Non-singular Origin Research Articles

Decelerating to accelerating FRW universe with variable G and Λ in conharmonically flat space

General exact solutions of the Einstein’s field equations by using conharmonically flat space with variable gravitational and cosmological “constants” for a spatially homogeneous and isotropic Friedmann–Robertson–Walker (FRW) model filled with perfect fluid has been obtained. To study the transit behaviour of Universe, we consider a law of variation of scale factor a(t)=(tket)1n which yields a time-dependent deceleration parameter (DP) q=−1+nk(k+t)2, comprising a class of models that depicts a transition of the universe from the early decelerated phase to the recent accelerating phase. We find that the time-dependent DP is reasonable for the present day Universe and give an appropriate description of the evolution of the universe. For n=0.27k, we obtain q0=−0.73 which is similar to observed value of DP at present epoch. It is also observed that for n ≥ 2 and k=1, we obtain a class of transit models of the universe from early decelerating to present accelerating phase. For k=0, the universe has non-singular origin. In these models, we arrive at the decision that, from the structure of the field equations, the behaviour of Λ and G are related. Taking into consideration the observational data, we conclude that the Λ behaves as a positive decreasing function of time whereas G is increasing and tend to a constant value at the late time. Our derived model is in good agreement with ΛCDM model. Some physical and geometric properties of the models are also discussed.

Bianchi type-I transit cosmological models with time dependent gravitational and cosmological constants: reexamined

The present study reexamines the recent work of Pradhan et al. (Indian J. Phys. 88: 757, 2014) and obtained general exact solutions of the Einstein's field equations with variable gravitational and cosmological "constants" for a spatially homogeneous and anisotropic Bianchi type-I space-time. To study the transit behaviour of Universe, we consider a law of variation of scale factor $a(t) = \left(t^{k} e^{t}\right)^{\frac{1}{n}}$ which yields a time dependent deceleration parameter $q = - 1 + \frac{nk}{(k + t)^{2}}$, comprising a class of models that depicts a transition of the universe from the early decelerated phase to the recent accelerating phase. We find that the time dependent deceleration parameter is reasonable for the present day Universe and give an appropriate description of the evolution of the universe. For $n = 0.27k$, we obtain $q_{0} = -0.73$ which is similar to observed value of deceleration parameter at present epoch. It is also observed that for $n \geq 2$ and $k = 1$, we obtain a class of transit models of the universe from early decelerating to present accelerating phase. For $k = 0$, the universe has non-singular origin. In these models, we arrive at the decision that, from the structure of the field equations, the behaviour of cosmological and gravitational constants and are related. Taking into consideration the observational data, we conclude that the cosmological constant behaves as a positive decreasing function of time whereas gravitational constant is increasing and tend to a constant value at late time. $H(z)/(1+z)$ data ($32$ points) and model prediction as a function of redshift for different $k$ and $n$ are successfully presented by using recent data (Farooq and Ratra, Astrophys. J. 66: L7, 2013). Some physical and geometric properties of the models are also discussed.

CONNECTING THE NONSINGULAR ORIGIN OF THE UNIVERSE, THE VACUUM STRUCTURE AND THE COSMOLOGICAL CONSTANT PROBLEM

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial vacuum structure for the theory and are responsible for the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → -∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. The nontrivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

NONSINGULAR ORIGIN OF THE UNIVERSE AND THE COSMOLOGICAL CONSTANT PROBLEM

We consider a nonsingular origin for the universe starting from an Einstein static universe in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field ϕ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe and ϕ → -∞, describing our present universe. Surprisingly, avoidance of singularities and stability as ϕ → ∞ imply a positive but small vacuum energy as ϕ → -∞. Zero vacuum energy density for the present universe is the "threshold" for universe creation.

NONSINGULAR ORIGIN OF THE UNIVERSE AND ITS PRESENT VACUUM ENERGY DENSITY

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking of scale invariance. After spontaneous symmetry breaking of scale invariance it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → - ∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities are instrumental in the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → - ∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

Early-Universe and Evolution of the Present Universe: Exact Solution Models

The evolution of the Robertson-Walker type universes consisting of radiating perfect fluid distribution coupled with zero-mass scalar field in which the gravitational parameter G varies with cosmic time t are studied. Unified descriptions of the early evolution of the universe consisting of different phases are investigated. The different properties of the cosmological solutions are discussed and the physical behaviour of the model universes during the radiation-dominated era and also during the big bang scenario are studied. Here we obtain models which are geometrically closed and are thereby ever expanding and evolve from rest from a non-singular hot origin with maximum (finite) energy density and temperature and a small minimum (non-zero) gravitational coupling G.

Bouncing braneworlds

We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commences its expansion from a quasi-singular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The non-singular and quasi-singular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.

Evidence for the quantum birth of our universe

We present evidence for a nonsingular origin of the Universe with intial conditions determined by quantum physics and relativistic gravity. In particular, we establish that the present temperature of the microwave background and the present density of the Universe agree well with our predictions from these intial conditions, after evolution to the present age using the Einstein-Friedmann equation. Remarkably, the quantum origin for the Universe naturally allows its evolution at exactly the critical density. We also discuss the consequences of these results to some fundamental aspects of quantum physics in the early Universe.

Internal symmetry of hadrons: Finsler geometrical origin

The microlocal space of hadronic matter extension has recently been characterized as a Finsler space. This consideration of hadrons extended as composites of constituents can give rise to a dynamical theory of hadrons. The macrospaces, the space-time of common experience (the Minkowski flat space-time) and the Robertson-Walker background space-time of the universe, are found to appear as the “averaged” space-times of the Finsler space that describes the anisotropic nature of the microdomain of hadrons. From the assumed property of the fields of the constituents in the microspace it is possible to find the field (or wave) equations of the particles (or constituents) through the quantization of space-time at small distances (to an order of or less than a fundamental length). If the field (or wave) function is separable in the functions of the coordinates of the underlying manifold and the directional arguments of the Finsler space, then the former part of the field function is found to satisfy the Dirac equation in the Minkowski space-time or in the Robertson-Walker space-time according to the nature of the underlying manifold. In the course of finding a solution for the other part of the field function a relation between the mass of the particle and a parameter in the metric of the space-time has been obtained as a byproduct. This mass relation has cosmological implications and is relevant in the very early stage of the evolution of the universe. In fact, it has been shown elsewhere that the universe might have originated from a nonsingular origin with entropy and matter creations that can account for the observed photon-to-baryon ratio and total particle number of the present universe. The equations in the directional arguments for the constituents in the hadron configuration are found here and give rise to an additional quantum number in the form of an “internal” helicity that can generate the internal symmetry of hadron if one incorporates the arguments of Budini in generating the internal isospin algebra from the conformal reflection group. This consideration can also account for the meson-baryon mass differences.

Self-similar scalar field collapse: Naked singularities and critical behavior.

Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again. There is a singularity at one point of these solutions, however it is not visible to observers at finite radius. The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes. The properties of these solutions are discussed in detail. The paper also contains some speculation about the significance of self-similarity in recent numerical studies.