological models formulated in the background of the Hubble function in the F (R , G) theory of gravity, where R and G , respectively, denote the Ricci scalar and Gauss–Bonnet invariant. The actions of the bouncing cosmology are studied with a consideration of the different viable models that can resolve the difficulty of singularity in standard Big Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late evolution time. The phantom at the bounce epoch is analogous to quintessence behavior. Finally, we formulate the perturbed evolution equations and investigate the stability of the two bouncing solutions. [ABSTRACT FROM AUTHOR]

In this paper, we have presented a bouncing cosmological model of the Universe in an extended theory of gravity. The dynamical behaviour of the model obtained from the flat FLRW space‐time along with the violation of null energy condition have been shown. The geometrical parameters show singularity behaviour at the bouncing epoch. The parameters involved in the scale factor play a major role in the bouncing behaviour. In addition, the coupling parameter that resulted in the minimal matter‐geometry coupling in the extended gravity has significant role to avoid the singularity of equation of state parameter at the bouncing epoch. Using a linear homogeneous perturbation calculation, we show the dynamical stability of the model. In this paper, a bouncing cosmological model of the Universe is presented in an extended theory of gravity. The dynamical behaviour of the model obtained from the flat FLRW space‐time along with the violation of null energy condition have been shown. The geometrical parameters show singularity behaviour at the bouncing epoch. The parameters involved in the scale factor play a major role in the bouncing behaviour. In addition, the coupling parameter that resulted in the minimal matter‐geometry coupling in the extended gravity has significant role to avoid the singularity of equation of state parameter at the bouncing epoch. Using a linear homogeneous perturbation calculation the dynamical stability of the model is shown. [ABSTRACT FROM AUTHOR]

We investigate the existence of high dense compact objects in the light of Rastall gravity theory. The material content is driven by an imperfect fluid distribution and the inner geometry is described by the Tolman–Kuchowicz space–time. The validity of the obtained model is checked by studying the main salient features such as energy–density, radial and tangential pressures and anisotropy factor. Since Einstein gravity theory shares the same vacuum solution with Rastall gravity theory, the interior geometry is joining in a smoothly way with the exterior Schwarzschild's solution. The equilibrium of the model under different gradients is analyzed by using the modified hydrostatic equilibrium equation, containing the so–called Rastall gradient. The compact structure has a positive anisotropy factor which enhances the balance and stability mechanisms. To check the potentially stable behavior, we employ Abreu's and adiabatic index criterion. It was found that the model is completely stable. The incidence of the Rastall's parameter γ on all the physical quantities that characterize the model is described by the help of graphical analysis. Concerning the γ spectrum we have considered 0.3142 ≤ γ ≤ 0.3157 . All the results are compared with the general relativity case. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f (R , T) scenario. To do so we use modified Durgapal–Fuloria metric potential and the pressure anisotropy condition is imposed in order to obtain the effective anisotropic factor Δ ̃. Besides, a notable and viable election on f (R , T) gravity formulation is taken. The choice of f (R , T) function modifies the matter sector only, including new ingredients to the physical parameters that characterize the model such as density, pressure, subliminal speeds of sound, surface redshift etc. We analyze all the physical and mathematical general requirements of the configuration taking M = 1. 04 M ⊙ and varying χ from − 0. 1 to 0.1. It is shown by the graphical procedure that χ < 0 yields a more compact object in comparison when χ ≥ 0 (where χ = 0. 0 corresponds to general relativity) and increases the value of the surface redshift. However, negative values of χ introduce in the system an attractive anisotropic force (inward) and the configuration is completely unstable (corroborated employing Abreu's criterion). Furthermore, the model in Einstein gravity theory presents cracking while for χ > 0 the system is fully stable. The relationship between effective radial pressure p ̃ r and effective density ρ ̃ is discussed and obtained. This is achieved by establishing the corresponding equation of state. • We have obtained new analytic relativistic anisotropic spherical solutions for modified Durgapal–Fuloria potential in the framework of f (R , T) gravity theory. • We use pressure anisotropy condition to obtain a physically viable expression for effective anisotropic factor (Δ). • We have shown that the present f (R , T) model is stable while the cracking appears inside the model in case of Einstein's gravity (GR) which shows that the f (R , T) gravity theory could be more useful to discover the stable model than the Einstein theory. • We established the relationship between pressure and density as p = f (ρ) and discovered an approximate equation of state for the present model. [ABSTRACT FROM AUTHOR]

The present work is devoted to the study of anisotropic compact matter distributions within the framework of five-dimensional Einstein–Gauss–Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman–Kuchowicz spacetime. The Gauss–Bonnet Lagrangian L GB is coupled to the Einstein–Hilbert action through a coupling constant, namely α . When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor. These effects are contrasted with the corresponding general relativity results. Besides, we have checked the incidence on an important mechanism: equilibrium by means of a generalized Tolman–Oppenheimer–Volkoff equation and stability through relativistic adiabatic index and Abreu's criterion. Additionally, the behavior of the subliminal sound speeds of the pressure waves in the principal directions of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing the causality condition and energy conditions, respectively. All these subjects are illuminated by means of physical, mathematical and graphical surveys. The M–I and the M–R graphs imply that the stiffness of the equation of state increases with α ; however, it is less stiff than GR. [ABSTRACT FROM AUTHOR]