Connecting the Non-Singular Origin of the Universe, the Vacuum Structure and the Cosmological Constant Problem

Abstract

We consider a non-singular origin for the Universe starting from an Einstein static Universe, the so called "emergent universe" scenario, in the framework of a theory which uses two volume elements √ −gd 4 x and Φd 4 x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field φ are considered in the action. The first order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of scale invariance (S.I.). After S.S.B. of S.I., it is found that a non trivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for φ → ∞ relevant for the non-singular origin of the Universe, followed by an inflationary phase and φ → −∞, describing our present Universe. The dynamics of the scalar field becomes non linear and these non linearities produce a non trivial vacuum structure for the theory and are responsible for the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in φ → −∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. The non trivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

Stability of the Einstein static universe in f(R, T) gravity

“…Another possibility has been recently reported in the context of two measure theories (TMT) where the scale invariance is spontaneously broken due to the intrinsic features of the TMT dynamics. This allows for a non-singular EU solution describing an initial phase of evolution that precedes the inflationary phase [158][159][160]. The presence of such a pre-inflationary phase in the EU scenario has observable consequences, namely on the anisotropies within the CMB spectrum at large scales, see e.g., [161][162][163].…”

Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

“…We therefore evade this theorem simply by not satisfying the required axioms for the theorem to hold true in either instance. There are further counterexamples to this theorem, namely emergent universes [36,37] because a scalar field can the violate energy condition (as in inflation). These have been criticised as not being stable to quantum perturbations [68][69][70][71] but they can be so with the correct potential [72,73].…”

“…We note that current inflationary literature often no longer includes a radiation phase prior to the start of inflation, however in keeping with Madsen and Ellis [1], we will include this phase at the outset. Whether it is included or not makes no difference to the cyclic models; however its inclusion allows a simple representation also of emergent universe models [35][36][37].…”

“…There are closed cycles around F 1. The red solution beginning at the Einstein static universe E1 corresponds to the emergent universe scenario [35][36][37], where the universe starts off asymptotically as an Einstein static universe, passes through a phase like what we see today, and ultimately tends towards a flat universe, expanding forever due to the ultimate dominance of the cosmological constant. These can correspond to the universe today.…”

One hundred years of the cosmological constant: from “superfluous stunt” to dark energy

“…In this scenario, the universe inflates from a static Einstein state after an indefinite period of time, thus reviving the Eddington-Lemaître model (figure 2) in the context of the modern theory of cosmic inflation. 51 This scenario again offers the prospect of an arbitrary long time for the cosmological constant to decay from a very large value (Guendelman 2011;Guendelman and Labraña 2013). However, it once again predicts a time-varying equation of state for dark energy, a phenomenon that has not been observed to date.…”