Narrow Results

An exact solution of brane universe is studied and the result indicates that Friedmann equations on the brane are modified with an extra term. This term can play the role of dark energy and make the universe accelerate. In order to derive the ΛCDM Universe from this global brane model, the new solutions are obtained to describe the 5D manifold.

This paper is devoted to investigate the recently proposed modified Gauss–Bonnet $f({𝒢},T)$ gravity, with ${𝒢}$, the Gauss–Bonnet term, coupled with $T$, the trace of energy–momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important $f({𝒢},T)$ gravity models with anisotropic background. In particular, the Noether symmetry equations for modified $f({𝒢},T)$ gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss–Bonnet gravity may be used to reconstruct $\mathrm{\Lambda }$CDM cosmology without involving any cosmological constant.

Locally Rotationally Symmetric (LRS) Bianchi type-I metric is examined in the presence of perfect fluid. Exact solutions of Einstein’s field equations (EFE) have been studied by taking into account a hyperbolic scale factor. We observed that the model has initial singularity. It is found that the Universe approaches isotropy at late times. Through state finder pair $\{r,s\}$, it is observed that at late cosmic time, the model behaves analogous to $\mathrm{\Lambda }$CDM model. Energy conditions of the model are studied and it is found that null energy condition (NEC), weak energy condition (WEC) and dominant energy conditions (DEC) are satisfied for our model while SEC is violated. We investigate some physically and geometrically realistic models in order to develop a viable cosmological model.

We applied the theory of regularly varying (RV) functions to the analysis of the cosmological parameters for the $\mathrm{\Lambda }$CDM model with the matter-dominated evolution. Carroll et al. proved in 1992 that for this type of universe with the curvature $k=0,-1$, the expression $H(t)t$ ($H(t)$ is the Hubble parameter) depends solely on the density parameter $\mathrm{\Omega }(t)$. Using this result, we infer for such universe the complete asymptotics of all main cosmological parameters. More specifically, the following is derived. If the limit $\omega ={lim}_{t\to \infty }\mathrm{\Omega }(t)$ does exist and $\omega \ne 0$, then the cosmological constant $\mathrm{\Lambda }$ is equal to $0$. If $\omega =0$, then for the expansion scale factor $a(t)$ of a flat universe, we have $a(t)\sim e^{\sqrt{\mathrm{\Lambda }/3}t}$. On the other hand, if the limit ${lim}_{t\to \infty }\mathrm{\Omega }(t)$ does not exist, then $a(t)$ bounces between two power functions and therefore has infinitely many flexion points. Hence, the deceleration parameter in this case changes the sign infinitely many times.

By using a cosmographic analysis of the redshift data of type Ia supernovae, we are able to get the expansion of the scale factor, obtaining the current values of the Hubble, deceleration, jerk and snap parameters. Our data is then used to compare the fitness of various proposed alternative cosmological models. Since our method assumes only the validity of general relativity at the cosmic scale, along with the isotropy and homogeneity of the universe, they are very useful for comparison between different cosmological models, including the fitness of ΛCDM model. Our method is based on the order expansion of the scale factor present in the FRW metric and using a Monte Carlo integration to find the best fit order parameters of the scale factor to reproduce the observed data, we make use of parallel paradigm to improve the computational time behind the model. We find the known result of an accelerated expansion of the universe. With access to better measurements of type Ia supernovae redshifts and more data, the cosmographic results will be significantly improved.