Dynamical behaviors of FRW universe containing a positive/negative potential scalar field in loop quantum cosmology

The dynamical behaviors of FRW Universe containing a posivive/negative potential scalar field in loop quantum cosmology scenario are discussed. The method of the phase-plane analysis is used to investigate the stability of the Universe. It is found that the stability properties in this situation are quite different from the classical cosmology case. For a positive potential scalar field coupled with a barotropic fluid, the cosmological autonomous system has five fixed points and one of them is stable if the adiabatic index $\gamma $ satisfies $0<\gamma <2$ . This leads to the fact that the universe just have one bounce point instead of the singularity which lies in the quantum dominated area and it is caused by the quantum geometry effect. There are four fixed points if one considers a scalar field with a negative potential, but none of them is stable. Therefore, the universe has two kinds of bounce points, one is caused by the quantum geometry effect and the other is caused by the negative potential, the Universe may enter a classical re-collapse after the quantum bounce. This hints that the spatially flat FRW Universe containing a negative potential scalar field is cyclic.     

No-boundary measure of the universe

We consider the no-boundary proposal for homogeneous isotropic closed universes with a cosmological constant and a scalar field with a quadratic potential. In the semiclassical limit, it predicts classical behavior at late times if the scalar field is large enough. The classical histories may be singular in the past or bounce at a finite radius. This probability measure selects inflationary histories but is biased towards small numbers of e-foldings N. However, to obtain the probability of our observations in our past light cone these probabilities should be multiplied by exp(3N). This volume weighting is similar to that in eternal inflation. In a landscape potential, it would predict that the Universe underwent a large amount of inflation and could have always been semiclassical.     

Big bounce from spin and torsion

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density e μ gT⁴{\epsilon \propto gT^4} was on the order of n²/m_Pl²{n^2/m_{\rm Pl}^2} (in natural units), where n μ gT³{n \propto gT^3} is the fermion number density and g is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles (g ≈ 100), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about 10³² times smaller than its present value, giving ≈ 50 μm. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.     

Quantum nature of the big bang

Some long-standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big-bang singularity in loop quantum cosmology are significantly extended as follows: (i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the "emergent time" idea; (ii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously; (iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the nonperturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime.     

Quantum bounce and cosmic recall

Loop quantum cosmology predicts that, in simple models, the big bang is replaced by a quantum bounce. A natural question is whether the universe retains, after the bounce, its memory about the previous epoch. More precisely, does the Universe retain various properties of the state after evolving unitarily through the bounce, or does it suffer from recently suggested cosmic amnesia? We show that this issue can be answered unambiguously at least within an exactly solvable model. A semiclassical state at late times on one side of the bounce, peaked on a pair of canonically conjugate variables, strongly bounds the fluctuations on the other side, implying semiclassicality. For a model universe growing to 1 megaparsec, the change in relative fluctuation across the bounce is less than 10(-56) (becoming smaller for larger universes). The universe maintains (an almost) total recall.     

Genericness of inflation in isotropic loop quantum cosmology

Nonperturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector are already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semidefinite potentials it is always possible to choose, without fine-tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with the generic occurrence of bounce at small volumes, particle horizon is absent, thus eliminating the horizon problem of the standard big bang model.     

How quantum is the big bang?

When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.     

Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may look like. This, then, has to be taken into account for effective equations which describe the evolution properly and can be used for further phenomenological investigations. Here, we provide the first analysis with interacting matter with new effective equations valid for weak self-interactions or small masses. They differ from the free scalar equations by crucial terms and have an important influence on the bounce and the space-time around it. Especially the role of squeezed states, which have often been overlooked in this context, is highlighted. The presence of a bounce is proven for uncorrelated states, but as squeezing is a dynamical property and may change in time, further work is required for a general conclusion.     

Expanding and collapsing scalar field thin shell

This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr?m geometry. The Israel junction conditions between Reissner-Nordstr?m spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien–Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when p is an explicit function of R. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.     

Generalized Exact Cosmologies with Interacting Yang-Mills and Nonlinear Scalar Fields

It has been shown that the set of the Einstein-Yang-Mills equations and the nonlinear scalar field have generalized solutions with a homogeneous scalar field, which interacts with the YM field in the Friedmann Universe.     

Model for a Universe described by a non-minimally coupled scalar field and interacting dark matter

In this work the evolution of a Universe model is investigated where a scalar field, non-minimally coupled to space-time curvature, plays the role of quintessence and drives the Universe to a present accelerated expansion. A non-relativistic dark matter constituent that interacts directly with dark energy is also considered, where the dark matter particle mass is assumed to be proportional to the value of the scalar field. Two models for dark matter pressure are considered: the usual one, pressureless, and another that comes from a thermodynamic theory and relates the pressure with the coupling between the scalar field and the curvature scalar. Although the model has a strong dependence on the initial conditions, it is shown that the mixture consisted of dark components plus baryonic matter and radiation can reproduce the expected red-shift behavior of the deceleration parameter, density parameters and luminosity distance.     

A Quantum Cosmological Bianchi I Model with Interacting Spinor and Scalar Fields

A Bianchi I model of the Universe filled with interacting nonlinear spinor and scalar fields is studied within quantum geometrodynamics. Three types of interaction are considered: gradient, Yukawa, and axion ones. For massless fermion fields, the variables in the Wheeler – de Witt equation will separate. The solution can be interpreted using a two-component perfect liquid. One component corresponds to a massless scalar field, while the other – to a nonlinear spinor field. The interaction between the spinor and scalar fields can lead to elimination of singularity of the wave function. There is a possibility of existence of a discrete spectrum of the quantum Universe, as well as tunneling from the region with a rigorous equation of state to the region of the de Sitter vacuum.     

Acceleration Field of a Universe Modeled as a Mixture of Scalar and Matter Fields

A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon from the string theory) and a matter field (classical particles) is analyzed. The particles are created at the expense of the gravitational energy through an irreversible process whereas the scalar field is supposed to interact only with itself and to be minimally coupled with the gravitational field. The irreversible processes of particle creation are related to the non-equilibrium pressure within the framework of the extended (causal or second-order) thermodynamic theory. The scalar field (inflaton or tachyon) is described by an exponential potential density added by a parameter which represents its asymptotic value and can be interpreted as the vacuum energy. This model can simulate three phases of the acceleration field of the Universe, namely, (a) an inflationary epoch with a positive acceleration followed by a decrease of the acceleration field towards zero, (b) a past decelerated period where the acceleration field decreases to a maximum negative value followed by an increase towards zero, and (c) a present accelerated epoch. For the energy densities there exist also three distinct epochs which begin with a scalar field dominated period followed by a matter field dominated epoch and coming back to a scalar field dominated phase.     

Some exact solutions of magnetized viscous model in string cosmology

In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.     

A higher-dimensional Bianchi type-I inflationary Universe in general relativity

A five-dimensional Bianchi type-I inflationary Universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary Universe, a flat region in which the potential V is constant is considered. Some physical and kinematical properties of the Universe are also discussed.     

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the Big Bang could be a result of the first-order phase transition driven by a change in the scalar curvature of the 4D spacetime in an expanding cold Universe filled with a nonlinear scalar field φ and neutral matter with an equation of state p = νε (where p and ε are the pressure and energy density of the matter, respectively). We consider the Lagrangian of a scalar field with nonlinearity φ⁴ in a curved spacetime that, along with the term–ξR|φ|² quadratic in φ (where ξ is the interaction constant between the scalar and gravitational fields and R is the scalar curvature), contains the term ξRφ₀(φ + φ⁺) linear in φ, where φ₀ is the vacuum mean of the scalar field amplitude. As a consequence, the condition for the existence of extrema of the scalar-field potential energy is reduced to an equation cubic in φ. Provided that ν > 1/3, the scalar curvature R = [κ(3ν–1)ε–4Λ] (where κ and Λ are Einstein’s gravitational and cosmological constants, respectively) decreases with decreasing ε as the Universe expands, and a first-order phase transition in variable “external field” parameter proportional to R occurs at some critical value R _c < 0. Under certain conditions, the critical radius of the early Universe at the point of the first-order phase transition can reach an arbitrary large value, so that this scenario of unrestricted “inflation” of the Universe may be called “hyperinflation.” After the passage through the phase-transition point, the scalar-field potential energy should be rapidly released, which must lead to strong heating of the Universe, playing the role of the Big Bang.     

Constraints on strongly coupled chameleon fields from the experimental test of the weak equivalence principle for the neutron

The chameleon scalar field is considered as a possible cause of accelerated expansion of the Universe. The chameleon field induces an interaction potential between particle and massive body. Previous experiments with falling cold neutrons intended to measure the neutron coherent scattering lengths and verification of the weak equivalence principle for the neutron are used to constrain the parameters characterizing the strength of the scalar chameleon fields.     

Einstein-Rosen inflationary Universe in general relativity

Einstein-Rosen inflationary Universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary Universe, we have considered a flat region in which the potential V is constant. Some physical properties of the model are discussed.     

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.     

Chameleon field and the late time acceleration of the Universe

In the present work, it is shown that a chameleon scalar field having a non-minimal coupling with dark matter can give rise to a smooth transition from a decelerated to an accelerated phase of expansion for the Universe. It is surprising to note that the coupling with the chameleon scalar field hardly affects the evolution of the dark matter sector, which still redshifts as a ^⃛.