Search Results (38)

We investigate the influence of the higher-order curvature corrections on a static configuration with constant density in Einstein–Gauss–Bonnet (EGB) gravity. This analysis is applied to both neutral and charged fluid distributions in arbitrary spacetime dimensions. The EGB field equations are generated, and the condition of pressure isotropy is shown to generalise the general relativity equation. The gravitational potentials are unique in all spacetime dimensions for neutral gravitating spheres. Charged gravitating spheres are not unique and depend on the form of the electric field. Our treatment is extended to the particular case of a charged fluid distribution with a constant energy density and constant electric field intensity. The charged EGB field equations are integrated to give exact models in terms of hypergeometric functions which can also be written as a series. Full article

We propose a mechanism for symmetry breaking or restoration that can occur in the middle of inflation, due to the coupling of the Gauss–Bonnet term to a charged scalar. The Gauss–Bonnet coupling results in an inflaton-dependent effective squared mass of the charged scalar, which can change its sign (around the symmetric point) during inflation. This can lead to spontaneous breaking of the symmetry, or to its restoration, if it is initially broken. We show the conditions under which the backreaction of the Gauss–Bonnet coupling on the inflationary background is negligible, such that the predictions of a given inflationary model are unaffected by the symmetry breaking/restoration process. Full article

In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations: Einstein–Gauss–Bonnet as well as cubic Lovelock gravities with vacuum, cosmological constant, perfect fluid, spatial curvature, and some of their combinations. Our analysis suggests that it is possible to set constraints on the parameters of the above-mentioned models from the simple requirement of the existence of a smooth transition from the initial singularity to a realistic low-energy regime. Initially, anisotropic space naturally evolves into a configuration with two isotropic subspaces, and if one of these subspaces is three-dimensional and is expanding while another is contracting, we call it realistic compactification. Of course, the process is not devoid of obstacles, and in our paper, we review the results of the compactification occurrence investigation for the above-mentioned models. In particular, for vacuum and $\mathrm{\Lambda }$-term EGB models, compactification is not suppressed (but is not the only possible outcome either) if the number of extra dimensions is $D⩾2$; for vacuum cubic Lovelock gravities it is always present (however, cubic Lovelock gravity is defined only for $D⩾3$ number of extra dimensions); for the EGB model with perfect fluid it is present for $D=2$ (we have not considered this model in higher dimensions yet), and in the presence of spatial curvature, the realistic stabilization of extra dimensions is always present (however, such a model is well-defined only in $D⩾4$ number of extra dimensions). Full article

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and ${\alpha }_0=t_0{H}_0$ and the fractional derivative order $\mu$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and ${\alpha }_0$, indicating that the solution is consistent with an accelerated expansion at late times with the values ${\alpha }_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $\mu =1.48\pm 0.17$ (consistent with ${\mathrm{\Omega }}_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_0=19.0\pm 0.7$ [Gyr] at 1$\sigma$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $\mathrm{\Lambda }$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology. Full article

Higher derivative terms in the gravitational action are natural from the perspective of quantum gravity, but are perceived as leading to a lack of well-posedness. The Gauss–Bonnet term has second-order equations of motion, but does not impact gravitational dynamics in 4D, so one might expect that it is not physically relevant. We discuss how signatures can show up in tunnelling processes and whether these will likely be physically accessible in Higgs vacuum decay. Full article

Kaluza–Klein theory attempts a unification of gravity and electromagnetism through the hypothesis that spacetime has five dimensions, of which only four are observed. The original model gives rise to the standard Einstein–Maxwell theory after dimensional reduction. However, in five dimensions, the Einstein–Hilbert action is not unique, and one can add to it a Gauss–Bonnet term, giving rise to nonlinear corrections in the dimensionally reduced action. We consider such a model, which reduces to Einstein gravity nonminimally coupled to nonlinear electrodynamics. The black hole solutions of the four-dimensional model modify the Reissner–Nordström solutions of general relativity. We show that in the modified solutions, the gravitational field presents the standard singularity at $r=0$, while the electric field can be regular everywhere if the magnetic charge vanishes. Full article

We review recent trends in inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems hot Big Bang theory inflation solves, and a somewhat introductory presentation of single-field inflationary theories with minimal and non-minimal couplings, we review how inflation can be realized in terms of several string-motivated models of inflation, which involve Gauss–Bonnet couplings of the scalar field, higher-order derivatives of the scalar field, and some subclasses of viable Horndeski theories. We also present and analyze inflation in the context of Chern–Simons theories of gravity, including various subcases and generalizations of string-corrected modified gravities, which also contain Chern–Simons correction terms, with the scalar field being identified with the invisible axion, which is the most viable to date dark matter candidate. We also provide a detailed account of vacuum $f\left(R\right)$ gravity inflation, and also inflation in $f(R,\varphi )$ and kinetic-corrected $f(R,\varphi )$ theories of gravity. At the end of the review, we discuss the technique for calculating the overall effect of modified gravity on the waveform of the standard general relativistic gravitational wave form. Full article

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians to select symmetries. Furthermore, we extend the prescription to the first prolongation of the Noether vector. It is possible to show that the latter application provides a general constraint on the infinitesimal generator $\xi$, related to the spacetime translations. This approach can be used for several applications. In the second part of the work, we consider a gravity theory, including the coupling between a scalar field $\varphi$ and the Gauss–Bonnet topological term $\mathcal{G}$. In particular, we study a gravitational action containing the function $F(\mathcal{G},\varphi )$ and select viable models by the existence of symmetries. Finally, we evaluate the selected models in a spatially flat cosmological background and use symmetries to find exact solutions. Full article

We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and $\Lambda$ term. We study so-called cosmological-type solutions defined on the product manifold $M=\mathbb{R}\times {\mathbb{R}}^3\times K$, where K is $6d$ a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on K, we obtain exact cosmological solutions with exponential dependence of scale factors (upon t-variable) governed by two non-coinciding Hubble-like parameters: $H>0$ and h obeying $H+2h\ne 0$. We also present static analogs of these cosmological solutions (for $H\ne 0$, $h\ne H$, and $H+2h\ne 0$). The islands of stability for both classes of solutions are outlined. Full article

We perform a detailed study of the phase-space of the field equations of an Einstein–Gauss–Bonnet scalar field cosmology for a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, we assume two cases for the coupling function of the scalar field with the Gauss–Bonnet term: the exponential function and the power–law function. We write the field equations in dimensionless variables and study the equilibrium points using normalized and compactified variables. We recover previous results, but also find new asymptotic solutions not previously studied. Finally, these couplings provide a rich cosmological phenomenology. Full article

This investigation aims to explore certain variables which are considered responsible for generating pressure anisotropy in dynamical spherically symmetric stellar systems against the background of the stringy-inspired Gauss–Bonnet modification of general relativity. We explore the hydrostatic equilibrium of self-gravitating systems by taking into account the modified form of Tolman–Oppenheimer–Volkoff for the quadratic-$f\left(\mathcal{G}\right)$ gravitational model. In this respect, we formulate a differential equation in terms of the Weyl curvature scalar, also described as an evolution equation, which is essential for understanding the evolution of the stellar structure. Finally, we conclude that the existence of some fluid variables such as shear, heat flux and the irregular behavior of energy density in the presence of an extra degree $f\left(\mathcal{G}\right)$-terms in the fluid flow that are the elements that cause anisotropy in the initially isotropic stellar structure. The comparison of the presented results with those of the classical model shows that they are physically relevant and compatible. Full article

Any new gravitational theories can be built with the help of a gauge theory with local Poincare symmetry. This local Poincare symmetry can set up a space-time with torsion. In the present study, the authors working on the parametrization approach towards Hubble’s parameter in the frame of modified teleparallel Gauss-Bonnet gravity which is established on the torsion invariant $\mathcal{T}$ and the teleparallel equivalent of the Gauss-Bonnet term ${\mathcal{T}}_{\mathcal{G}}$, say $\mathcal{F}(\mathcal{T},{\mathcal{T}}_{\mathcal{G}})$ gravity. In particular, gravity is responsible for an integrated explanation of the cosmological history from early-time inflation to late-time acceleration expansion, by lacking the addition of a cosmological constant. The domino effect acquired is reliable with recent cosmological outcomes. A transition scenario from a decelerating phase to an accelerating phase of cosmic evolution has been detected. Using the combined datasets (SNe-Ia+BAO+CMB+$H\left(z\right)$), we have constrained the transition redshift $z_t$ (at which the universe transit from a decelerating phase to an accelerating) and established the best fit value of $z_t$. Next, we paralleled the renovated results of $q\left(z\right)$ and $\omega \left(z\right)$ and found that the outcomes are well-suited with a $\mathrm{\Lambda }$CDM universe. Full article

Ostrogradsky’s, Dirac’s, and Horowitz’s techniques in terms of higher-order theories of gravity produce identical phase-space structures. The problem with these techniques is manifested in the case of Gauss–Bonnet–dilatonic coupled action in the presence of higher-order term, in which case, classical correspondence cannot be established. Here, we explore another technique developed by Buchbinder and their collaborators (BL) and show that it also suffers from the same disease. However, when expressing the action in terms of the three-space curvature, and removing ‘the total derivative terms’, if Horowitz’s formalism or even Dirac’s constraint analysis is pursued, all pathologies disappear. Here, we show that the same is true for BL formalism, which appears to be the simplest of all the techniques to handle. Full article

In this paper, we studied the bouncing behavior of the cosmological models formulated in the background of the Hubble function in the $F(R,\mathcal{G})$ theory of gravity, where R and $\mathcal{G}$, 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. Full article

We confront $f(T,T_G)$ gravity, with big bang nucleosynthesis (BBN) requirements. The former is obtained using both the torsion scalar, as well as the teleparallel equivalent of the Gauss–Bonnet term, in the Lagrangian, resulting to modified Friedmann equations in which the extra torsional terms constitute an effective dark energy sector. We calculate the deviations of the freeze-out temperature $T_f$, caused by the extra torsion terms in comparison to $\Lambda$CDM paradigm. Then, we impose five specific $f(T,T_G)$ models and extract the constraints on the model parameters in order for the ratio $|\Delta T_f/T_f|$ to satisfy the observational BBN bound. As we find, in most of the models the involved parameters are bounded in a narrow window around their general relativity values as expected, asin the power-law model, where the exponent n needs to be $n\lesssim 0.5$. Nevertheless, the logarithmic model can easily satisfy the BBN constraints for large regions of the model parameters. This feature should be taken into account in future model building. Full article