Narrow Results

This paper explores isotropic polytropes within the framework of the $f(R,G)$ modified gravity theory. We derive the field equations that govern these systems and develop the Lane–Emden equations for both mass (baryonic) density and total energy density, utilizing two different polytropic equations of state. Our analysis shows that the constructed models feature positive and finite density and pressure, which decrease as expected towards the outer boundary, aligning with the typical behavior of self-gravitating objects. Additionally, the energy–momentum tensor meets the required energy conditions, confirming the physical viability of the models. The compactness factor remains below the critical limit, signifying stability and providing insights into gravitational redshift. Analysis of the sound speed confirms adherence to causality, while the adiabatic index indicates a degree of stiffness within the system. These findings advance our understanding of self-gravitating objects in $f(R,G)$ gravity and lay the groundwork for future research in this field.

In this paper, we study the $F(R,G)$ gravity model with an interacting model by flat-FRW metric in a viscous fluid. We consider that the universe dominates with components of dark matter and dark energy. This means that the dark matter component derives from Extended Bose–Einstein Condensate (EBEC) and the components of dark energy arise from the $F(R,G)$ gravity. After obtaining the Einstein equation, the energy density and the pressure of dark energy are written in terms of the geometry of the curvature and the Gauss–Bonnet terms, and components of dark matter and viscous fluid. Also, the corresponding continuity equations are written with the presence of interaction terms. In what follows, we employ the EBEC regime instead of the normal dark matter by the dark matter Equation of State (EoS) as $p_{\mathrm{\text{dm}}}=\alpha {\rho }_{\mathrm{\text{dm}}}+\beta {\rho }_{\mathrm{\text{dm}}}^2$, which arises from the gravitational form. The EoS can be expressed from the perspective of the virial expansion, in which the first and second terms represent normal dark matter and quantum ground state. Next, the corresponding Friedmann equations reconstruct in terms of the redshift parameter, then by using the scenario of the power-law cosmology for the scale factor, we fit the present model with the Hubble amounts of 51 supernova data by the likelihood analysis. In that case, we acquire the cosmological parameters of dark energy in terms of the redshift parameter, and by plotting these graphs, we see that the universe is currently undergoing an accelerated expansion phase. Finally, we investigate the stability of the present model with the sound speed parameter.

This investigation deals with the dynamics of spherical collapse of dissipative perfect fluid in $f(R,G)$ gravity theory. We construct the dynamical equation of the collapsing stellar fluid by adopting the Misner–Sharp technique. Furthermore, we derive the heat transport equation and couple it with the dynamical equation to obtain the collapsing rate. We observe that the contribution due to extra terms of $f(R,G)$ in Einstein’s field equations increases the rate of collapse for some cases, while decreases it for some other cases.

Current study highlights the physical characteristics of charged anisotropic compact stars by exploring some exact solutions of modified field equations in $f(R,G)$ gravity. A comprehensive analysis is performed from the obtained solutions regarding stability, energy conditions, regularity, sound velocity and compactness. These solutions can be referred to model the compact celestial entities. In particular, a compact star named, $\mathrm{\text{Her}}X-1$ has been modeled which indicates that current solution fits and is in conformity to the observational data as well. A useful and interesting fact from this model arises that relative difference between two forces of anisotropic pressure and electromagnetic force may occur inside the aforementioned compact star. This is another mechanism which is essential for stability of the compact object and prevent stellar object to annihilate.

In the current study, we discuss Gödel-type universe in $f(R,G)$ gravity. Analysis has been done by considering anisotropic and perfect fluid distributions. Energy conditions for two proposed $f(R,G)$ gravity models have been studied for suitable values of model parameters. Furthermore, Tolman–Oppenheimer–Volkoff equation has been developed with cylindrical coordinates in $f(R,G)$ gravity. The graphical analysis for both these models suggests that Tolman–Oppenheimer–Volkoff equation is obeyed in a specific interval for the radial coordinate $r$. A polytropic equation of state has been discussed for two $f(R,G)$ gravity models. By analyzing the energy conditions, it is concluded that Gödel-type universe with both $f(R,G)$ gravity models supports the expansion of the universe for certain range of radial coordinates.

We present investigation devoted to the dynamical study of relativistic hydrodynamics with some thermodynamical characteristics in $f(R,G)$ gravity towards spatially homogeneous isotropic cosmological model filled with isotropic fluid. We govern the features of the derived cosmological model by considering the power-law inflation for the average scale factor. The temperature and entropy density of the proposed model are positive definite. We also discuss the energy conditions to our solutions. The strong energy condition violated, which indicates the accelerated expansion of the proposed model.

There are a number of different theories which tend to explain the concept of universe’s accelerated expansion. Among these theories, modified gravity is the most promising one. This paper elaborates matter distribution along with different characteristics of anisotropic compact stars in $f(R,G)$ gravity background. Specifically, to profoundly understand physical behavior of the compact stars, we considered six compact stars, namely: Her X-1 (${\mathrm{\text{CS}}}_1$), SAXJ1808.4-3658 (${\mathrm{\text{CS}}}_2$), 4U1820-30 (${\mathrm{\text{CS}}}_3$), PSR J 1614 2230 (${\mathrm{\text{CS}}}_4$), VELA X-1 (${\mathrm{\text{CS}}}_5$) and Cen X-3 (${\mathrm{\text{CS}}}_6$) and calculated the corresponding quantities such as energy density ($\rho$), radial pressure ($p_r$) and tangential pressure ($p_t$) using three distinct models of $f(R,G)$ gravity. For simplicity, $f(R,G)$ gravity is divided into two parts as: $f(R,G)=f_1(R)+f_2(G)$. The first part $f_1(R)$ is considered Hu–Sawicki like model, while the second part $f_2(G)$ is considered logarithmic like for Model 1 and power law like for Model 2 and Model 3. Predominantly, measurements of anisotropy, the energy conditions (ECs) and stability aspects of models for considered compacts stars are presented using graphical techniques. Furthermore, we also established that for the $f(G)$ model parameter ($n>0$), all the six stars show conventional behavior.

In this article, we examine the universe’s dynamical behaviour in the context of the $f(R,G)$ theory of gravity, where $R$ and $G$ represent the Ricci scalar and Gauss-Bonnet invariant, respectively. The modified field equations are solved for the selection of $f(R,G)$ function as $f(R,G)=R^{\beta }{G}^{1-\beta }$ and of the deceleration parameter as a linear function of Hubble parameter, i.e., $q=n+mH$. We predict the best fit values of model parameters that would be in agreement with the recent observational datasets. We use the CC, Pantheon and BAO datasets as well as the Bayesian analysis and likelihood function together with the MCMC method. Further, we examine the physical behavior of cosmographic parameters corresponding to the constrained values of the model parameters as well as the energy density and pressure. The model obtained exhibits a transition from decelerating to accelerating expansion phases of the universe. We show that our $f(R,G)$ model can explain the late accelerating expansion of the universe without calling any dark energy term in the energy-momentum tensor.

The main purpose of this research is to examine a number of interior configurations of stable anisotropic objects formed in the shape of spherical charged stars within the gravity region described by $f(R,G)$, where $G$ represents the Gauss–Bonnet invariant and $R$ defines the Ricci Scalar in this scenario. The formation of these charged stars is investigated using the solutions found by Karori and Barua, among several feasible models within the theory of $f(R,G)$ gravity. The study explores the behavior of these realistically charged compact stars, analyzing various physical components through the use of graphs. Furthermore, the feasibility of our model is assessed by evaluating it against different energy conditions. Additionally, topics such as density modification, stress evolution, various forces, star stability, anisotropy measurement, state parameter equations, and charge distribution are discussed.

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in $f(R,G)$ gravity, where $R$ and $G$ both signify the Ricci scalar and Gauss–Bonnet invariant. Furthermore, in order to determine the model’s behavior, it must have the late-time universe’s behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor $a(t)$. The model’s actions are accelerating and expanding at the moment, and $\mathrm{\Lambda }$CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology $\mathrm{\Lambda }$CDM in late times.

This work deals with the investigation of several physical elements that contribute to the construction of stellar objects in the $f(R,G)$ theory, where $R$ and $G$ symbolize the Ricci and Gauss–Bonnet scalars, respectively. In the presence of an anisotropic source, we offer the fundamental formalization of this modified theory. To establish the physical viability of our models, we employ various methods. Energy conditions (ECs) will be derived to ensure the physical validity of our models within the context of $f(R,G)$ gravity. Moreover, we examine the physical viability through the assessment of radial and tangential sound speeds. Additionally, we analyze the equation of state (EoS) parameter and the anisotropic factor in the presence of the electromagnetic field’s influence. Dense stars are shown to be stable under anisotropy measures and exhibit their physical behavior under anisotropic stresses. We identify regions where the systems occupy high compactness and maintain stable ECs with a particular electric charge contribution.

In this study, our primary focus lies in meticulously exploring the intricacies of the universe by employing a flat Friedmann–Lemaître–Robertson–Walker (FLRW) model within the framework of $f(R,G)$ gravity. In our analysis, the $f(R,G)$ function is delineated as the sum of two distinct components, commencing with a quadratic correction of the geometric term denoted by $f(R)$, structured as $f(R)=R+\xi R^2$, alongside a matter term denoted by $f(G)=\lambda G^2$, where $R$ and $G$ symbolize the Ricci scalar and Gauss–Bonnet invariant, respectively. In the pursuit of solutions to the gravitational field equations within the $f(R,G)$ formalism, we embrace a specific expression for the scale factor, represented as $a={sinh}^{\frac{1}{\alpha }}(\beta t)$ [D. Rabha and R. R. Baruah, The dynamics of a hyperbolic solution in $f(R,G)$ gravity, Astron. Comput. 45 (2023) 100761]. In this context, the parameters $\alpha$ and $\beta$ intricately shape the scale factor’s behavior. The model posits the intriguing prospect of perpetual cosmic acceleration when $0<\alpha <1.19$, signifying a continuous expansion of the universe. Conversely, for $\alpha \ge 1.19$, the model proposes a pivotal transition from an early deceleration phase to the present accelerated epoch, a transformative shift in line with our understanding of cosmic evolution. Furthermore, the model demonstrates its credibility by satisfying Jean’s instability condition during the shift from a radiation-dominated era to a matter-dominated era, substantiating the formation of cosmic structures. In our analysis, a central focus is directed toward scrutinizing the equation of state parameter $\omega$ within our model. We delve into a comprehensive examination of the scalar field and meticulously assess the energy conditions surrounding the derived solution. To establish the robustness of our model, we deploy an array of diagnostic tools, including the Jerk, Snap, and Lerk parameters, along with the Om diagnostic, Classical stability of the model, and statefinder diagnostic tools, Observational Constraints on the Model Parameters. The outcomes, intertwined with a detailed analysis of both the results and the inherent intricacies of the model, are diligently clarified and presented.