Narrow Results

The paper investigates the static, non-commutative solutions of wormholes (WHs) that exhibit spherical symmetry. The study is conducted in the setting of modified Gauss–Bonnet gravity. Our investigation employs two methods: to construct a shape function using a viable $f(G)$ gravity model and to infer the $f(G)$ model through a specific shape function. We then carefully analyze the energy constraints for both methods. Our findings reveal the following results. For each value of $r$, the first technique provides a physically viable solution of WH related to the ordinary matter. The second approach has a feasible solution only when the values of $r$ are high. This study analyzes the complex procedure of the development of cosmic structures to demonstrate a connection between hypothetical and observed data.

In this work, the cosmic solutions, particularly the well-known $\mathrm{\Lambda }$CDM model, are investigated in the framework of the Gauss–Bonnet (GB) gravity, where the gravitational action incorporates the GB invariant function. We utilize a specialized formulation of the deceleration parameter in terms of the Hubble parameter $H$, given by $q=-1-\frac{Ḣ}{H^2}$, to solve the field equations. To identify the appropriate model parameters, we align them to the most recent observational datasets, which include 31 data points from the Cosmic Chronometers, Pantheon+, and BAO datasets. The physical characteristics of the cosmographic parameters, such as pressure and energy density, that correlate to the limited values of the model parameters, are examined. The evolution of the deceleration parameter suggests a transition from a decelerated to an accelerated phase of the universe. Additionally, we examine the stability of the assumed model and provide an explanation for late-time acceleration using the energy conditions. The behavior of the equation of state parameter has been analyzed through dynamical variables by constraining various parameters in light of the recent observational data. This study has resulted in a quintessence-like evolution.

This paper is devoted to analyze the dynamics of plane symmetric gravitational collapse as well as energy density inhomogeneity in f(G) gravity. The field equations are constructed for dissipative isotropic source and Darmois junction conditions are used to discuss the process of collapse. We use Misner–Sharp mechanism to develop dynamical equation and couple it with transport equation to explore the impact of gravitational force on the collapsing rate. For constant f(G) model, we conclude that the rate of collapse slows down. Finally, we discuss the relationship between the Weyl tensor and physical quantities.

In this paper, we study noncommutative static spherically symmetric wormhole solutions in the context of modified Gauss–Bonnet gravity. We explore these solutions either by assuming a viable $f(G)$ model to construct shape function or by specifying the shape function to deduce $f(G)$ model. The energy conditions are discussed for both types of wormholes. In the first case, we find a physically acceptable wormhole solution threaded by normal matter for all values of radial coordinate $r$ while the second case gives physical solution only for large values of $r$.

In this paper, we study the role of Gauss–Bonnet term for the early and late time accelerating phases of the universe with the help of two viable $f(G)$ models in the background of flat FRW universe model. These models show inflationary behavior as well as the present accelerating expansion of the universe. The contribution of Gauss–Bonnet term in pressure and energy density is used to calculate equation of state (EoS) parameter for the modified fluid which behaves like cosmological constant with $Ḣ=0$. We discuss early inflation and late accelerating expansion of the universe through scale factor evaluated from equation of continuity numerically.

We investigate interior solutions for static spherically symmetric metric in the background of $f(G)$ gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law $f(G)$ model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter $\omega =-1.5$. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman–Oppenheimer–Volkoff equation.

This paper explores evolution of dissipative axially symmetric collapsing fluid under the dark effects of $f(G)$ gravity. We formulate the dynamical variables and study the effects of dark sources in pressure anisotropy as well as heat dissipation. The structure scalars (scalar functions) as well as their role in the dynamics of source are investigated. Finally, we develop heat transport equation to examine the thermodynamic aspect and a set of equations governing the evolution of dynamical variables. It is concluded that dark sources affect thermodynamics of the system, evolution of kinematical quantities as well as density inhomogeneity.

We explore cosmological perturbations in a modified Gauss–Bonnet $f(G)$ gravity, using a $1+3$ covariant formalism. In such a formalism, we define gradient variables to get perturbed linear evolution equations. We transform these linear evolution equations into ordinary differential equations using a spherical harmonic decomposition method. The obtained ordinary differential equations are time-dependent and then transformed into redshift-dependent. After these transformations, we analyze energy-density perturbations for two fluid systems, namely, for a Gauss–Bonnet field-dust system and for a Gauss–Bonnet field-radiation system for three different pedagogical $f(G)$ models: trigonometric, exponential and logarithmic. For the Gauss–Bonnet field-dust system, energy-density perturbations decay with increase in redshift for all the three models. For the Gauss–Bonnet field-radiation system, the energy-density perturbations decay with increase in redshift for all of the three $f(G)$ models for long wavelength modes whereas for short wavelength modes, the energy-density perturbations decay with increasing redshift for the logarithmic and exponential $f(G)$ models and oscillate with decreasing amplitude for the trigonometric $f(G)$ model.

In this work, we have discussed the anisotropic compact stars in the framework of modified Gauss–Bonnet gravity, named by f(G) theory of gravity. We have found the equations of motion of stars with respect to spherically symmetric metric, describing interior geometry of the compact stellar object, anisotropic mode of the matter distribution in the presence of electromagnetic field and quintessence field. We have taken the metric coefficients in the form $\mu ={\mathrm{\text{Br}}}^{\alpha }+{\mathrm{\text{Cr}}}^{\beta }$ and $\lambda ={\mathrm{\text{Ar}}}^{\gamma }$ as well as a particular form of $f(G)=G^2$, where the powers and coefficients of r are constants. The unknown constants are evaluated by matching between interior and exterior Reissner–Nordström–de Sitter metric. We have analyzed some physical aspects like energy density, radial and tangential pressures, anisotropic parameter of matter distribution, energy conditions, mass-radius relation, compactness factor, surface redshift, and stability of our resulting solutions through graphical behavior by comparing to the observational data of different types of compact stars like 4U1820-30, Vela X-1 and SAXJ1808.4-3658. We conclude that all physical attributes maintain their experimental ranges which deliver our anisotropic compact star models are viable and also stable upto certain region in $f(G)$ gravity theory.

The purpose of this study is to investigate the parametrization form of the deceleration parameter in relation to the redshift z. The parameter is represented by the equation $q(z)=q_0+q_1\frac{z(1+z)}{{(1+z)}^2}$, which offers the desirable quality of allowing the sign to be flipped from a decelerating phase to an accelerating phase. We have investigated the Hubble parameter by evaluating the specified parametric form of q and derived constraints on the related free parameters $H_0$, $q_0$ and $q_1$ with confidence limits of 1$\sigma$ and 2$\sigma$ by using the ${\chi }^2$-minimization approach. Furthermore, we have constrained the current value of the deceleration parameter $q_0=-0.457_{-0.0023}^{+0.0022}$ and obtained that the current universe is accelerating. We have examined the characteristics of our model by assuming the two distinct forms of $f(G)=\alpha G^{m+1}$ and $f=\frac{{\alpha }_1{G}^n+{\beta }_1}{{\alpha }_2{G}^n+{\beta }_2}$. In addition, we have examined the evolutionary paths of energy density, pressure and EoS parameters in order to deduce the universe’s accelerating behavior. In order to verify the feasibility of our cosmological model, we also investigate the behavior of various energy conditions.

LRS Bianchi type I space time is considered to explore bulk viscous string model in modified $f(G)$ gravity. Field equations are solved with some physically viable condition. It is observed that the string phase of the universe disappears. The Gauss–Bonnet invariant significantly effects on galactic fluid. The universe is expanding and isotropic at large time. Some physical parameters are also discussed in detail.

Work reported in this study demonstrates the reconstruction schemes for the $f(G)$ gravity in the framework of bulk viscosity and holographic background evolution by considering the universe filled by the viscous fluid that is just special class of more general fluids as described in Nojiri and Odintsov [Inhomogeneous equation of state of the universe: Phantom era, future singularity, and crossing the phantom barrier, Phys. Rev. D72 (2005) 023003]. The bulk viscous pressure has been considered as $\mathrm{\Pi }=-3H\xi$, with $\xi ={\xi }_0+{\xi }_{1}H+{\xi }_2(Ḣ+H^2)$. Considering the scale factor in power law form and taking holographic dark energy (HDE) with density ${\rho }_{\mathrm{\Lambda }}=3c^3{M}_p^2{L}^{-2}$ and generalized extended holographic dark energy (EGHRDE) with density ${\rho }_{\mathrm{\Lambda }}=3c^2(\alpha Ḣ+\beta H^2)$, a specific case of Nojiri–Odintsov holographic DE ([Unifying phantom inflation with late-time acceleration: Scalar phantom–non-phantom transition model and generalized holographic dark energy, Gen. Relativ. Gravit.38 (2006) 1285]) we have derived solutions for $f(G)$ and the subsequent effective equation of state parameters have been found to behave like quintom irrespective of the choice of $c^2$. Finally, considering $f(G)$ as quintessence scalar field we have explored the possibility of quasi-exponential expansion and warm inflation.

In this study, we investigated scalar field in $f(G)$-gravity by using LRS Bianchi type-I universe. Massless and massive scalar field models are separately constructed in $f(G)$-gravity. Massless scalar field models are examined in the cases of constant and exponential potential fields. For all models, solutions of field equations are obtained under the consideration of $A=B^n$. $f(G)$ functions for each model are separately attained in theory. It is shown that constructed models in the presence of massless scalar field permit quintessence scalar field. Also, it is observed that each model indicates expanding universe with deceleration. Also, kinematical quantities are analyzed in the light of obtained solutions. All models are concluded with a geometric and physical perspective.

The treatment of (1+3)-covariant perturbation in a multifluid cosmology with the consideration of $f(G)$ gravity, $G$ being the Gauss–Bonnet term, is done in this paper. We define a set of covariant and gauge-invariant variables to describe density, velocity and entropy perturbations for both the total matter and component fluids. We then use different techniques such as scalar decomposition, harmonic decomposition, quasi-static approximation together with the redshift transformation to get simplified perturbation equations for analysis. We then discuss a number of interesting applications like the case where the universe is filled with a mixture of radiation and Gauss–Bonnet fluids as well as dust with Gauss–Bonnet fluids for both short- and long-wavelength limits. Considering polynomial $f(G)$ model, we get numerical solutions of energy density perturbations and show that they decay with increase in redshift. This feature shows that under $f(G)$ gravity, specifically under the considered $f(G)$ model, one expects that the formation of the structure in the late Universe is enhanced.

Motivated by the work of Nojiri and Odintsov [Phys. Lett. B 631 (2005) 1–6, arXiv:hep-th/0508049 [hep-th]], this work reports on the cosmology and baryogenesis of modified $f(G)$ gravity by assuming the background evolution as generalized holographic dark energy (GHDE). For vacuum energy density, modified $f(G)$ gravity is reconstructed and found to be of positive behavior. The equation of state (EoS) parameter under the purview of vacuum energy density comes out to be quintom. The reconstructed modified $f(G)$ gravity in GHDE shows positive behavior, and its corresponding EoS parameter is phantom. There is a chance of a big rip singularity and the slow roll parameters are analyzed. Quasi exponential expansion and warm inflation are observed. Finally, baryogenesis is studied. The study suggests that either there may be symmetry between the number density of baryons and antibaryons in the far future, or the generalized second law of thermodynamics is satisfied by the model.