Study of QCD generalized ghost dark energy in FRW universe

A phenomenological generalized ghost dark energy model has been studied under the framework of FRW universe. In ghost dark energy model the energy density depends linearly on Hubble parameter (H) but in this dark energy model, the energy density contains a the sub-leading term which is depends on $\mathcal{O} (H^2)$, so the energy density takes the form $\rho_D=\alpha H+ \beta H^2$, where $\alpha$ and $\beta$ are the constants. The solutions of the Friedman equation of our model leads to a stable universe. We have fitted our model with the present observational data including Stern data set. With the help of best fit results we find the adiabatic sound speed remains positive throughout the cosmic evolution, that claims the stability of the model. The flipping of the signature of deceleration parameter at the value of scale factor $a=0.5$ indicates that the universe is at the stage of acceleration i.e. de Sitter phase of the universe at late time. Our model shows that the acceleration of the universe begin at redshift $z_{ace}\approx 0.617$ and the model is also consistent with the current observational data.Comment: 9 pages, 9 figure

Lorentzian wormhole in the framework of loop quantum cosmology

In this paper, we construct a traversable static Lorentzian wormhole in the effective scenario of Loop Quantum Cosmology (LQC), where the field equations are modified due to the ultraviolet (UV) corrections introduced at large space-time curvatures. A stable wormhole can be constructed in the effective scenario without the violation of Null energy condition (NEC) by physical matter at the throat. The NEC is effectively violated due to the corrections in the field equations from LQC, resolving the Weyl curvature singularity at the throat. However, the physical matter does violate the Strong energy condition (SEC), suggesting the interesting possibility that dark energy can be harnessed into a wormhole. A possible explanation for this is the presence of inherent pressure isotropy in the UV-corrected field equations (discussed and compared to braneworld wormholes in the discussion). No additional exotic ingredient (violating NEC) is required, avoiding quantum instabilities. The tidal forces at the throat do not diverge and also the throat is found to be stable. The wormhole features an attractive geometry. LQC can resolve both types of curvature singularities appearing at the black hole center and wormhole throat, without exotic matter.Comment: 10 Pages, 4 Figure

A generalized family of anisotropic compact object in general relativity

We present model for anisotropic compact star under the general theory of relativity of Einstein. In the study a 4-dimensional spacetime has been considered which is embedded into the 5-dimensional flat metric so that the spherically symmetric metric has class 1 when the condition $e^{\lambda}=\left(\,1+C\,e^{\nu} \,{\nu'}^2\,\right)$ is satisfied ($\lambda$ and $\nu$ being the metric potentials along with a constant $C$). A set of solutions for the field equations are found depending on the index $n$ involved in the physical parameters. The interior solutions have been matched smoothly at the boundary of the spherical distribution to the exterior Schwarzschild solution which necessarily provides values of the unknown constants. We have chosen the values of $n$ as $n=2$ and $n$=10 to 20000 for which interesting and physically viable results can be found out. The numerical values of the parameters and arbitrary constants for different compact stars are assumed in the graphical plots and tables as follows: (i) LMC X-4 : $a=0.0075$, $b=0.000821$ for $n=2$ and $a=0.0075$, $nb=0.00164$ for $n\ge 10$, (ii) SMC X-1: $a=0.00681$, $b=0.00078$ for $n=2$, and $a=0.00681$, $nb=0.00159$ for $n \ge 10$. The investigations on the physical features of the model include several astrophysical issues, like (i) regularity behavior of stars at the centre, (ii) well behaved condition for velocity of sound, (iii) energy conditions, (iv) stabilty of the system via the following three techniques - adiabatic index, Herrera cracking concept and TOV equation, (v) total mass, effective mass and compactification factor and (vi) surface redshift. Specific numerical values of the compact star candidates LMC X-4 and SMC X-1 are calculated for central and surface densities as well as central pressure to compare the model value with actual observational data.Comment: 20 pages, 9 figures, 2 Table

Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions

In this paper we have explored the possibility of constructing a traversable wormhole on the Shtanov-Sahni braneworld with a timelike extra dimension. We find that the Weyl curvature singularity at the throat of the wormhole can be removed with physical matter satisfying the NEC $\rho+p \geq 0$, even in the absence of any effective $\Lambda$-term or any type of charge source on the brane. (The NEC is however violated by the effective matter description on the brane arising due to effects of higher dimensional gravity.) Besides satisfying NEC the matter constituting the wormhole also satisfies the Strong Energy Condition (SEC), $\rho+3p \geq 0$, leading to the interesting possibility that normal matter on the brane may be harnessed into a wormhole. Incidentally, these conditions also need to be satisfied to realize a non-singular bounce and cyclic cosmology on the brane\cite{Sahni4} where both past and future singularities can be averted. Thus, such a cyclic universe on the brane, constituted of normal matter can naturally contain wormholes. The wormhole shape function on the brane with a time-like extra dimension represents the tubular structure of the wormhole spreading out at large radial distances much better than in wormholes constructed in a braneworld with a spacelike extra dimension and have considerably lower mass resulting in minimization of the amount of matter required to construct a wormhole. Wormholes in the Shtanov-Sahni (SS) braneworld also have sufficiently low tidal forces, facilitating traversability. Additionally they are found to be stable and exhibit a repulsive geometry. We are left with the intriguing possibilty that both types of curvature singularity can be resolved with the SS model, which we discuss at the end of the concluding section.Comment: 31 Pages, 16 Figure

Pre-training Transformers on Indian Legal Text

Natural Language Processing in the legal domain been benefited hugely by the emergence of Transformer-based Pre-trained Language Models (PLMs) pre-trained on legal text. There exist PLMs trained over European and US legal text, most notably LegalBERT. However, with the rapidly increasing volume of NLP applications on Indian legal documents, and the distinguishing characteristics of Indian legal text, it has become necessary to pre-train LMs over Indian legal text as well. In this work, we introduce transformer-based PLMs pre-trained over a large corpus of Indian legal documents. We also apply these PLMs over several benchmark legal NLP tasks over both Indian legal text, as well as over legal text belonging to other domains (countries). The NLP tasks with which we experiment include Legal Statute Identification from facts, Semantic segmentation of court judgements, and Court Judgement Prediction. Our experiments demonstrate the utility of the India-specific PLMs developed in this work

Lorentzian wormholes in an emergent universe

A non-singular Emergent Universe (EU) scenario within the realm of standard Relativistic physics requires a generalization of the Equation of State (EoS) connecting the pressure and energy density. This generalized EoS is capable of describing a composition of exotic matter, dark energy and cosmological dust matter. Since the EU scenario is known to violate the Null Energy Condition, we investigate the possibility of presence of static, spherically symmetric and traversable Lorentzian wormholes in an EU. The obtained shape function is found to satisfy the criteria for wormhole formation, besides the violation of the NEC at the wormhole throat and ensuring traversability such that tidal forces are within desirable limits. Also, the wormhole is found to be stable through linear stability analysis. Most ${importantly}$, the numerical value of the emergent universe parameter $B$ as estimated by our wormhole model is in agreement with and lies within the range of values as constrained by observational data in a cosmological context. Also, the negative sign of the second EU parameter $A$ as obtained from our wormhole model is in agreement with the one required for describing an EU, which further indicates on the existence of such wormholes in an emergent universe ${without}$ accounting for any additional exotic matter field or any modification to the gravitational sector.Comment: 13 pages, 3 figure