Modified Gauss Bonnet Gravity Research Articles

Viable wormhole solutions in modified Gauss–Bonnet gravity

In this paper, we use the embedding class-I technique to examine the effect of charge on traversable wormhole geometry in the context of f(G) theory, where G is the Gauss–Bonnet term. For this purpose, we consider static spherical spacetime with anisotropic matter configuration to investigate the wormhole geometry. The Karmarkar condition is used to develop a shape function for the static wormhole structure. Using this developed shape function, we construct a wormhole geometry that satisfies all the required constraints and connects asymptotically flat regions of the spacetime. To analyze the existence of traversable wormhole geometry, we evaluate the behavior of energy conditions for various models of this theory. This study reveals that viable traversable wormhole solutions exist in this modified theory.

On covariant perturbations with scalar field in modified Gauss–Bonnet gravity

We investigate cosmological perturbations of f(G) gravity in the presence of a scalar field. Using the 1+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+3$$\\end{document} covariant formalism, we present the energy overdensity perturbation equations responsible for large scale structure formation. After applying harmonic decomposition method together with the redshift transformation technique, we obtain the fully perturbed equations in redshift space. The equations are solved to study the growth of matter overdensities contrast with redshift. For both short- and long-wavelength modes, we obtain numerical results for particular functional form f(G) models and scalar field. We find that, for this choice the energy overdensity perturbations decay with increase in redshift. However, for both short- and long-wavelength modes, the perturbations which include amplitude effects due to the f(G) models with a scalar field do differ remarkably from those in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM. The results reduce to GR results in the limit of f(G)→G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(G)\\rightarrow G$$\\end{document} and in the absence of scalar field.

Expansion-free cluster of stars in modified Gauss–Bonnet gravity

The aim of this paper is to investigate the expansion-free model of star cluster in modified Gauss-Bonnet gravity. To achieve this, we analyze a model of a star cluster which is dissipative, anisotropic and viscous. The modified field equations as well as junction conditions are applied in order to study the general distribution of anisotropic fluid exhibiting dissipation with varying dominant stress components. We also integrate the condition of vanishing expansion into our analysis. To gain insight into the significance of motion that does not involve expansion, we discuss two distinct ways of defining the radial velocity of a fluid element. The study demonstrates the emergence of a cavity in the evolution of star clusters when expansion is not present. Moreover, we determine the shear-free and expansion-free collapse of the star cluster by analyzing the relative velocity among adjacent fluid layers. The Skripkin model can be used to represent an expansion-free, non-dissipative, and isotropic star cluster. This provides a valuable tool for investigating the properties and behavior of these celestial bodies. The Skripkin model demonstrates homologous evolution for the shear-free case. We conclude that the exotic matter present in f(G,T) gravity are essential for understanding the dynamics of star cluster’s evolution. This indicates that the dark source terms should be taken into account when investigating the properties and behavior of the celestial bodies.

Bouncing universe in modified Gauss–Bonnet gravity

In this paper, a bouncing cosmological scenario is studied in the background of a flat FLRW model with a specific parametrized hyperbolic form of scale factor a in terms of t, where λ is taken as the model parameter. This model is discussed in f(R,G) formalism having structured as f(R,G)=R+F(G), where R is Ricci scalar and G is the Gauss–Bonnet invariant. The proposed functional form of the Hubble parameter is considered in such a way that it satisfies the bouncing criteria of the model, which is free from the initial singularity. The physical consequences of the model are discussed. In this model, one can see that the EoS parameter crosses the quintom line ω=−1 in the neighbourhood of bouncing point t=0, which is also a criteria for a successful bouncing cosmological model. Finally, we examine the stability of the model and find that all the essential features of bouncing model are satisfied successfully.

On 1 + 3 covariant perturbations of the quasi-Newtonian spacetime in modified Gauss–Bonnet gravity

The consideration of a [Formula: see text] covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of [Formula: see text] gravity theory in this study. This approach reveals the existence of integrability conditions which do not appear in noncovariant treatments. We constructed the integrability conditions in modified Gauss–Bonnet [Formula: see text] gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in [Formula: see text] gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian spacetime were constructed in the context of modified [Formula: see text] gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behavior of the overdensity and velocity perturbations using [Formula: see text] model was made. On the other hand, we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short- and long-wavelength modes in a dust-Gauss–Bonnet fluids was done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to [Formula: see text]CDM, it means [Formula: see text] the considered [Formula: see text] model results coincide with [Formula: see text]CDM.

Inflationary dynamics and swampland criteria for modified Gauss-Bonnet gravity compatible with GW170817

In this article we present an alternative formalism for the inflationary phenomenology of rescaled Einstein-Gauss-Bonnet models which are in agreement with the GW170817 event. By constraining the propagation velocity of primordial tensor perturbations, an approximate form for the time derivative of the scalar field coupled to the Gauss-Bonnet density is extracted. In turn, the overall degrees of freedom decrease and similar to the case of the canonical scalar field, only one scalar function needs to be designated, while the other is extracted from the continuity equation of the scalar field. We showcase explicitly that the slow-roll indices can be written in a closed form as functions of three dimensionless parameters, namely $x=\frac{1}{2\alpha}\bigg(\frac{\kappa\xi'}{\xi''}\bigg)^2$, $\beta=8H^2\xi''$ and $\gamma=\frac{\xi'\xi'''}{\xi''^2}$ and in turn, we prove that the Einstein-Gauss-Bonnet model can in fact produce a blue-tilted tensor spectral index if the condition $\beta\geq1$ is satisfied, which is possible only for Einstein-Gauss-Bonnet models with $\xi''(\phi_k)>0$. Afterwards, a brief comment on the running of the spectral indices is made where it is shown that $a_{\mathcal{S}}(k_*)$ and $a_{\mathcal{T}}(k_*)$ in the constrained case are approximately of the order $\mathcal{O}(10^{-3})$, if not smaller. Last but not least, we examine the conditions under which the Swampland criteria are satisfied. We connect the tracking condition related to scalar field theories with the present models, and we highlight the important feature of the models we propose that the tracking condition can be satisfied only if the Swampland criteria are simultaneously satisfied, however the cases with $\xi\sim1/V$ and $\xi\sim V$ are excluded, as they cannot describe the inflationary era properly.

Analysis of hyperbolically symmetric fluid configurations in modified Gauss–Bonnet gravity

This paper studies in detail the general physical properties inherent to the static fluid configurations possessing hyperbolic symmetry through the mechanism of modified Gauss–Bonnet gravity (GBG). The energy density of the anisotropic fluid configuration seems to be essentially negative, which indicates that any possible application of these fluid distributions needs severe physical constraints wherein quantum processes become significant. Several exact hyperbolically symmetric solutions with their corresponding generating functions are presented by imposing certain conditions (i.e., conformal flatness, vanishing complexity factor and stiff equation of state) on the fluid variables in the presence of higher-curvature GBG-corrections. Few of the provided stellar solutions exhibit the evolution of hyperbolically symmetric matter configurations whose center of symmetry is surrounded by a vacuum cavity.

Some interesting aspects of modified Gauss–Bonnet gravity

The main idea behind this paper is to study [Formula: see text] theory of gravity, where [Formula: see text] is Gauss–Bonnet (GB) term and [Formula: see text] is the scalar field. Scalar field has been introduced to explore gravitational interaction between geometry and scalar field. Field equations in Friedmann–Robertson–Walker (FRW) cosmology are constructed and found to be coherent with the existing literature. Exponential solutions are reconstructed. The coupling of the scalar field to the GB term leads to viable results. Further, we probe the oscillating universe in the said gravity model using linear trace term. Energy conditions are explored and graphically analyzed in detail to substantiate our work. Behavior of the Hubble and deceleration parameter is also examined. It is evident from the results that our model provides us with acceptable bouncing solutions for chosen parameters.

Anisotropic compact stars in presence of electromagnetic field, quintessence field and cosmological constant in f(G) gravity

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 [Formula: see text] and [Formula: see text] as well as a particular form of [Formula: see text], 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 [Formula: see text] gravity theory.

Collapsing axial system and f(𝒢,T) gravity

The motive of this paper is to investigate the evolution of dissipative axially symmetry collapsing fluid in the presence of dark sources. For this purpose, we use the modified Gauss–Bonnet gravity as an exotic energy candidate. We formulate the dynamical variables and investigate the impacts of dark sources upon the heat dissipation and pressure anisotropy. We find scalar functions through orthogonal decomposition of Riemann tensor. The physical behavior of these scalars has been examined for matter as well as dark source configurations. Moreover, we develop a set of EEs related to the evolution of dynamical variables, heat transport equation, Weyl tensor and super-Poynting vector. These equations discuss collapse features like thermodynamics, density inhomogeneity and gravitational radiations in presences of exotic terms. It has been shown that the dark source terms have an effect on the thermodynamics of the system, evolution of kinematical variables and density inhomogeneity. The exotic terms can generate repulsive radiations which can induce cosmic expansion. Finally, the physical significance of modified Gauss–Bonnet gravity is explored in association to the stellar 4U1820-30.

Reconstruction of modified Gauss–Bonnet gravity for emergent universe

We present a flat emergent universe model in modified Gauss–Bonnet gravity in four dimensions. The emergent universe model is free from a big-bang singularity and also describes the observed universe fairly well. It is assumed that the present universe emerged from a static Einstein universe phase that exists in the infinite past. To obtain the flat emergent universe model, we reconstruct mimetic modified [Formula: see text]-gravity ([Formula: see text] representing Gauss–Bonnet terms). The functional form of [Formula: see text]-gravity is determined with or without matter, and can accommodate the early inflation and late accelerating phases satisfactorily. In contrast, in Einstein’s general theory of relativity, a flat emergent universe was obtained within the modified matter sector.

Reconstruction of cosmological models are inspired by generalization of the Chaplygin gas

This paper considers models arising from the composition of the modified Gauss–Bonnet gravity (the Gauss–Bonnet invariant) and the general relativity (the Ricci scalar) against the background of a flat, homogeneous, and isotropic space-time described by the Friedmann–Robertson–Walker metric. Advantages arising fromapplying a theory containing higher-order invariants (Gauss–Bonnet invariant) consist in the presence of additional degrees of freedom, which makes it possible to study the influence of small-order effects on the dynamics of the system under study, which are in search and confirmed by cosmological observational data. We reconstructed two models with a power-law and exponential dependence on the Gauss–Bonnet invariant, where the model ansatz is a combination of the inverse Weierstrass elliptic function and the power-law function describing the Hubble parameter. This facilitates obtaining a quasi-Dieter law of the change of the scale factor in the initial and late epochs of the Universe. The application of the special function is inspired by generalization equation of state of the Chaplygin gas type, the Weierstrass gas. The application of the equation of state with such dependence makes allows obtaining a quasi-periodic universe. The equations of state are based on the Chaplygin gas are model equations of state and describe well the evolution of both the early and the modern universe. The obtained two particular models are investigated for the fulfillment of the energy conditions, which makes it possible to carry out analysis at a late stage of evolution of the universe and using perturbation theory covering the period of the early universe. For the power-law and exponential models, the perturbations of the Hubble parameter decrease in a finite time are shown, providing a way out of the inflationary stage of evolution of the universe.

On the study of complexity for charged self-gravitating systems

In modified Gauss–Bonnet gravity, this paper investigates the complexity factor for static anisotropic self-gravitating fluid which is influenced by an electric charge. For the self-gravitating system, we evaluate the Maxwell field equations, the Tolman–Oppenheimer–Volkoff equation and the mass function. We formulate the structure scalars by an orthogonal splitting of the Riemann tensor for the self-gravitating system and identify one of these scalars as the complexity factor. Then with the help of two different models, we observe the corresponding complexity factor involved in the subsequent changes of static spheres. The structure scalars and complexity factor are found to be dependent on the components of the effective part as well as electromagnetic part.

Role of f(G) gravity in the study of non-static complex systems

The concept of complexity for dynamical spherically symmetric dissipative self-gravitating configuration (Herrera et al. Phys. Rev. D, 98, 104059 (2018). doi:10.1103/PhysRevD.98.104059) is generalized in the scenario of modified Gauss–Bonnet gravity. For this purpose, a spherically symmetric fluid with locally anisotropic, dissipative, and non-dissipative configurations is considered. We choose the same complexity factor for the structure as we did for the static case, while we consider the homologous condition for the simplest pattern of evolution. In this approach, we formulate structure scalars that demonstrate the essential properties of the system. A fluid distribution that fulfills the vanishing complexity constraint and proceeds homologously corresponds to isotropic, geodesic, homogeneous, and shear-free fluid. In the dissipative case, the fluid is still geodesic but it is shearing, and there is a wide range of solutions. In the last, the stability of vanishing complexity is examined.

Charged gravastars in modified Gauss–Bonnet gravity

This work probes the influence of charge field on the unique stellar structure, regarded as gravastar, under the corrections of [Formula: see text] theory, i.e. [Formula: see text] theory, where [Formula: see text] is named as Gauss–Bonnet invariant. The gravastar has also been recognized as an alternate candidate of black hole structure and is illustrated by three distinct regions termed as (1) the exterior (2) the intermediate thin shell (3) the interior domain. We discussed the mathematical solutions for each of three regions separately with the assistance of different equation-of-states (EoS). The exterior charged vacuum domain is expressed by the Reissner–Nordström solution. The central region is illustrated by the EoS, i.e. a positive pressure of ultra-relativistic matter is equal to the energy density. Whereas, the interior domain reflects that the negative pressure is equal to energy density and manifests a non-attractive force over the central spherical shell. We deduce that in the context of [Formula: see text] theory, the nonsingular charged model with distinct physical features, such as energy, length, entropy, is physically viable and consistent.

Influence of f(G) gravity on the complexity of relativistic self-gravitating fluids

In this paper, we extend the notion of complexity for the case of nonstatic self-gravitating spherically symmetric structures within the background of modified Gauss–Bonnet gravity (i.e. [Formula: see text] gravity), where [Formula: see text] denotes the Gauss–Bonnet scalar term. In this regard, we have formulated the equations of gravity as well as the relations for the mass function for anisotropic matter configuration. The Riemann curvature tensor is broken down orthogonally through Bel’s procedure to compose some modified scalar functions and formulate the complexity factor with the help of one of the scalar functions. The CF (i.e. complexity factor) comprehends specific physical variables of the fluid configuration including energy density inhomogeneity and anisotropic pressure along with [Formula: see text] degrees of freedom. Moreover, the impact of the dark source terms of [Formula: see text] gravity on the system is analyzed which revealed that the complexity of the fluid configuration is increased due to the modified terms.

Gravastars in modified Gauss–Bonnet gravity

This paper aims to discuss the viable and analytic solution of the spherically symmetric gravastar model under the influence of modification of Gauss–Bonnet gravity, i.e., f(G) gravity, where G is the Gauss–Bonnet curvature term. For this purpose, we evaluate the field equations in corresponding theory and conservation equation with the help of an effective energy–momentum tensor. A mathematical formalism of the gravastar’s three regions, i.e., interior de-Sitter region, thin shell, and the exterior Schwarzschild vacuum region have been discussed. We, then analyze different realistic features, in particular energy, entropy, and length of the shell. The viability of these physical features is then examined through the graphical representations separately. Within the framework of an alternative theory, we have obtained the exact and singularity free model of gravastar.

Anisotropic compact stellar objects in modified Gauss–Bonnet gravity

This paper is devoted to studying anisotropic compact stellar structures by adopting embedding class-1 technique in the background of modified Gauss–Bonnet gravity. The unknown constants are evaluated by the matching of interior spacetime with the Schwarzschild exterior geometry corresponding to f ( G ) = χ G n model, where χ and n are positive constants. The observed masses of compact star candidates (SAX J1808.4-3658, Vela X-1, PSR J0348+0432, 4U 1608-52) are used with the condition of vanishing radial pressure at the stellar surface to predict their radii. We have examined viability and stability of the resulting solution through graphical behavior of matter variables, energy constraints, adiabatic index and causality condition. It is found that embedding class-1 solution for anisotropic compact stars is viable and stable in this theory.

Gravitational waves in modified Gauss–Bonnet gravity

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

Dynamical analysis of self-gravitating stars in modified Gauss-Bonnet gravity

In this paper, we have continued the work of Herrera \emph{et al.} \cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a spherically symmetric fluid exhibiting locally anisotropic pressure along with the energy density, is taken under consideration. The perturbation scheme is imposed on modified field equations and the dynamical equations. The collapse equation is devised from these perturbed equations which stimulates to disclose the instability zone under both Newtonian and post-Newtonian constraints. It is wrapped up by concluding that dynamical instability is interpreted by the adiabatic index $\Gamma$ which relies on the anisotropic pressure, energy density and the dark source terms due to $f(G)$ gravity.