Narrow Results

We consider conformally invariant form of the actions in Einstein, Weyl, Einstein–Cartan and Einstein–Cartan–Weyl space in general dimensions (> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein–Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb–Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.

By assuming generalized nonlinear and linear interaction term between dark matter and dark energy, we investigate the cosmic accelerated expansion of the universe. For this reason, we suppose a flat fractal universe platform as well as Tsallis holographic dark energy model. The Hubble horizon is being adopted as an infrared cutoff and extracted different cosmological parameters as well as plane. It is observed that equation-of-state parameter exhibits the quintom-like nature while (${\omega }_d$–${\omega }_d^{\prime }$) lies in thawing and freezing regions for different parametric values for both the cases. Furthermore, the squared sound speed shows stable behavior for nonlinear interaction term but shows the partially stable behavior for linear term. For both cases, the deceleration parameter leads to the accelerated phase of the universe and the consequences are comparable with observational data. The results for $r$–$s$ plane, leads to the quintessence and phantom region of the universe for nonlinear case while this plane represents the Chaplygin gas behavior for linear term. The $Om$ diagnostic also shows the satisfying results.

This paper deals with the construction of locally rotationally symmetric (LRS) Bianchi type-II (B-II) cosmological models obtained by solving Einstein field equations coupled with an attractive massive scalar field (MSF) when the source of gravitation is the mixture of cosmic string cloud and anisotropic dark energy (DE) fluid which are minimally interacting. We have obtained exact cosmological models by using (i) shear scalar is proportional to the scalar expansion of the space–time and (ii) a power-law relation between the average scale factor of the universe and the scalar field. Our models represent string cosmological model and DE model in the presence of MSF. Using our model, we determine cosmological parameters such as energy densities, deceleration parameter, statefinders and equation of state parameter. We, also, present the tension density and energy density of the string. We discuss the physical aspects of these cosmological parameters. It is observed that our models represent accelerated expansion phenomenon of our universe as confirmed by Supernova Ia experiment.

In this paper, we study cosmic evolution and current expansion via generalized ghost pilgrim dark energy (PDE) model for FRW universe in $f(R)$ gravity. For this purpose, we consider both interacting and non-interacting forms of dark energy (DE) model and reconstruct $f(R)$ model using red-shift parameter. In order to analyze the effects of the DE model, we formulate some standard cosmological parameters such as Hubble, effective equation of state (EoS) and statefinder parameters as well as ${\omega }_c$–${\omega }_c^{\prime }$ plane. We also investigate the stability criteria for both interacting and noninteracting models through the squared speed of sound. It is concluded that the best-fit results are found for the positive curvature parameter in the presence of the noninteracting model. For the interacting model, the cosmic evolution is well explained by closed and open universe models while the flat geometry effectively describes the current cosmos.

This paper examines the cosmic evolution and current expansion for flat FRW universe through generalized ghost pilgrim dark energy model in $f(R)$ gravity. For this purpose, we reconstruct the models in terms of red-shift parameter with respect to three scale factors, i.e. power-law, intermediate and a scale factor defining two unified phases. We study compatibility of reconstructed $f(R)$ models through $r$-$s$ planes whereas graphical analysis of squared speed of sound leads to investigate their stability. We also explore the behavior of cosmological parameters such as equation of state and deceleration parameters. Moreover, we study the existence of freezing/thawing regions via $\omega$-${\omega }^{\prime }$ planes. We conclude that squared speed of sound identifies both stability/instability of reconstructed $f(R)$ models while equation of state and deceleration parameters specifies transition from decelerated to accelerated expanding cosmos. The $\omega$-$\acute{\omega }$ planes discover thawing as well as freezing regions for particular values of pilgrim parameter.

This present communication is an outcome of the investigation on newly proposed holographic dark energy model such as the Tsallis holographic dark energy (THDE) with Hubble horizon cutoff regarded as IR cutoff (infrared cutoff) for a spatially homogeneous and anisotropic Marder space-time in the framework of general relativity theory (GRT). Here, we have constructed the THDE models with Hubble horizon cutoff in three different ways, based on the following possibilities: (i) a varying deceleration parameter proposed by Mishra et al., (ii) hybrid expansion law (HEL) proposed by Akarsu et al. and (iii) a linearly varying deceleration parameter (LVDP) given by Akarsu and Dereli. The rapid expansion of the cosmos is thus justified for obtained models through the deceleration parameter (DP). In this way, the equation of state (EoS) parameter (${\omega }_{\mathrm{\text{DE}}}$) of the models describe the phantom and quintessence phases of the cosmos. Also, we compare the cosmological parameters of the obtained models with the parameters of $\mathrm{\Lambda }$CDM model, which indicates that the models-I and II are nearly identical to the $\mathrm{\Lambda }$CDM model.

The stability issue of Generalized modified gravitational models is discussed with particular emphasis to de Sitter solutions. Two approaches are briefly presented.