We present a holographic model of the Dvali-Gabadadze-Porrati scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalizes the normal Dvali-Gabadadze-Porrati branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and a holographic dark energy with the Hubble scale as the infrared cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an energy density component cannot do the same job on the normal Dvali-Gabadadze-Porrati branch (without Gauss-Bonnet modifications) nor in a standard four-dimensional relativistic model. The acceleration on the brane is also presented as being induced through an effective dark energy which corresponds to a balance between the holographic one and geometrical effects encoded through the Hubble parameter.

We present an holographic brane-world model of the Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet term (GB) in the bulk. We show that an holographic dark energy component with the Ricci scale as the infrared cutoff can describe the late-time acceleration of the Universe. In addition, we show that the dimensionless holographic parameter is very important in characterizing the DGP branches, and in determining the behavior of the Ricci dark energy as well as the asymptotic behavior of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantomlike behavior with no big rip if the holographic parameter is strictly larger than 1/2. For smaller values, the brane hits a big rip or a little rip. On the other hand, we have shown that the introduction of the GB term avoids the big rip and little rip singularities on both branches but cannot avoid the appearance of a big freeze singularity for some values of the holographic parameter on the normal branch, however, these values are very unlikely because they lead to a very negative equation of state at the present and therefore we can speak in practice of singularity avoidance. At this regard, the equation of state parameter of the Ricci dark energy plays a crucial role, even more important than the GB parameter, in rejecting the parameter space where future singularities appear.

Extended teleparallel gravity, characterized by functionF(Q), whereQis the non-metricity scalar, is one of the most promising approaches to general relativity. In this paper, we reexamine a specific dynamical dark energy model, which is indistinguishable from the $$\Lambda $$Λ CDM model at the present time and exhibits a special event in the future, withinF(Q) gravity. To constrain the free parameters of the model, we perform Markov chain Monte Carlo (MCMC) analysis, using the last data from $$\hbox {Pantheon}^{+}$$Pantheon+ and the latest measurements of the H(z) parameter, combined. On the basis of this analysis, we find that our dynamical dark energy model, in the context of F(Q) gravity, lies in the quintessence regime rather than in the phantom regime, as in the case of general relativity. Furthermore, this behavior affects the future expansion of the Universe, as it becomes decelerating at a $$1\sigma $$1σ confidence level for $$z<-0.5$$z<-0.5 , showing a bounce at $$z_{\text {B}}\approx -0.835$$zB≈-0.835 . We support our conclusion with a cosmographic analysis.

In this paper, we explore one of Einstein’s alternative formulations which involves the non-metricity scalar, Q, within the framework of f(Q) theory. Our study focuses on solving the modified Friedmann equations for the case of dust matter, $$\rho =\rho _{m}$$ρ = ρ m , and a form of $$f(Q) = \alpha + \beta Q^n$$f ( Q ) = α + β Q n . We investigate the behavior of our model in both linear $$(n=1)$$( n = 1 ) and nonlinear $$(n\ne 1)$$( n ≠ 1 ) scenarios at the background and perturbation levels. By employing the Markov chain Monte Carlo (MCMC) method, we constrain our model using observational datasets including redshift space distortion, cosmic chronometers, and Pantheon $$^+$$+ . Without using any parameterization of the growth rate index which quantifies the deviation from the $$\Lambda $$Λ CDM model, both models exhibit good accuracy in describing the redshift space distortion. We further analyze the dynamics of the Universe using cosmography parameters, where our model exhibits a phase transition between deceleration and acceleration phases at $$z=0.789$$z = 0.789 . Our findings reveal that our model exhibits a phantom-like behavior based on statefinder diagnostic analysis. Interestingly, the model demonstrates a rich variety of behaviors, resembling either a quintessence-like scenario for $$(n<1)$$( n < 1 ) or phantom-like scenario for $$(n\ge 1)$$( n ≥ 1 ) . Using the MCMC best fit and parameterizing the growth index, the evolution of the growth index also depends on the parameter n, either remaining constant (in the linear case) or showing a decreasing trend (in the nonlinear case), indicating a weaker growth rate of density perturbations during earlier cosmic times. Finally, we compare our findings of the growth index with the values obtained in the literature.

The background cosmological dynamics of the late Universe is analysed on the framework of a dark energy model described by an holographic Ricci dark energy

To study the effect of the anti–de Sitter/conformal field theory correspondence (AdS/CFT) on the primordial inflationary era, we consider a universe filled with a tachyon field in a slow-roll regime. In this context, the background and perturbative parameters characterizing the inflationary era are related to the standard one by correction terms. We show a clear agreement between the theoretical prediction and the observational data for the above-mentioned model. The main results of our work are illustrated for an exponential potential. We show that, for a suitable conformal anomaly coefficient, AdS/CFT correspondence might leave its imprints on the spectrum of the gravitational waves amplitude with a tensor to scalar ratio, $r$, of the perturbations compatible with Planck data.