A new class of holographic dark energy models in LRS Bianchi Type-I

In this paper, we examine the LRS Bianchi-type-I cosmological model with holographic dark energy. The exact solutions to the corresponding field equations are obtained by using the generalized hybrid expansion law (HEL). The EoS parameter [Formula: see text] for DE is found to be time-dependent and redshift-dependent and its exiting range for derived model is agreeing well with the current observations. Here, we likewise apply two mathematical diagnostics, the statefinders ([Formula: see text]) and [Formula: see text] plan to segregate HDE model from the [Formula: see text]CDM model. Here, the [Formula: see text] diagnostic trajectories are good tools to classify the dynamical DE model. We found that our model lies in both thawing region and freezing region. We also construct the potential as well as dynamics of the quintessence and tachyon scalar field. Some physical and geometric properties of this model along with the physical acceptability of cosmological solution have been discussed in detail.

f(T) cosmology with nonzero curvature

We investigate exact and analytic solutions in [Formula: see text] gravity within the context of a Friedmann–Lemaître–Robertson–Walker background space with nonzero spatial curvature. For the power-law theory [Formula: see text] we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature. That Milne-like solution is asymptotic behavior for the scale factor near the initial singularity for the model [Formula: see text]. The analytic solution for that specific theory is presented in terms of Painlevé series for [Formula: see text]. Moreover, from the value of the resonances of the Painlevé series we conclude that the Milne-like solution is always unstable while for large values of the independent parameter, the field equations provide an expanding universe with a de Sitter expansion of a positive cosmological constant. Finally, the presence of the cosmological term [Formula: see text] in the studied [Formula: see text] model plays no role in the general behavior of the cosmological solution and the universe immerge in a de Sitter expansion either when the cosmological constant term [Formula: see text] in the [Formula: see text] model vanishes.

Circuit Complexity from Cosmological Islands

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of quantum extremal islands in negative (or positive) cosmological constant with radiation in the background of Friedmann-Lemai^tre-Robertson-Walker (FLRW) space-time, i.e., the presence and absence of islands in anti de Sitter and the de Sitter space-time having SO(2, 3) and SO(1, 4) isometries, respectively. Without using any explicit details of any gravity model, we study the behavior of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, out-of-time ordered correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

New class of exact solutions to Einstein–Maxwell-dilaton theory on four-dimensional Bianchi type IX geometry

We construct new classes of cosmological solution to the five dimensional Einstein–Maxwell-dilaton theory, that are non-stationary and almost conformally regular everywhere. The base geometry for the solutions is the four-dimensional Bianchi type IX geometry. In the theory, the dilaton field is coupled to the electromagnetic field and the cosmological constant term, with two different coupling constants. We consider all possible solutions with different values of the coupling constants, where the cosmological constant takes any positive, negative or zero values. In the ansatzes for the metric, dilaton and electromagnetic fields, we consider dependence on time and two spatial directions. We also consider a special case of the Bianchi type IX geometry, in which the geometry reduces to that of Eguchi–Hanson type II geometry and find a more general solution to the theory.

Circuit Complexity from Cosmological Islands

Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of Quantum Extremal Islands in negative (or positive) Cosmological Constant with radiation in the background of Friedmann-Lemaî tre-Robertson-Walker (FLRW) space-time. Without using any explicit details of any gravity model, we study the behaviour of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

A brief review of general relativity

The first chapter in Part II contains basic information on general relativity and all necessary notations and formulas. The consideration is concise but rather brief; it is not meant to replace a textbook on general relativity. Covariant derivatives, curvature tensors, Bianchi identities, covariant equations, the classical limit and Einstein equations are covered. The fact that the Schwarzschild solution and the cosmological solution contain singularities, which can be interpreted as indicating a need for quantum gravitational theory, is addressed. In addition, the applicability of general relativity and Planck units are discussed.

Broadening quantum cosmology with a fractional whirl

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

Bounce and Stability in the Early Cosmology with Anomaly-Induced Corrections

An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential e-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, we explore both stable expansion and the bounce solutions in the models with non-zero cosmological constant and the presence of background radiation. The critical part of the analysis concerns stability for small perturbations of the Hubble parameter. It is shown that the stability is possible for the variations in the bounce region, but not in the sufficiently distant past in the contraction phase.