Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler–DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler–DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.     

Cosmographic study of the universe’s specific heat: a landscape for cosmology?

Non-abelian gauge field inflation is studied in the context of warm inflation scenario. We introduce this scenario as a mechanism that gives an end for gauge-flation model. Slow-roll parameters and perturbation parameters are presented for this model. We find the general conditions which are required for this model to be realizable in slow-roll approximation. We also develop our model in the context of intermediate and logamediate scenarios which are exact solutions of inflationary field equation in the Einstein theory. General expressions of slow-roll parameters, tensor–scalar ratio and scalar spectral index are presented in terms of inflaton field for these two cases. Our model is compatible with recent observational data from Planck satellite.     

Inflation with hyperbolic potential in the braneworld model

In this paper we study inflationary dynamics with a scalar field in an inverse coshyperbolic potential in the braneworld model. We note that a sufficient inflation may be obtained with the potential considering slow-roll approximation in the high energy limit. We determine the minimum values of the initial inflaton field required to obtain sufficient inflation and also determine the relevant inflationary parameters. The numerical values of spectral index of the scalar perturbation spectrum are determined by varying the number of e-foldings for different initial values of the inflaton field. The result obtained here is in good agreement with the current observational limits.      

Slow Modes in Passive Advection

The anomalous scaling in the Kraichnan model of advection of the passive scalar by a random velocity field with nonsmooth spatial behavior is traced to the presence of slow resonance-type collective modes of the stochastic evolution of fluid trajectories. We show that the slow modes are organized into infinite multiplets of descendants of the primary conserved modes. Their presence is linked to the nondeterministic behavior of the Lagrangian trajectories at high Reynolds numbers caused by the sensitive dependence on initial conditions within the viscous range where the velocity fields are more regular. Revisiting the Kraichnan model with smooth velocities, we describe the explicit solution for the stationary state of the scalar. The properties of the probability distribution function of the smeared scalar in this state are related to a quantum mechanical problem involving the Calogero–Sutherland Hamiltonian with a potential.Partially supported by NSF Grant DMS-9205296     

Quantum Creation of Closed Universe with Both Effects of Tunnelling and Well

A new “twice loose shoe“ method in the Wheeler-DeWitt equation of the universe wavefunction on the cosmic scale factor a and a scalar field φ is suggested,We analyze both the affections coming from the tunnelling effect of α and the potential well effect of φ,and obtain the initial values α0 about a primary closed universe which is born with the largest probability in the quantum manner,Our result is able to overcome the “large field difficulty“ of the universe quantum creation probabiltiy with only tunnelling effect.This new born universe has to suffer a startup of inflation,and then comes into the usual slow rolling inflation.The universe with the largest probalility maybe has a “gentle“ inflation of an eternal chaotic infltion.this depends on a new parameter q which describes the tunnelling character.     

Relativistie Cosmology With Quantum Corrections

Homogeneous isotropic, anisotropic, and inhomogeneous cosmological models are studied using Einstein's general relativity with quntum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The aemiclassical quantum eorrections of the scalar fields can avoid the initial cosmological singularity and they lead to an inflationary evolution stage as transient attrator. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation.     

A scalar field influenced Robertson-Walker model

We show that if a scalar field similar to the one mediating inflation is effective even now, then the Robertson-Walker model may have some interesting properties under certain conditions. In this case even a spatially closed universe may expand forever. A dust universe has alwaysq=1/2 for all values of spatial curvature. The critical density is also less than in the standard Robertson-Walker model.     

The unification of inflation and late-time acceleration in the frame of <Emphasis Type="Italic">k</Emphasis>-essence

By using the formulation of the reconstruction, we explicitly construct models of k-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the higher derivative terms, the solution describing the unification can be stable in the space of solutions, which makes the restriction for the initial condition relaxed. The higher derivative terms also eliminate tachyon. Therefore we can construct a model describing the time development, which cannot be realized by a usual inflaton or quintessence models of the canonical scalar field due to the instability or the existence of tachyon. We also propose a mechanism of the reheating by the quantum effects coming from the variation of the energy density of the scalar field.     

Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions, including the exponential expansion solutions of the scalar factor a for the bubble. We show that exponential expansion of the bubble continues with a short period, no matter whether the bubble is closed, flat, or open. The exponential expansion ends spontaneously when the bubble becomes large, that is, the scalar factor a of the bubble approaches a Planck length lp. We show that it is the quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.     

Cosmological perturbations in transient phantom inflation scenarios

We present a model of inflation where the inflaton is accommodated as a phantom field which exhibits an initial transient pole behavior and then decays into a quintessence field which is responsible for a radiation era. We must stress that the present unified model only deals with a single field and that the transition between the two eras is achieved in a smooth way, so the model does not suffer from the eternal inflation issue. We explore the conditions for the crossing of the phantom divide line within the inflationary era along with the structural stability of several critical points. We study the behavior of the phantom field within the slow-climb approximation along with the necessary conditions to have sufficient inflation. We also examine the model at the level of classical perturbations within the Newtonian gauge and determine the behavior of the gravitational potential, contrast density and perturbed field near the inflation stage and the subsequent radiation era.     

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.     

The evolution equation of the scalar field in the new inflationary universe

We derive an effective evolution equation for the scalar field driving inflation in the new inflationary universe. We use a perturbative calculation scheme proposed recently by Morikawa and Sasaki. The relevant initial conditions and dynamical constraints for the Coleman-Weinberg effective potential to appear in the evolution equation are discussed as well as the form of the particle production damping term. The validity of these conditions in the new inflationary universe model is discussed.     

An Explicit Family of Probability Measures for Passive Scalar Diffusion in a Random Flow

We explore the evolution of the probability density function (PDF) for an initially deterministic passive scalar diffusing in the presence of a uni-directional, white-noise Gaussian velocity field. For a spatially Gaussian initial profile we derive an exact spatio-temporal PDF for the scalar field renormalized by its spatial maximum. We use this problem as a test-bed for validating a numerical reconstruction procedure for the PDF via an inverse Laplace transform and orthogonal polynomial expansion. With the full PDF for a single Gaussian initial profile available, the orthogonal polynomial reconstruction procedure is carefully benchmarked, with special attentions to the singularities and the convergence criteria developed from the asymptotic study of the expansion coefficients, to motivate the use of different expansion schemes. Lastly, Monte-Carlo simulations stringently tested by the exact formulas for PDF’s and moments offer complete pictures of the spatio-temporal evolution of the scalar PDF’s for different initial data. Through these analyses, we identify how the random advection smooths the scalar PDF from an initial Dirac mass, to a measure with algebraic singularities at the extrema. Furthermore, the Péclet number is shown to be decisive in establishing the transition in the singularity structure of the PDF, from only one algebraic singularity at unit scalar values (small Péclet), to two algebraic singularities at both unit and zero scalar values (large Péclet).     

Mixmaster Universe Models with Matter in Jordan-Brans-Dicke Theory

We discuss the dynamics of anisotropic Bianchitype IX models in Jordan-Brans-Dicke cosmological theoryrendering the evolution of a universe model with closedspace near its beginning before inflation sets in. This paper displays how, when writtenin terms of reduced variables, the field equations allowstraightforward partial integration. The mean expansionH, the scalar field, and the three scale factors aregiven in terms of the volume expansion.     

The premature recollapse problem in closed inflationary universes

We discuss whether closed universe can avoid recollapsing before inflation ensues. We show that in general closed universe are not equivalent to recollapsing universes or positive curvature universes. Closed universes will not in general recollapse if the matter content violates the strong energy condition. This violation is also a necessary condition for inflation to occur. When the strong energy condition holds closed universes can only recollapse if they possess S³ or S²×S¹ spatial topology. Even when the topology is S³ and the strong energy condition holds it is not known whether anisotropic closed universes do all recollapse. We give examples to show that closed universes which begin in an extremely anisotropic state cannot recollapse until they are close to isotropy. This suggests that if the initial conditions prior to inflation are sufficiently anisotropic then the universe cannot recollapse until it has been isotropized by inflation. We also discuss the existence of inflation in isotropic cosmological models in R+R² lagrangian theories of gravity and extend a result of Whitt to show that such theories are conformally equivalent to general relativity plus a scalar field with an asymmetric potential.     

Warm tachyon inflation and swampland criteria

In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.     

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.     

Non-gravitating scalar field in the FRW background

We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy–momentum tensor of the scalar field ϕ vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy–momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy–momentum tensor. The space dependent solution therefore is not non-gravitating. Our conclusion is applicable to other space–time dependent non-gravitating solutions as well. We study hybrid inflation scenario in this model when purely time dependent non-gravitating field is coupled to another scalar field χ.     

Warm Gauge-Flation with General Dissipative Coefficient

In this work, we study the effects of generalized dissipative coefficient on the slow-roll inflation driven by non-Abelian gauge field minimally coupled to gravity. The dynamics of warm intermediate and logamediate inflationary models during weak and strong dissipative regimes is analyzed. In both cases, we explore effective scalar potential, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio under slow-roll conditions. We conclude that our gauge-flationary model with generalized dissipative coefficient remains consistent with the recent data for dissipative parameter m = 3 and m = 1 for weak and strong dissipative eras, respectively.     

Inflation,large scale structure and particle physics

We review experimental and theoretical developments in inflation and its application to structure formation, including the curvaton idea. We then discuss a particle physics model of supersymmetric hybrid inflation at the intermediate scale in which the Higgs scalar field is responsible for large scale structure, show how such a theory is completely natural in the framework extra dimensions with an intermediate string scale.