Exact inhomogeneous models of cosmological inflation

Exact spherically symmetric solutions of the Einstein equations with quasi-vacuum source p = −ε are found in the form of spatially inhomogeneous Tolman metrics describing the inflationary stage of the evolution of the universe. Ul’yanov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 3–7, February, 1998.     

Decay of cosmological constant in self-consistent inflation

The symmetric vacuum state in gauge theories with spontaneous symmetry breaking is symmetric in both internal and space-time variables. We consider this vacuum state as a Bose condensate of physical Higgs particles, defined over an asymmetric vacuum state, and identify the energy density of their self-interaction with the cosmological constant in the Einstein equation. In this picture, spontaneous symmetry breaking proceeds as decay. Decoherence of coherent oscillations of a scalar field in the course of decay provides the effective mechanism for damping of coherent oscillations, leading to the regime of slow evaporation of a Bose condensate. This mechanism is responsible for self-consistent inflation without fine-tuning of the potential parameters. The physical self-consistency in this model is provided by incorporating the origin of the cosmological constant in the dynamics of spontaneous breaking of particle symmetries. Received: 28 September 2000 / Revised version: 16 January 2001 / Published online: 25 April 2001     

Natural chaotic inflation in supergravity

We propose a chaotic inflation model in supergravity. In the model the Kahler potential has a Nambu-Goldstone-type shift symmetry of the inflaton chiral multiplet which ensures the flatness of the inflaton potential beyond the Planck scale. We show that chaotic inflation naturally takes place by introducing a small breaking term of the shift symmetry in the superpotential. This may open a new branch of model building for inflationary cosmology in the framework of supergravity.     

On a nonlinear electrodynamics generated via gravitational nonminimal coupling

A nonlinear electrodynamics is generated via graviational nonminimal coupling. As a result, a neutral test particle will not follow geodesics on the whole. A general static spherically symmetric solution is also obtained. An interesting feature of the solution is the presence of a parameter similar to the “Schwarzschild radius”, which separates the solutions with a negative “effective Einstein constant” from those with a positive one.     

Classification of extended chaotic inflation potentials

Brans-Dicke gravity is remarkable not only in that General Relativity and Mach's Principle find a common enlarged scenario where they are mutually consistent, but also in that it provides a very interesting quantum cosmological model within the inflationary paradigm. The interplay between the Brans-Dicke scalar Φ and the inflaton field σ plays an important rôle during the course of inflation, and although the dynamics as such is governed by the potential, the onset and the end of inflation are determined by the values of both fields jointly. The relative position of the beginning – and end-of-inflation curves (BoI and EoI respectively) is the most relevant factor in determining the resulting quantum cosmological scenario. The classification of potentials that is given in this paper is based on the criterion of whether the BoI and EoI boundaries enclose a finite or infinite area in the (σ,Φ) plane where inflation takes place. It is shown that this qualitative classification distinguishes two classes of potentials that yield very different cosmologies and it is argued that only those theories in which BoI and EoI enclose a finite area in the (σ,Φ) plane are compatible with our observable universe.     

Primordial inflation and present-day cosmological constant from extra dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρ _Λ ∼M ⁸/M _P ⁴, where M _P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D=2 extra dimensions with radius b(t) curled up at the ADD length scale b ₀=M _P /M ²∼0.1 mm. Vacuum fluctuations in the compactified space perturb b ₀ very slightly, generating a small present-day cosmological constant.The radius of the compactified dimensions is predicted to be b ₀≈k ^1/40.09 mm (or equivalently M≈2.4 TeV/k ^1/8), where the Casimir energy density is k/b ⁴.Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M∼10⁻¹⁷ cm, rolls down its potential to b ₀.     

A simple coupling with cosmological implications

In this paper the metric is coupled with a dimensionless scalar field in a simple manner; thus, a scalar-metric formulation of gravitation is obtained which leads to satisfactory results in its applications to cosmology; in particular, the missing-matter problem does not hold. The simplicity of the scheme is noticeable.