Non-singular model universe from a perfect fluid scalar-metric cosmology

To seek for a singularity free model universe from a perfect fluid scalar-metric cosmology, we work in the “Emergent Cosmology” (EC) paradigm which is a non-singular alternative for cosmological inflation. By using two methods including Linear Stability Theory and Effective Potential Formalism, we perform a classical analysis on the possible static solutions (that are called usually as Einstein Static Universes (ESU)in literature) in order to study EC paradigm in a FRW background. Our model contains a kinetic term of the scalar field minimally coupled to the background geometry without a potential term. The matter content of the model consists of a perfect fluid plus a cosmological constant \(\Lambda \) as a separate source. In the framework of a local dynamical system analysis, we show that in the absence or presence of \(\Lambda \), depending on some adopted values for the free parameters of the underlying cosmological model with flat and non-flat spatial geometries, one gets some static solutions which are viable under classical linear perturbations. By extending our study to a global dynamical system analysis, we show that in the presence of \(\Lambda \) with non-flat spatial geometries there is a future global de Sitter attractor in this model. Following the second method, we derive a new static solution that represents a stable ESU but this time without dependence on the free parameters of the cosmological model at hand. As a whole, our analysis suggests the possibility of graceful realization of a non-singular EC paradigm (i.e. leaving the initial static phase and entering the inflation period as the universe is evolving) through either preserving or violation of the strong energy condition.     

On the existence of perturbed robertson-walker universes

Solutions of the full nonlinear field equations of general relativity near the Robertson-Walker universes are examined, together with their relation to linearized perturbations. A method due to Choquet-Bruhat and Deser is used to prove existence theorems for solutions near Robertson-Walker constraint data of the constraint equations on a spacelike hypersurface. These theorems allow one to regard the matter fluctuations as independent quantities, ranging over certain function spaces. In the k = ?1 case the existence theory describes perturbations which may vary within uniform bounds throughout space. When k = +1 a modification of the method leads to a theorem which clarifies some unusual features of these constraint perturbations. The k = 0 existence theorem refers only to perturbations which die away at large distances. The connection between linearized constraint solutions and solutions of the full constraints is discussed. For k = ±1 backgrounds, solutions of the linearized constraints are analyzed using transverse-traceless decompositions of symmetric tensors. Finally the time-evolution of perturbed constraint data and the validity of linearized perturbation theory for Robertson-Walker universes are considered.     

Nonstandard model of the expanding universe

A reformulation of general relativity is proposed with the relativity principle being invalid. Consequently the space-time manifold carries a natural (1+3)-foliation, where the foliation variables supersede the metric as the fundamental object. The Einstein equations become modified by some kind of foliation energy, but otherwise remain part of the dynamics. The theory is applied to a homogeneous and isotropic universe; the generation of mass can be explained by conversion of foliation energy and inflation is driven by the negative foliation pressure.     

Friedmann universe in a quantum gravity model

It is shown that, in a model theory of gravity, which quantises only the conformal part, the Robertson-Walker universe has a nonsingular evolution. The method also shows that there arises a lower bound to the physical length scale in any static metric with positive curvature.     

Quantum graviton creation in a model universe

Quantization in the spatially inhomogeneous, anisotropic, Gowdy three-torus solution of Einstein's equations leads to the production of gravitons from empty space. The creation of pairs of gravitons occurs only in wave modes with wavelength exceeding the horizon size at an initial time. The final number of created gravitons in any mode is proportional to the number of causally unconnected regions at the initial time over the wavelength of that mode. At large times, graviton number is well defined since the solution is in WKB form. The creation process produces the anisotropic collisionless radiation identical to that discussed by Doroshkevich, Zel'dovich, and Novikov which characterizes the large time classical solution. Near the singularity, the model behaves like an empty Bianchi Type I universe at each point in space (local Kasner). The canonical methods of Arnowitt, Deser, and Misner yield a reduced Hamiltonian from which the classical equations of motion are obtained. The quantization of the rapidly varying gravitational field component resembles the procedures used by Parker or Zel'dovich et al. to study particle creation in curved spacetime.     

A point-particle model universe

The observable cosmos is modeled as a set of point-particles, representing the galaxies, which perturb a dust-filled, Robertson-Walker space-time. The analysis proceeds only to first order in=8G/c ² and employs a metric suggested by McVittie [General Relativity and Cosmology (Chapman and Hall, London, 1965)], whose original work this paper seeks to develop. Necessary and sufficient conditions are found for the metric to give rise to an energy tensor of a chosen form appropriate to the modeling. In particular, a second-order equation is found which governs a certain time-independent potential. A class of solutions to this equation is established, and the associated singularities of the mass density are shown to be of a Dirac type.     

A special anisotropic model of the universe

Applying laws of the kind previously published by the author for isotropic models, we obtain an anisotropic cosmological model with a Bianchi I metric. The interesting features of this model are its simplicity and the easy way we may define overall Hubble and deceleration parameters.     

Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetime

We demonstrate the possibility of removing the divergences in the energy-momentum tensor by identifying divergent terms with renormalizations of the coupling constants in the gravitational field equation, modified to include a cosmological term and terms quadratic in the curvature. The model studied is that of a classical Robertson-Walker metric and a quantized minimally coupled neutral scalar field. The theory is constructed first with an ultraviolet cutoff as a phenomenological ansatz. The cutoff is then removed in an attempt to obtain a more fundamental theory, whereupon the question arises of the covariance and uniqueness of the resulting renormalized energy-momentum tensor. In the case of a massless field in a spatially flat universe, an apparent infrared divergence is discussed from the point of view of operational determination of the renormalized coupling constants. In the other cases, although the divergences are successfully accounted for by renormalization, we are left with finite leading terms which do not appear to be identifiable with geometrical tensors; the significance of this result is under investigation. If these anomalous terms are dropped, the renormalized energy-momentum tensor agrees with that defined by adiabatic regularization, provided that the limit of slow time variation taken in that method is generalized to a limit of “spacetime flatness.”     

Expanding (3+1)-dimensional universe from a lorentzian matrix model for superstring theory in (9+1) dimensions

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous works in which the Wick rotation was used to make the model well?defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte?Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some "critical time," after which the space has SO(3) symmetry instead of SO(9).     

A parabolic matter-radiation model of the universe

A study of matter-radiation universes under certain supplementary conditions specified in the introduction shows us that the only model of this class compatible with observations is a parabolic universe which at the present time is almost the same as an Einstein-de Sitter model. The numerical values obtained for Hubble's constant, the age of the universe and the matter density at the present time are quite acceptable. We can also obtain some limits for the mass of neutrinos. The advantage of this parabolic model is that it gives the same results as thet ^2/3 model at the present time and what is more could be used in studying problems of the formation of galaxies, after the recombination epoch, where matter and radiation have comparable importance.     

Building a Quantum Spacetime

A quantum spacetime is constructed from the freedata given at past null infinity. One starts with afield equation for a scalar function Z on the initialsurface and then shows that the solution depends on four constants of integration. Theseconstants become the spacetime points and the levelsurfaces of the scalar function, i.e., Z = const, becomenull hypersurfaces on the derived spacetime. A phase space together with a complex structure areconstructed on past null infinity. This Hilbert space ofincoming gravitons possesses a natural foliation whichdefines superselection sectors on the space of asymptotic quantum states. The dynamics of nullsurface quantization provides spacetime-valued quantumoperators on the superselection sectors. It is shownthat the spacetime points themselves become operators with nonvanishing commutationrelations.     

An interacting dark energy model in a non-flat universe

In this paper, an interacting dark energy model in a non-flat universe is studied, with taking interaction form $C=\alpha H\rho _{de}$ C = α H ρ d e . And in this study a property for the mysterious dark energy is aforehand assumed, i.e. its equation of state $w_{\Lambda }=-1$ w Λ = - 1 . After several derivations, a power-law form of dark energy density is obtained $\rho _{\Lambda } \propto a^{-\alpha }$ ρ Λ ∝ a - α , here $a$ a is the cosmic scale factor, $\alpha $ α is a constant parameter introducing to describe the interaction strength and the evolution of dark energy. By comparing with the current cosmic observations, the combined constraints on the parameter $\alpha $ α is investigated in a non-flat universe. For the used data they include: the Union2 data of type Ia supernova, the Hubble data at different redshifts including several new published datapoints, the baryon acoustic oscillation data, the cosmic microwave background data, and the observational data from cluster X-ray gas mass fraction. The constraint results on model parameters are $\Omega _{K}=0.0024\,(\pm 0.0053)^{+0.0052+0.0105}_{-0.0052-0.0103}, \alpha =-0.030\,(\pm 0.042)^{+0.041+0.079}_{-0.042-0.085}$ Ω K = 0.0024 ( ± 0.0053 ) - 0.0052 - 0.0103 + 0.0052 + 0.0105 , α = - 0.030 ( ± 0.042 ) - 0.042 - 0.085 + 0.041 + 0.079 and $\Omega _{0m}=0.282\,(\pm 0.011)^{+0.011+0.023}_{-0.011-0.022}$ Ω 0 m = 0.282 ( ± 0.011 ) - 0.011 - 0.022 + 0.011 + 0.023 . According to the constraint results, it is shown that small constraint values of $\alpha $ α indicate that the strength of interaction is weak, and at $1\sigma $ 1 σ confidence level the non-interacting cosmological constant model can not be excluded.     

Phantom cosmologies from the simplest parameterization of the DE model using observational data in a BI type universe

To scrutinize the nature of dark energy,many equations of state have been proposed.In this context,we examine the simplest parameterization of the equation of state parameter of dark energy in an anisotropic Bianchi type I universe compared with the ΛCDM model.Using different combinations of data samples,including Pantheon and Pantheon + H(z),alongside applying the minimization of the χ² function of the distance modulus of data samples,we obtain the constrained values of cosmographic ...     

Analogue model for an expanding universe

Over the last few years numerous papers concerning analogue models of (and for) gravity have been published. It has been shown that the dynamical equations for several condensed matter systems, (e.g., simple fluids, superfluids, Bose–Einstein condensates with a sink or a vortex) permit perturbations that are governed by the same type of wave equation as light in a curved spacetime—the curved-space d'Alembertian equation. More recently, several papers have been released which use analogue models to simulate the expanding universe. In this article the de Sitter universe will be simulated using a freely expanding three-dimensional Bose–Einstein condensate with spherical symmetry. Initially the condensate is in a harmonic trap, which is then suddenly switched off. At the same time a small perturbation is injected in the center of the condensate cloud. The motion of this perturbation in the expanding condensate will be discussed, and (after some transformations) the similarity of this system to an expanding universe will be exhibited. Finally, we briefly discuss questions of experimental observability of these effects. Presented at the 4th Australasian conference on General Relativity and Cosmology, Monash University, Melbourne, 7–9 January 2004     

Thermodynamical interpretation of the interacting holographic dark energy model in a non-flat universe

Motivated by the recent work of Wang, Lin, Pavon, and Abdalla [B. Wang, C.Y. Lin, D. Pavon, E. Abdalla, Phys. Lett. B 662 (2008) 1, arXiv: 0711.2214 [hep-th]], we generalize their work to the non-flat case. In particular, we provide a thermodynamical interpretation for the holographic dark energy model in a non-flat universe. For this case, the characteristic length is no more the radius of the event horizon (RE$R_E$) but the event horizon radius as measured from the sphere of the horizon (L  ). Furthermore, when interaction between the dark components of the holographic dark energy model in the non-flat universe is present its thermodynamical interpretation changes by a stable thermal fluctuation. A relation between the interaction term of the dark components and this thermal fluctuation is obtained. In the limiting case of a flat universe, i.e. k=0$k=0$, all results given in [B. Wang, C.Y. Lin, D. Pavon, E. Abdalla, Phys. Lett. B 662 (2008) 1, arXiv: 0711.2214 [hep-th]] are obtained.