A comment on the Brans-Dicke cosmology for a radiation universe

The cosmological solutions of Brans-Dicke theory for a radiation universe obtained so far are commented on. Some problematic solutions are corrected and the conditions corresponding to singularity-free solutions are investigated.     

一类无奇点宇宙模型

按照Penrose-Hawking的奇点定理,在场源物质无旋、无加速且能量密度满足条件ρ+3p≥0的宇宙模型中一定存在奇点.本文研究了场源物质有旋时的无奇点宇宙模型,获得了几种无奇点的宇宙解.     

Solution of dirac equation in a singularity-free Kaluza-Klein cosmological model

The singularity-free solution of (4 + D) -dimensional Einstein field equations for the Kaluza-Klein cosmological model is obtained. Then the Dirac equations are solved in this model.     

A quantum cosmological model based on Einstein's universe

The conformal factor and a massless scalar field are quantized on Einstein background spacetime. A singularity-free cosmological model is obtained and discussed.     

Quantum cosmological model with a scalar field as source

It is shown that if both the conformal factor and scalar field are quantized on a background spacetime, a singularity-free cosmological model can be obtained and the quantum states must be zero-energy ones.     

离散时空中的奇性自由的Friedmann宇宙解

由尘埃物质粒子的集合来形成一个理想的离散时空的Friedmann宇宙模型并证明了它是奇性 自由的. 关键词： 离散时空 尘埃物质 Friedmann宇宙 奇性自由     

Extending the predictive power of perturbative QCD using the principle of maximum conformality and the Bayesian analysis

The European Physical Journal C - We present herein a new class of singularity-free interior solutions to describe realistic anisotropic compact stellar objects with spherically symmetric matter...     

A class of new LRS Bianchi type-I perfect fluid universes with decaying vacuum energy density Λ

A class of new LRS Bianchi type-I cosmological models with a variable cosmological term is investigated in presence of perfect fluid. A procedure to generate new exact solutions to Einstein’s field equations is applied to LRS Bianchi type-I space-time. Starting from some known solutions a class of new perfect fluid solutions of LRS Bianchi type-I are obtained. The cosmological constant Λ is found to be positive and a decreasing function of time which is supported by results from recent supernovae Ia observations. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Mini-bangs in cosmology and astrophysics

The ideas originally proposed to discuss continuous creation of matter are reconsidered in the context of the big bang cosmological models. It is shown that singularity-free big bang models are possible under the modified field equations of general relativity. However, the case is made out that matter creation takes place in several mini-bangs at different epochs rather than in one big bang. The implications of this idea for high energy astrophysics and for gravitational radiation are discussed.     

Lumps and rouge waves for a $$$$-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics

A specific class of singularity-free cosmological model has recently been considered in light of different observational data such as observed Hubble data, BAO data from luminous red galaxy survey by Slowan digital sky survey (SDSS) and CMB data from WMAP. However, it is observed that only 12–14 data points are used to study the viability of the model in late time. In this paper, we discuss the viability of all the models belonging to the same class of EU in light of union compilation data (SNIa) which consists of over a hundred data points, thus getting a more robust test for viability. More importantly, it is crucial that we can distinguish between the various models proposed in the class of solution obtained. We discuss here why with the present observational data it is difficult to distinguish between all of them. We show that the late-time behaviour of the model is typical to any asymptotically de Sitter model.     

Stationary rotating string world models with a magnetic field

Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.     

Exact Inhomogeneous Cosmological Models with Yang–Mills Fields

The exact solutions of Einstein–Yang–Mills equations in a class of spherically symmetric cosmological models are found with several coordinate conditions both with the account and without the account cosmological constant.     

Soliton solutions to the einstein equations in five dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or a negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(anti)-de Sitter [(A)dS] metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with a negative cosmological constant that asymptotically approach AdS5/gamma but have less energy than AdS5/gamma. We present evidence that these solutions are the lowest-energy states within their asymptotic class.     

Anisotropic strange stars in Tolman–Kuchowicz spacetime

We attempt to study a singularity-free model for the spherically symmetric anisotropic strange stars under Einstein’s general theory of relativity by exploiting the Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) metric. Further, we have assumed that the cosmological constant \(\varLambda \) is a scalar variable dependent on the spatial coordinate r. To describe the strange star candidates we have considered that they are made of strange quark matter distribution, which is assumed to be governed by the MIT bag equation of state. To obtain unknown constants of the stellar system we match the interior Tolman–Kuchowicz metric to the exterior modified Schwarzschild metric with the cosmological constant, at the surface of the system. Following Deb et al. (Ann Phys 387:239, 2017) we have predicted the exact values of the radii for different strange star candidates based on the observed values of the masses of the stellar objects and the chosen parametric values of the \(\varLambda \) as well as the bag constant \({\mathcal {B}}\). The set of solutions satisfies all the physical requirements to represent strange stars. Interestingly, our study reveals that as the values of the \(\varLambda \) and \({\mathcal {B}}\) increase the anisotropic system become gradually smaller in size turning the whole system into a more compact ultra-dense stellar object.     

Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations by Maurya and Gupta, Astrophys. Space Sci.333, 149 (2011) are modified by introducing the variable cosmological term. Motivated by Tiwari et al, Indian J. Pure Appl. Math.31, 1017 (2000), some particular values of the cosmological term are taken to obtain well-behaved solutions of the Einstein–Maxwell field equations. All the results given by Maurya and Gupta can be obtained as particular cases of our solutions by choosing a cosmological term equal to zero.     

Higher dimensional spherically symmetric inhomogeneous cosmological model with heat flow

We study spherically symmetric inhomogeneous cosmological model with heat flow in higher dimensional space-time and present a class of solutions in which the velocity field is shear-free. Some of these solutions are analogous to the known solutions in 4-dimension while some are totally new.     

Anisotropic Bianchi-I universe with phantom field and cosmological constant

We study an anisotropic Bianchi-I universe in the presence of a phantom field and a cosmological constant. Cosmological solutions are obtained when the kinetic energy of the phantom field is of the order of anisotropy and dominates over the potential energy of the field. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration. A class of new cosmological solutions is obtained for an anisotropic universe in case an initial anisotropy exists which is bigger than the value determined by the parameter of the kinetic part of the field. Later, an autonomous system of equations for an axially symmetric Bianchi-I universe with phantom field in an exponential potential is studied. We discuss the stability of the cosmological solutions.      

Einige Lösungen der Einsteinschen Feldgleichungen mit idealer Flüssigkeit,die sich in einen fünfdimensionalen flachen Raum einbetten lassen

All solutions of the Einstein equations for a perfect fluid are given, which are invariantly characterized by: embedding class one, Petrov typeD, zero acceleration of matter. Among these solutions are inhomogeneous cosmological models and special solutions with spherical symmetry.     

Bianchi-IX string cosmological model in Lyra geometry

A class of cosmological solutions of massive strings for the Bianchi-IX space-time are obtained within the framework of Lyra geometry. Various physical and kinematical properties of the models are discussed     

On singularity-free spacetimes

We consider here the metric for the singularity-free family of fluid models. The metric is unique for cylindrically symmetric space-time with metric potentials being separable functions of radial and time coordinates in the comoving coordinates. It turns out that fluid models separate out into two classes, withρ ≠μp in general butρ = 3p in particular andp =ρ. It is shown that in both the cases radial heat flow can be incorporated without disturbing the singularity-free character of the spacetime. The geodesics of the singularity-free metric are studied and the geodesic completeness is established. Several previously known solutions are derived as particular cases.