Pre-inflationary Stage Research Articles

Suppression of the long-wavelength CMB spectrum from the Hartle–Hawking wave function in the Starobinsky-type inflation model

Abstract The lack of correlations on the large scale cosmic microwave background (CMB) anisotropy provides a potential window to probe beyond the standard inflationary scenario. In this paper, we investigate the primordial power spectrum based on the Hartle–Hawking (HH) no-boundary proposal for a homogeneous, isotropic, and spatially-closed universe that leads to Starobinsky-type inflation after the classicalization. While we found that there is no suppression at large scales in the standard R + R 2 theory, we also found that it is possible to sufficiently suppress the large-scale power spectrum if a pre-inflationary stage is introduced to the Starobinsky-type model. In addition, such a pre-inflationary stage will be helpful to explain the preference of large e -foldings of the HH proposal. We calculate the C l T T correlation function and show that our proposal gives a better fit to the Planck CMB data. This suggests that our universe might have begun with a compact HH state with a small positive curvature.

Observational Consequences of an Interacting Multiverse

The observability of the multiverse is at the very root of its physical significance as a scientific proposal. In this conference we present, within the third quantization formalism, an interacting scheme between the wave functions of different universes and analyze the effects of some particular values of the coupling function. One of the main consequences of the interaction between universes can be the appearance of a pre-inflationary stage in the evolution of the universes that might leave observable consequences in the properties of the CMB.

Thermal gravitational-wave background in the general pre-inflationary scenario

We investigate the primordial gravitational waves (PGWs) in the general scenario where the inflation is preceded by a pre-inflationary stage with the effective equation of state w. Comparing with the results in the usual inflationary models, the power spectrum of PGWs is modified in two aspects: one is the mixture of the perturbation modes caused by he presence of the pre-inflationary period, and the other is the thermal initial state formed at the Planck era of the early Universe. By investigating the observational imprints of these modifications on the B-mode polarization of cosmic microwave background (CMB) radiation, we obtain the constraints on the conformal temperature of the thermal gravitational-wave background T<5.01× 10−4 Mpc−1 and a tensor-to-scalar ratio r<0.084 (95% confident level), which follows the bounds on total number of e-folds N>63.5 for the model with w=1/3, and N>65.7 for that with w=1. By taking into account various noises and the foreground radiations, we forecast the detection possibility of the thermal gravitational-wave background by the future CMBPol mission, and find that if r>0.01, the detection is possible as long as T>1.5× 10−4 Mpc−1. However, the effect of different w is quite small, and it seems impossible to determine its value from the potential observations of CMBPol mission.

Scalar perturbation produced at the pre-inflationary stage in Eddington-inspired Born–Infeld gravity

We investigate the scalar perturbation produced at the pre-inflationary stage driven by a massive scalar field in Eddington-inspired Born–Infeld gravity. The scalar power spectrum exhibits a peculiar rise for low k-modes. The tensor-to-scalar ratio can be significantly lowered compared with that in the standard chaotic inflation model in general relativity. This result is very affirmative considering the recent dispute on the detection of gravitational wave radiation between PLANCK and BICEP2.

Discrete modes in gravitational waves from the big-bang

We develop a new approach to gravitational waves in which the Einstein equations are governed by the cosmological constant which is related to the existence of a manifold which is closed. We study an example in which the matter Lagrangian is described by the scalar (inflaton) field. There are only three dynamical solutions. In one of them the universe is initially static but begins to increase until an inflationary stage. We calculate the dynamics of GW in this primordial pre-inflationary stage of the universe. We found that there should be an infinite number of polarization modes in order to the fields can be quantized. Finally, we calculate the energy density due to the gravitational waves.

Locally rotationally symmetric (LRS) Bianchi type II string dust viscous fluid cosmological models in Lyra geometry

In the present study, a locally rotationally symmetric Bianchi type II string dust cosmological model with varying bulk viscosity in the framework of Lyra geometry is investigated. To get the deterministic solution, we have assumed that shear (σ) is proportional to the expansion (θ) and ζθ = constant, where ζ is the coefficient of bulk viscosity. The ansatz ζθ = constant, was found to coincide with the occurrence of Little Rip (LR) cosmology using Friedmann–Robertson–Walker metric (Breviket al. Phys. Rev. D, 84, 103508-1-6 (2011)). The model describes the pre-inflationary stage of the universe. The presence of viscosity leads to inflationary-like solutions. Anisotropy is maintained because of the presence of strings. The presence of bulk viscosity prevents the matter density from vanishing. In a special case, the model represents the isotropy of the universe. The universe passes through a decelerating stage to an accelerating phase, which is in agreement with Ries et al.’s (Astrophys. J. 607, 665 (2004). doi:10.1086/383612 ) type Ia supernovae astronomical observations. The displacement vector (β) of Lyra geometry is a decreasing function of time analogous to the cosmological constant (Λ) of general relativity. We have attempted to explore the possibility of constructing a string dust viscous fluid cosmological model in Bianchi type II space–time with displacement vector (β) in Lyra geometry using the geometric condition that shear is proportional to expansion.

No-hair conjectures, primordial shear, and protoinflationary initial conditions

Anisotropic inflationary background geometries are analyzed in the context of an extended gauge action where the electric and magnetic susceptibilities are not bound to coincide and depend on the inflaton field. After deriving various classes of solutions with electric and magnetic hairs, we discuss the problem of the initial boundary conditions of the shear parameter and consider a globally neutral plasma as a possible relic of a preinflationary stage of expansion. While electric hairs are washed out by the finite value of the protoinflationary conductivity, magnetic hairs can persist and introduce a tiny amount of shear causing a different inflationary rate of expansion along orthogonal spatial directions. The plasma interactions are a necessary criterion to discriminate between physical and unphysical initial conditions but they are not strictly sufficient to warrant the stability of a given magnetic solution.

Precursor of Inflation

We investigate a nonsingular initial state of the Universe which leads to inflation naturally. The model is described by a scalar field with a quadratic potential in Eddington-inspired Born-Infeld gravity. The curvature of this initial state is given by the mass scale of the scalar field, which is much smaller than the Planck scale. Therefore, in this model, quantum gravity is not necessary in understanding this preinflationary stage, no matter how large the energy density becomes. The initial state in this model evolves eventually to a long inflationary period which is similar to the usual chaotic inflation.

Weyl invariance and the conductivity of the protoinflationary plasma

We consider a globally neutral Lorentzian plasma as a possible remnant of a preinflationary stage of expansion and pose the problem of the suitable initial conditions for the evolution of the large-scale electromagnetic inhomogeneities. During the protoinflationary regime, the Weyl invariance of the Ohmic current guarantees that the comoving conductivity is approximately constant. The subsequent breaking of Weyl invariance by the masses of the charge carriers drives the conductivity to zero. The newly derived conducting initial conditions for the amplification of large-scale magnetic fields are contrasted with the conventional vacuum initial conditions. It is shown, in a specific class of examples, that when the number of inflationary e-folds is close to minimal, the effects of the conducting initial conditions cannot be neglected.

LARGE SCALE ANISOTROPY DUE TO PRE-INFLATIONARY PHASE OF COSMIC EVOLUTION

We show that perturbations generated during the anisotropic pre-inflationary stage of cosmic evolution may affect cosmological observations today for a certain range of parameters. Due to the anisotropic nature of the universe during such early times, it might explain some of the observed signals of large scale anisotropy. In particular, we argue that the alignment of CMB quadrupole and octopole may be explained by the Sachs–Wolfe effect due to the large scale anisotropic modes from very early times of cosmological evolution. We also comment on how the observed dipole modulation of CMB power may be explained within this framework.

Bouncing braneworld cosmologies and initial conditions to inflation

We examine the full nonlinear dynamics of closed Friedmann-Robertson-Walker universes in the framework of $D$-branes formalism. Friedmann equations contain additional terms arising from the bulk-brane interaction that provide a concrete model for nonsingular bounces in the early phase of the Universe. We construct nonsingular cosmological scenarios sourced with perfect fluids and a massive inflaton field, which are past eternal, oscillatory, and may emerge into an inflationary phase due to nonlinear resonance mechanisms. Oscillatory behavior becomes metastable when the system is driven into a resonance window of the parameter space of the models, with consequent breakup of KAM tori that trap the inflaton, leading the Universe to the inflationary regime. A construction of the resonance chart of the models is made. Resonance windows are labeled by an integer $n\ensuremath{\ge}2$, where $n$ is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom. They are typically small compared to the volume of the whole parameter space, and we examine the constraints imposed by nonlinear resonance in the physical domain of initial configurations so that inflation may be realized. We discuss the complex dynamics arising in this preinflationary stage, the structural stability of the resonance pattern and some of its possible imprints in the physics of inflation. We also approach the issue of initial configurations that are connected to a chaotic exit to inflation. Pure scalar field bouncing cosmologies are constructed. Contrary to models with perfect fluid components, the structure of the bouncing dynamics is highly sensitive to the initial amplitude and to the mass of the inflaton; dynamical potential barriers allowing for bounces appear as a new feature of the dynamics. We argue that if our actual Universe is a brane inflated by a parametric resonance mechanism triggered by the inflaton, some observable cosmological parameters should then have a signature of the particular resonance from which the brane inflated.

Fine-tuning solution for hybrid inflation in dissipative chaotic dynamics

We study the presence of chaotic behavior in phase space in the preinflationary stage of hybrid inflation models. This is closely related to the problem of initial conditions associated with these inflationary types of model. We then show how an expected dissipative dynamics of fields just before the onset of inflation can solve or ease considerably the problem of initial conditions, driving the system naturally toward inflation. The chaotic behavior of the corresponding dynamical system is studied by computation of the fractal dimension of the boundary in phase space separating inflationary from noninflationary trajectories. The fractal dimension for this boundary is determined as a function of the dissipation coefficients appearing in the effective equations of motion for the fields.

Causality and cosmic inflation

In the context of inflationary models with a pre-inflationary stage, in which the Einstein equations are obeyed, the weak energy condition is satisfied, and spacetime topology is trivial, we argue that homogeneity on super-Hubble scales must be assumed as an initial condition. Models in which inflation arises from field dynamics in a Friedman-Robertson-Walker background fall into this class but models in which inflation originates at the Planck epoch, {\it eg.} chaotic inflation, may evade this conclusion. Our arguments rest on causality and general relativistic constraints on the structure of spacetime. We discuss modifications to existing scenarios that may avoid the need for initial large-scale homogeneity.

Past-instability conjecture and cosmological attractors in generalized isotropic universes.

We conjecture that all homogeneous and isotropic physically reasonable cosmological solutions of general relativity theory are in general past unstable in the generalized framework of higher order gravity theories. In this respect we provide a detailed perturbation analysis of the most interesting of these solutions and find that the results support our conjecture. We show that, in general, radiation solutions of higher order gravity are nonperturbative (bouncing or singular) as we approach the singularity in the past. A well-known flat radiation solution of quadratic gravity is shown not to be an attractor as t\ensuremath{\rightarrow}0. We prove that the quasiexponential phase in higher order gravity theories cannot be an attractor to solutions which may describe a preinflationary stage in these theories. However, this last conclusion may be altered if additional conditions are imposed and this situation is similar to the stability properties of the Starobinski inflationary solution. Other examples of a nongeneric-type in acordance with our conjecture are discussed and these include the Milne universe.

Prohibition of large inhomogeneity in the preinflationary stage.

We examine the spherically symmetric and asymptotically spatially flat inhomogenous initial data of an inflaton field to see its effect on the evolution of space-time. We search for the apparent horizon in those initial data and show the relation of the scale of inhomogeneity and the amplitude of the inflaton field to the formation of a horizon. We find that for a certain range of Hubble constant there is no regular initial condition but the bag of gold singularity appears if the inhomogeneity of the inflaton field is large enough ($\ensuremath{\delta}\ensuremath{\varphi}\ensuremath{\gtrsim}{m}_{\mathrm{Pl}}$).