The energy-momentum tensor coming from one-parameter effective Yang- Mills theory is here used to describe the matter-energy content of the homogeneous and isotropic Friedmann cosmology in its early stages. The behavior of all solutions is examined. Particularly, it is shown that only solutions corresponding to an open model allow the universe to evolve into an accelerated expansion. This result appears as a possible mechanism for an inflationary phase produced by a vector field. Further, depending on the value of some parameters characterizing the system, the resulting models are classified as singular or nonsingular.
The big bang singularity of the expanding-universe Friedmann solution of the Einstein gravitational field equation can be regularized by the introduction of a degenerate metric and a nonzero length scale $b$. The result is a nonsingular bounce of the cosmic scale factor with a contracting prebounce phase and an expanding postbounce phase. The corresponding maximum values of the curvature and the energy density occur at the moment of the bounce and are proportional to powers of $1/b$. This article presents a detailed calculation of the dynamics of such a nonsingular bounce. In addition, a compa…
A short introduction to cosmological models that go from an era of accelerated collapse to an expanding era without displaying a singularity is presented.
We study spatially homogeneous and isotropic solutions to the equations of motion derived from dilaton gravity, in the presence of a special combination of higher derivative terms in the gravitational action. All solutions are nonsingular. For initial conditions resembling those in the pre-big-bang scenario, there are solutions corresponding to a spatially flat, bouncing Universe originating in a dilaton-dominated contracting phase and emerging as an expanding Friedmann Universe.
Making use of the T-duality symmetry of superstring theory, and of the double geometry from Double Field Theory, we argue that cosmological singularities of a homogeneous and isotropic universe disappear. In fact, an apparent big bang singularity in Einstein gravity corresponds to a universe expanding to infinite size in the dual dimensions.
We propose a mechanism borrowed from string theory which yields a non-singular transition from a phase of Ekpyrotic contraction to the expanding phase of Standard Big Bang cosmology. The same mechanism converts the initial vacuum spectrum of cosmological fluctuations before the bounce into a scale-invariant one, and also changes the spectrum of gravitational waves into an almost scale-invariant one. The scalar and tensor tilts are predicted to be the same, in contrast to the predictions from the "String Gas Cosmology" scenario. The amplitude of the gravitational wave spectrum depends on the ra…
The observed value of the Higgs mass indicates an instability of the Higgs scalar at large energy scales, and hence also at large field values. In the context of early universe cosmology, this is often considered to lead to problems. Here we point out that we can use the instability of the Higgs field to generate an Ekpyrotic phase of contraction. In the context of string theory it is possible that at very high energy densities extra states become massless, leading to an S-brane which leads to the transition between a contracting phase in the past and the current expanding phase. Thus, the Hig…
We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-dilaton theory. Like their spherically symmetric counterparts, these solutions are nonsingular and asymptotically flat. The solutions are characterized by the winding number n and the node number k of the gauge field functions. For fixed n with increasing k the solutions tend to ``extremal'' Einstein-Maxwell-dilaton black holes with n units of magnetic charge.
It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is never…
We consider an eight-dimensional Einstein-Yang-Mills theory to explore whether Yang-Mills instantons formed in extra dimensions can induce the dynamical instability of our four-dimensional spacetime. We show that the Yang-Mills instantons in extra dimensions can trigger the expansion of our universe in four-dimensional spacetime as well as the dynamical compactification of extra dimensions. We also discuss a possibility to realize a reheating mechanism via the quantum back-reaction from the contracting tiny internal space with a smeared instanton.
A Nonsingular Logarithmic Bouncing Cosmology in $f(R,T)$ Gravity with Thermodynamic Viability
Maharaja Agrasen University（玛哈拉贾阿格拉森大学）；S.P.M. Science and Gilani Arts, Commerce College（SPM科学与吉拉尼艺术商业学院）；Pacif Institute of Cosmology and Selfology (PICS)（太平洋宇宙学与自我学研究所（PICS））；L N Gumilyov Eurasian National University（L.N.古米廖夫欧亚国立大学）；Sharda University（沙尔达大学）
The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein-Cartan cosmology, the Milne-McCrea universe with quantum corrections and a non-flat universe with bulk viscosity. Within these models, we probe into the initial singularity by using different techniques. Several nonsingular universes emerge, one of the possibilities being a static non-expanding and stable Einstein univ…
We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields which describe traversable wormholes (with flat and AdS asymptotics) and regular black holes, in particular, black universes. A black universe is a nonsingular black hole where, beyond the horizon, instead of a singularity, there is an expanding, asymptotically isotropic universe. The scalar field in these solutions is phantom (i.e., its kinetic energy is negative), minimally coupled to gravity and has a nonzero self-interaction potential. The …
Analyzing quantum cosmological scenarios containing one scalar field with exponential potential, we have obtained a universe model which realizes a classical dust contraction from very large scales, the initial repeller of the model, and moves to a stiff matter contraction near the singularity, which is avoided due to a quantum bounce. The universe is then launched in a stiff matter expanding phase, which then moves to a dark energy era, finally returning to the dust expanding phase, the final attractor of the model. Hence one has obtained a nonsingular cosmological model where a single scalar…
We review the general features of nonsingular universes ({\em i.e.} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations.
Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries.
The theory of general relativity is reformed to a genuine Yang-Mills gauge theory of the Poincaré group for gravity. Several pathologies of the conventional theory are thus removed, but not every GR vacuum satisfies the Y-M equations. The sector of GR solutions which survive is fully classified and it is found to include the Schwarzschild black hole. Two other solutions presented here have no GR counterpart and they describe expanding Friedmann universes with torsion which vanishes only asymptotically. They are discussed along with novel theoretical possibilities, such as a well-defined energy…
We examine an extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate Yang-Mills fields. Inhomogeneous perturbations about a homogeneous, isotropic minisuperspace background model are considered, by expanding the Yang-Mills fields in harmonics of the spatial directions which are taken to be three-spheres. The expansions are made explicit for $SO(N)$ gauge fields thereby obtaining formulae compatible with the formalism conventionally used in quantum cosmology. We apply these resul…
An oscillating universe cycles through a series of expansions and contractions. We propose a model in which ``phantom'' energy with a supernegative pressure ($p < - ρ$) grows rapidly and dominates the late-time expanding phase. The universe's energy density is then so large that the effects of quantum gravity are important at both the beginning and the end of each expansion (or contraction). The bounce can be caused by high energy modifications to the Friedmann equation governing the expansion of the universe, which make the cosmology nonsingular. The classic black hole overproduction of oscil…
We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions ar…
We analyze the early-time isotropic cosmology in the so-called energy-momentum-squared gravity (EMSG). In this theory, a $T_{μν}T^{μν}$ term is added to the Einstein-Hilbert action, which has been shown to replace the initial singularity by a regular bounce. We show that this is not the case, and the bouncing solution obtained does not describe our Universe since it belongs to a different solution branch. The solution branch that corresponds to our Universe, while nonsingular, is geodesically incomplete. We analyze the conditions for having viable regular-bouncing solutions in a general class …
General relativity with fermions has two independent symmetries: general coordinate invariance and local Lorentz invariance. General coordinate invariance is implemented by the Levi-Civita connection and by Cartan's tetrads both of which have as their action the Einstein-Hilbert action. It is suggested here that local Lorentz invariance is implemented not by a combination of the Levi-Civita connection and Cartan's tetrads known as the spin connection, but by independent Lorentz bosons L_i that gauge the Lorentz group, that couple to fermions like Yang-Mills fields, and that have their own Yang…
An oscillating universe cycles through a series of expansions and contractions. We propose a model in which ``phantom'' energy with $p < -ρ$ grows rapidly and dominates the late-time expanding phase. The universe's energy density is so large that the effects of quantum gravity are important at both the beginning and the end of each expansion (or contraction). The bounce can be caused by high energy modifications to the Friedmann equation, which make the cosmology nonsingular. The classic black hole overproduction of oscillating universes is resolved due to their destruction by the phantom ener…
In this paper we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian along with the restriction to homogeneity allows for an anomaly free effective quantization. In particular we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fiel…
In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein--Yang--Mills formulation. A brief outlook of existing studies of cosmological Yang--Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well …
We study the Einstein Yang-Mills Higgs equations in the $SO(3)$ representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in…
Twistor space constructions and actions are given for full Yang-Mills and conformal gravity using almost complex structures that are not, in general, integrable. These are used as the basis of a derivation of the twistor-string generating functionals for tree level perturbative scattering amplitudes of Yang-Mills and conformal gravity. The derivation follows by expanding and resumming the classical approximation to the path integral obtained from the twistor action. It provides a basis for exploring whether the equivalence can be made to extend beyond tree level and allows one to disentangle c…
The coincidence problem is studied for the dark energy model of effective Yang-Mills condensate in a flat expanding universe during the matter-dominated stage. The YMC energy $ρ_y(t)$ is taken to represent the dark energy, which is coupled either with the matter, or with both the matter and the radiation components. The effective YM Lagrangian is completely determined by quantum field theory up to 1-loop order. It is found that under very generic initial conditions and for a variety of forms of coupling, the existence of the scaling solution during the early stages and the subsequent exit from…
We consider homogeneous non-abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the…
