The big bang and inflation united by an analytic solution

Abstract

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data.The model simultaneously describes the Big Bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Fridemann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time, rather it oscillates around the potential minimum while settling down, unlike the slow roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations. 98.80.Cq,

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

“…Our goal in this paper is to provide a full set of analytic solutions that give all possible configurations of a homogeneous and isotropic universe as a function of time. This expands on our previous work in [13][14][15] by including additional degrees of freedom, in particular radiation. The effects of anisotropy are discussed elsewhere [16,17].…”

“…These are precisely the equations of motion derived from the isotropic limit of the action (3) in the a γ = 1 gauge [13]. The fields φ γ , s γ are decoupled except for the zero energy condition in Eq.…”

“…The crucial step introduced in [13], as suggested by 2T-physics, is to take advantage of the gauge symmetry of the conformally invariant action (3). The Einstein equations derived from the action (3), taken with only time dependent isotropic fields, yields gauge covariant cosmological equations for three fields a (τ ) , φ (τ ) , s (τ ) in any gauge.…”

“…The field re-definition from σ, a E to φ γ , s γ , is derived from the gauge transformation that connects the E and γ gauges [13] and is given in Eq. (17).…”

“…In a separate paper we will present the analytic solutions for the potentials V (σ) = For the potential 1, we can solve the Friedmann equations exactly for all time intervals before or after the big bang. The method, which is based on conformal symmetry, was introduced in previous papers [13]- [17]. It was applied to the cases of the flat and curved isotropic Friedmann universes without radiation or matter [14].…”