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Register a new userAccelerating Universe in Hybrid and Logarithmic Teleparallel Gravity
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Added by
Pardyumn Kumar Sahoo
Publication date
2020
fields
Physics
and research's language is
English
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Teleparallel gravity is a modified theory of gravity for which the Ricci scalar $R$ of the underlying geometry in the action is replaced by an arbitrary functional form of torsion scalar $T$. In doing so, cosmology in $% f(T)$ gravity becomes greatly simplified owing to the fact that $T$ contains only the first derivatives of the vierbeins. The article exploits this appealing nature of $f(T)$ gravity and present cosmological scenarios from hybrid and logarithmic teleparallel gravity models of the form $% f=e^{mT}T^n $ and $f=Dlog(bT)$ respectively, where $m$, $n$, $D$ and $b$ are free parameters constrained to suffice the late time acceleration. We employ a well motivated parametrization of the deceleration parameter having just one degree of freedom constrained with a $chi^{2}$ test from 57 data points of Hubble data set in the redshift range $0.07<z<2.36$, to obtain the expressions of pressure, density and EoS parameter for both the teleparallel gravity models and study their temporal evolution. We find the deceleration parameter to experience a signature flipping for the $chi^{2}$ value of the free parameter at $z_{tr}simeq0.6$ which is consistent with latest Planck measurements. Next, we present few geometric diagnostics of this parametrization to understand the nature of dark energy and its deviation from the $Lambda$CDM cosmology. Finally, we study the energy conditions to check the consistency of the parameter spaces for both the teleparallel gravity models. We find the SEC to violate for both the models which is an essential recipe to obtain an accelerating universe.
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The $f(R,T)$ theory of gravitation is an extended theory of gravitation in which the gravitational action contains both the Ricci scalar $R$ and the trace of energy momentum tensor $T$ and hence the cosmological models based on $f(R,T)$ gravity are eligible to describing late time acceleration of present universe. In this paper, we investigate an accelerating model of flat universe with linearly varying deceleration parameter (LVDP). We apply the linearly time varying law for deceleration parameters that generates a model of transitioning universe from early decelerating phase to current accelerating phase. We carry out the state-finder and Om(z) analysis, and obtain that LVDP model have consistency with astrophysical observations. We also discuss profoundly the violation of energy-momentum conservation law in $f(R,T)$ gravity and dynamical behavior of the model.
Teleparallel gravity is a modified theory of gravity in which the Ricci scalar $R$ of the Lagrangian replaced by the general function of torsion scalar $T$ in action. With that, cosmology in teleparallel gravity becomes profoundly simplified because it is second-order theory. The article present a complete cosmological scenario in $f(T)$ gravity with $f(T)=T+beta(-T)^{alpha}$, where $alpha,$ and $beta$ are model parameters. We present the profiles of energy density, pressure, and equation of state (EoS) parameter. Next to this, we employ statefinder diagnostics to check deviation from the $Lambda$CDM model as well as the nature of dark energy. Finally, we discuss the energy conditions to check the consistency of our model and observe that SEC violates in the present model supporting the acceleration of the Universe as per present observation.
In the present work, a new form of the logarithmic shape function is proposed for the linear $f(R,T)$ gravity, $f(R,T)=R+2lambda T$ where $lambda$ is an arbitrary coupling constant, in wormhole geometry. The desired logarithmic shape function accomplishes all necessary conditions for traversable and asymptotically flat wormholes. The obtained wormhole solutions are analyzed from the energy conditions for different values of $lambda$. It has been observed that our proposed shape function for the linear form of $f(R,T)$ gravity, represents the existence of exotic matter and non-exotic matter. Moreover, for $lambda=0$ i.e. for the general relativity case, the existence of exotic matter for the wormhole geometry has been confirmed. Further, the behaviour of the radial state parameter $omega_{r}$, the tangential state parameter $omega_{t}$ and the anisotropy parameter $triangle$ describing the geometry of the universe, has been presented for different values of $lambda$ chosen in $[-100,100]$.
In theories such as teleparallel gravity and its extensions, the frame basis replaces the metric tensor as the primary object of study. A choice of coordinate system, frame basis and spin-connection must be made to obtain a solution from the field equations of a given teleparallel gravity theory. It is worthwhile to express solutions in an invariant manner in terms of torsion invariants to distinguish between different solutions. In this paper we discuss the symmetries of teleparallel gravity theories, describe the classification of the torsion tensor and its covariant derivative and define scalar invariants in terms of the torsion. In particular, we propose a modification of the Cartan-Karlhede algorithm for geometries with torsion (and no curvature or nonmetricity). The algorithm determines the dimension of the symmetry group for a solution and suggests an alternative frame-based approach to calculating symmetries. We prove that the only maximally symmetric solution to any theory of gravitation admitting a non-zero torsion tensor is Minkowski space. As an illustration we apply the algorithm to six particular exact teleparallel geometries. From these examples we notice that the symmetry group of the solutions of a teleparallel gravity theory is potentially smaller than their metric-based analogues in General Relativity.
We study Kaluza-Klein cosmology in cuscuton gravity and find an exact solution describing an accelerating 4-dimensional universe with a stable extra dimension. A cuscuton which is a non-dynamical scalar field is responsible for the accelerating expansion and a vector field makes the extra dimensional space stable. Remarkably, the accelerating universe in our model is not exactly de Sitter.
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