The problems of singularity particle horizon and flatness in quantum cosmology

Classical relativistic cosmology is known to have the space-time singularity as an inevitable feature. The standard big bang models have very small particle horizons in the early stages which make it difficult to understand the observed homogeneity in the universe. The relatively narrow range of the observed matter density in the neighbourhood of closure density requires highly fine tuning of the early universe. In this paper it is argued that these three problems can be satisfactorily resolved in quantum cosmology. It is shown that it is extremely unlikely that the universe evolved to the present state from quantum states with singularity and particle horizon. Similarly, it is shown that of all possible states the Robertson-Walker model of flat spatial sections is the most likely state for the universe to evolve out of a quantum fluctuation. To demonstrate these results a suitable formalism for quantum cosmology is first developed.     

Event horizon as alternative to cosmological singularity

The general relativistic equations for a homogeneous istoropic metric of the most general form are considered. It is concluded that an event horizon is a possible alternative to a cosmological singularity for “usual” matter. This conclusion is illustrated by the case of a flat spatial universe.     

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.     

A braneworld universe from colliding bubbles

Much work has been devoted to the phenomenology and cosmology of the so-called braneworld universe, where the (3+1)-dimensional universe familiar to us lies on a brane surrounded by a (4+1)-dimensional bulk spacetime that is essentially empty except for a negative cosmological constant and the various modes associated with gravity. For such a braneworld cosmology, the difficulty of justifying a set of preferred initial conditions inevitably arises. The various proposals for inflation restricted to the brane only partially explain the homogeneity and isotropy of the resulting braneworld universe because the three-dimensional homogeneity and isotropy of the bulk must be assumed a priori. In this Letter we propose a mechanism by which a brane surrounded by AdS space arises naturally in such a way that the homogeneity and isotropy of both the brane and the bulk are guaranteed. We postulate an initial false vacuum phase of (4+1)-dimensional de Sitter, or possibly Minkowski, space subsequently decaying to a true vacuum of anti-de Sitter space, assumed discretely degenerate. This decay takes place through bubble nucleation. When two bubbles of the true AdS vacuum eventually collide, because of the degeneracy of the true AdS vacuum, a brane (or domain wall) inevitably forms separating the two AdS phases. It is on this brane that we live. The SO(3,1) symmetry of the collision geometry ensures the three-dimensional spatial homogeneity and isotropy of the universe on the brane as well as of the bulk. In the semi-classical (→0) limit, this SO(3,1) symmetry is exact. We sketch how the leading quantum corrections translate into cosmological perturbations.     

Essay: An Alternative to Inflation

Inflationary models are generally credited with explaining the large scale homogeneity, isotropy, and flatness of our universe as well as accounting for the origin of structure (i.e., the deviations from exact homogeneity) in our universe. We argue that the explanations provided by inflation for the homogeneity, isotropy, and flatness of our universe are not satisfactory, and that a proper explanation of these features will require a much deeper understanding of the initial state of our universe. On the other hand, inflationary models are spectacularly successful in providing an explanation of the deviations from homogeneity. We point out here that the fundamental mechanism responsible for providing deviations from homogeneity—namely, the evolutionary behavior of quantum modes with wavelength larger than the Hubble radius—will operate whether or not inflation itself occurs. However, if inflation did not occur, one must directly confront the issue of the initial state of modes whose wavelength was larger than the Hubble radius at the time at which they were born. Under some simple hypotheses concerning the birth time and initial state of these modes (but without any fine tuning), it is shown that non-inflationary fluid models in the extremely early universe would result in the same density perturbation spectrum and amplitude as inflationary models, although there would be no slow roll enhancement of the scalar modes.     

Is There Paradox with Infinite Space?

We argue that an infinite universe should not necessarily be avoided on philosophical grounds. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing lives: not simply permutations of various quantum states. The super-exponential growth in the rules of a cellular automata is used as an example of surpassing the holography bound. We also critically question the notion that our universe could simply be a simulation in somebody else's computer.     

Dark energy,curvature, and cosmic coincidence

The fact that the energy densities of dark energy and matter are similar currently, known as the coincidence problem, is one of the main unsolved problems of cosmology. We present here a model in which a spatial curvature of the universe can lead to a transition in the present epoch from a matter dominated universe to a scaling dark energy dominance in a very natural way. In particular, we show that if the exponential potential of the dark energy field depends linearly on the spatial curvature density of a closed universe, the observed values of some cosmological parameters can be obtained assuming acceptable values for the present spatial curvature of the universe, and without fine tuning in the only parameter of the model. We also comment on possible variations of this model, and realistic scenarios in which it could arise.     

The CST bounce universe model——A parametric study

A bounce universe model with a scale-invariant and stable spectrum of primordial density perturbations was constructed using a consistent truncation of the D-brane dynamics from Type IIB string theory. A coupling was introduced between the tachyon field and the adjoint Higgs field on the D3-branes to lock the tachyon at the top of its potential hill and to model the bounce process,which is known as the Coupled Scalar and Tachyon Bounce(CSTB) Universe. The CSTB model has been shown to be ghost free,and it fulfils the null energy condition; in addition, it can also solve the Big Bang cosmic singularity problem. In this paper we conduct an extensive follow-up study of the parameter space of the CSTB model. In particular we are interested in the parameter values that can produce a single bounce to arrive at a radiation-dominated universe. We further establish that the CSTB universe is a viable alternative to inflation, as it can naturally produce a sufficient number of e-foldings in the locked inflation epoch and in the post-bounce expansion to overcome the four fundamental limitations of the Big Bang cosmology, which are flatness, horizon,homogeneity and singularity, resulting in a universe of the current size.     

Cosmological textures

The notions of phase transitions and causality, combined with the standard cosmological model, lead to the appearance of topological defects in the early universe. The most familiar types of defects are solitons, strings, and domain walls. Another type can exist when the spatial universe is compact. When these appear the whole universe takes on a winding number, and the consequences are quite amusing; for example, it is possible that a closed universe can mimic open or flat universes. Another possibility is that the vacuum has a nonabelian magnetic field strength at all points in the universe.This essay received the fifth award from the Gravity Research Foundation for the year 1986-Ed.Work supported by the Department of Energy, contract DE-AC03-76SF00515.     

Coleman-Weinberg theory and the new inflationary universe scenario

It is argued that a new inflationary universe scenario, which provides a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, can be naturally implemented in the context of grand unified theories of the type of the Coleman-Weinberg theory.     

Brans-Dicke cosmology with time-dependent cosmological term

Berman and Som's solution for a Brans-Dicke cosmology with time-dependent cosmological term, Robertson-Walker metric, perfect fluid, and perfect gas law of state solves the horizon, homogeneity, and isotropy problems without requiring any unnatural fine tuning in the very early universe, thus being an alternative model to inflation. The model also does not need recourse to quantum cosmology, and solves the flatness and magnetic monopole problems.     

Weak Gravity Conjecture and Holographic Dark Energy Model with Interaction and Spatial Curvature

In the paper, we apply the weak gravity conjecture to the holographic quintessence model of dark energy. Three different holographic dark energy models are considered: without the interaction in the non-flat universe; with interaction in the flat universe; with interaction in the non-flat universe. We find that
only in the models with the spatial curvature and interaction term proportional to the energy density of matter, it is possible for the weak gravity conjecture to be satisfied. And it seems that the weak gravity conjecture favors an open universe and the decaying of matter into dark energy.     

Emergent universe scenario via Quintom matter

The emergent universe scenario provides a possible alternative to bouncing cosmology to avoid the Big Bang singularity problem. In this Letter we study the realization of the emergent universe scenario by making use of Quintom matter with an equation of state across the cosmological constant boundary. We will show explicitly the analytic and numerical solutions of emergent universe in two Quintom models, which are a phenomenological fluid and a nonconventional spinor field, respectively.     

Analysis of the Topology of the Kerr Metric

The equations of motion of a test particle are integrated for the field of a rotating Kerr black hole (BH) (in accordance with [1]). Due to the lack of analytical transformations for the Carter–Penrose diagrams (CPDs) for the Kerr metric, the topology of the Kerr BH is studied by analytical investigation of the equations of motion. Transformations for the CPDs for the Reisner–Nordström metric are analyzed. The problem of boundary conditions for the Reisner–Nordström topology is analyzed. A solution to this problem of boundary conditions is proposed. It is proved that, in the Reisner–Nordström topology, only one way to go to another universe is possible. For the Kerr topology, the possibility of the existence of an alternative transition to another universe that does not coincide with the universe for the ordinary transition is found. This alternative transition is performed through a surface with a zero radial coordinate (zero radius). Initial conditions for the falling particle are found that correspond to an alternative transition to another universe. The tidal forces acting on a falling body in the Kerr metric are estimated, and the possibility of the transition of the body to other universes without being destroyed by tidal forces is proved.     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

Time's arrow in an oscillating universe

In view of the time-symmetric nature of the laws of physics, time asymmetry in the universe must arise from “initial” conditions. A fully time-symmetric oscillating model is presented which exists in a highly compressed, highly ordered state att=0 and evolves forward, in the thermodynamic sense, as ∣t ∣ increases. This model offers the possibility of accounting for several fundamental and puzzling aspects of our universe, including matter-antimatter asymmetry, the large entropy per baryon, primordial density enhancements sufficient to form galaxies, and large-scale homogeneity.     

A universe embedded in a five-dimensional flat space

Since a homogeneous isotropic universe can be embedded in a flat space of five dimensions, the question is considered under what conditions a more general universe can be embedded in a five-dimensional flat space. On the assumption that the deviation from homogeneity is small, it is found that real inhomogeneities can occur only in the case of a universe filled with radiation, or a universe containing at least two different substances with different equations of state, as for example radiation and matter. In the case of a radiation-filled universe, the inhomogeneities can be of arbitrary size and can conceivably be the precursors of galaxies.     

A new inflationary universe scenario: A possible solution of the horizon,flatness, homogeneity,isotropy and primordial monopole problems

A new inflationary universe scenario is suggested, which is free of the shortcomings of the previous one and provides a possible solution of the horizon, flatness, homogeneity and isotropy problems in cosmology, and also a solution of the primordial monopole problem in grand unified theories.