Fine Tuning Free Paradigm of Two Measures Theory: K-Essence, Absence of Initial Singularity of the Curvature and Inflation with Graceful Exit to Zero Cosmological Constant State

TL;DR

This paper explores a scale-invariant Two Measures Field Theory in cosmology, demonstrating it can naturally produce inflation, avoid initial singularities, and address the cosmological constant problem without fine tuning.

Contribution

It presents a novel, fine-tuning free TMT model that yields diverse cosmological scenarios, including singularity avoidance, inflation with graceful exit, and small cosmological constant solutions.

Findings

Absence of initial curvature singularity with a singular derivative.

Power law inflation with graceful exit to zero or small CC.

Resolution mechanisms for the old cosmological constant problem.

Abstract

The dilaton-gravity sector of the Two Measures Field Theory (TMT)is explored in detail in the context of cosmology. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. The effective model represents an explicit example of the effective k-essence resulting from first principles without any exotic term in the fundamental action. Depending of the choice of regions in the parameter space, TMT exhibits different possible outputs for cosmological dynamics: a) Absence of initial singularity of the curvature while its time derivative is singular. This is a sort of "sudden" singularities studied by Barrow on purely kinematic grounds. b) Power law inflation in the subsequent stage of evolution. Depending on the region in the parameter space (but without fine tuning) the inflation ends with a graceful exit either into the state with zero cosmological constant (CC) or into the state driven by both a small CC and the field phi with a quintessence-like potential. c) Possibility of resolution of the old CC problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine tuning) in conventional field theories. d) TMT enables two ways for achieving small CC without fine tuning of dimensionfull parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories (i.e theories with only the measure of integration sqrt{-g} in the action. e) There is a wide range of the parameters such that in the late time universe: the equation-of-state w=p/\rho <-1; w asymptotically (as t\to\infty) approaches -1 from below; \rho approaches a constant, the smallness of which does not require fine tuning of dimensionfull parameters.