Narrow Results

Cosmological reconstruction is a powerful technique in modified gravity invented to find the analogy of different cosmological epochs in modified gravity. In this paper, I present the modified holographic reconstruction scheme for $f(T,{𝒯})$ theory of gravity where $T$ and ${𝒯}$ are the torsion scalar and trace of energy–momentum tensor in the context of flat FRW universe. For this reconstruction, I consider Hubble horizon as an infrared cutoff and focus on a particular model $f(T,{𝒯})=T+\gamma g({𝒯})$ (a correction to the teleparallel action depending on the matter content). Within this framework, I consider both the power law scale factor as well as the well-established cosmological bouncing scenario. Further, I explore various gravitational Lagrangians that can be reconstructed to yield analytical solution for symmetric, superbounce, oscillatory, singular bounce and matter bounce settings. The viability of these reconstructed models is then assessed through the EoS parameter ${\omega }_{\mathrm{\text{DE}}}$ and the ${\omega }_{\mathrm{\text{DE}}}-{\omega }_{\mathrm{\text{DE}}}^{\prime }$ plane $({\omega }_{\mathrm{\text{DE}}}^{\prime }=\frac{d{\omega }_{\mathrm{\text{DE}}}}{dlna})$. Notably, all the results align well with recent observational data.

The reconstruction scenario of well-established dark energy models such as pilgrim dark energy model and generalized ghost dark energy with Hubble horizon and $f(T,{𝒯})$ models is being considered. We have established $f(T,{𝒯})$ models and analyzed their viability through equation of state parameter and $\omega -{\omega }^{\prime }$ (where prime denotes derivative with respect to $lna$) plane. The equation of state parameter evolutes the universe in three different phases such as quintessence, vacuum and phantom. However, the $\omega -{\omega }^{\prime }$ plane also describes the thawing as well as freezing region of the universe. The recent observational data also favor our results.

After reviewing the $f(T,{𝒯})$ gravity, in which $T$ is the torsion scalar and ${𝒯}$ is the trace of the energy-momentum tensor, we refer to two cosmological models of this theory in agreement with observational data. Thereinafter, we consider a flat Friedmann–Robertson–Walker (FRW) universe filled by a pressureless source and look at the terms other than the Einstein terms in the corresponding Friedmann equations, as the dark energy (DE) candidate. In addition, some cosmological features of models, including equation of states and deceleration parameters, are addressed helping us in getting the accelerated expansion of the universe in quintessence era. Finally, we extract the scalar field as well as potential of quintessence, tachyon, K-essence and dilatonic fields for both $f(T,{𝒯})$ models. It is observed that the dynamics of scalar field as well as the scalar potential of these models indicate an accelerated expanding universe in these models.

In this paper, we formulate exact anisotropic interior solutions of the Einstein field equations preserving spherically symmetric geometry in the context of $f(T,{𝒯})$ gravity. To make the system close, we consider a linear function in torsion scalar $(T)$ and trace of energy–momentum tensor $({𝒯})$, and employ the well-known Karmarkar condition with metric potential of the form $e^{\lambda (r)}=1+c{r}^2{(\mathrm{\text{erf}}(1+a{r}^2))}^2$. We consider standard data of some well-known compact star models (Vela X-1, PSR J1614-2230, Cen X-3 and EXO 1785-248) to estimate the unknown model parameters. We perform physical analysis of the developed model in detail, which includes density profile, pressure profile, anisotropy factor, mass function, gravitational/surface redshift, compactness factor, energy bounds, stability criteria, and the equilibrium condition. The analysis leads us to conclude that solutions are well-behaved and physically viable.

The commitment behind this work is to find the solutions of compact stellar models by using the spherically symmetric static space-time and anisotropic matter distribution in the framework of $f(T,{𝒯})$ gravity. In this study, we used the new type of metric functions $\nu (r)=2log(c_1+r^2)+log(c_2)$ and evaluated other functions $\lambda (r)=log(1+16c_{2}F{r}^2)$ by the well-known Karmarkar condition. In this work, we use the rotated and spinning tetrad named as off-diagonal and most generic function of $f(T,{𝒯})$ gravity. We find the strange stellar solutions by incorporating the MIT bag equation of state $p_r=\frac{1}{3}(\rho -4B_g)$ to evaluate cosmological constant. Aiming at the simplicity of solutions we utilize the given data for masses and radii of compact objects PSR J1416-2230, 4 U 1608-52, Cen X-3, EXO 1785-248, SMC X-1. By graphical presentation of the core properties of compact models, we show by concluding that our solutions are graphically fit and physically admissible and interesting by having the compatibility with the compact stars study.

This paper is devoted to explore bouncing cosmology in $f(T,{𝒯})$ modified gravity. In the background of $f(T,{𝒯})$ modified theory with $T$ being Torsion scalar and ${𝒯}$ being the trace of energy–momentum tensor, the Hubble parameter is considered for the isotropic, flat, and homogenous universe. The standard bouncing scale factor has employed the exponential term to unify bounce with late-time acceleration. Phase portrait analysis reveals us that Minkowskian origin transfers to de Sitter origin in $(H,Ḣ)$-plane and as past infinite time $t\to -\infty$$\Rightarrow$$a(t)\to 0$ and $(H,Ḣ)\to$ constant which corresponds to some physical cosmological scenarios. Since field equations of $f(T,{𝒯})$ gravity are of second order, a one-dimensional autonomous system has been extracted. Finally, outcomes have been plotted graphically, and any type of singular behavior has not been experienced. The study of the equation of state parameter against cosmic time reveals that phantom phase is quite significant for both models. The inertial force in terms of Hubble parameter and cosmic time gives rise to pseudo Rip. The study of cosmographic parameters tells us that the present model corresponds to $\mathrm{\Lambda }$CDM at a large value of cosmic time.

This paper explores the aspects of compact stars in $f(T,{𝒯})$ gravity, where $T$ and ${𝒯}$ express the torsion and trace of the energy–momentum tensor. To achieve this goal, we consider a spherically symmetric spacetime with an anisotropic source of fluid. In particular, the Krori–Barua (KB) spacetime is considered to explore the solution of compact stars. In addition, we select three specific types of compact stars models, namely J1416-2230, 4U 1608-52 and Cen X-3. We develop the field equations using the KB spacetime with some specific form of $f(T,{𝒯})$ gravity. In addition, we consider the Schwarzschild geometry for the matching conditions at the boundary. Then, we calculate the values of all the relevant parameters by imposing matching conditions. We provide detailed graphical analysis to discuss the physical acceptability of different parameters, namely energy density, pressure, anisotropy and gradient. We also examine the stability of compact stars by exploring energy conditions, equations of state, conditions of causality, redshift functions, mass functions and compactness functions. Finally, we find that the obtained solutions are physically viable and also having good properties for the compact star models.

Inflationary cosmology was the subject of an investigation in the $f(T,{𝒯})$ gravity context, for which $T$ stands for the torsion scalar while ${𝒯}$ is the trace of the energy–momentum tensor using three different class of inflation potentials well known in the literature. In order to find the range of geometry-matter coupling parameter to describe cosmological inflation scenario, we determined the slow-roll parameters and predict the scalar spectral index $n_s$, the tensor to scalar ratio $r$ and tensor spectral index $n_T$ in function in inflation potential parameters. The results show that the range of geometry-matter coupling parameter found is in agreement with the PLANCK 2018 data and WMAP data.

By making use of two viable Lagrangian $f(T,{𝒯})$ models, we investigate the behavior of the state parameter of the interacting viscous dark energy. We, from constant deceleration parameter, explore the cosmological implications of the viscosity and interaction between the dark energy and dark matter in terms of redshift. We then construct the viscosity and the interaction parameters that are respectively parameterized by $d_o^{\eta }({\rho }_{\mathrm{\text{DE}}})$ and $\xi$ and obtain interesting results. Later, we investigate the behavior of some bulk viscosity models describing little rip and pseudo rip future singularities within $f(T,{𝒯})$ modified gravity. We obtain interesting gravitational equations of motion for viscous dark energy coupled with dark matter. The solution of these equations gives us an analytic expression for characteristic properties of these cosmological models.