Scale invariance, new inflation and decaying Lambda terms

TL;DR

This paper explores a scale-invariant gravitational theory with measure fields, leading to a scalar potential that supports both inflationary and late-time accelerating universe scenarios, including a decaying cosmological constant.

Contribution

It introduces a novel gravitational framework with measure fields that naturally yields a zero-energy vacuum and a scalar potential suitable for inflation and dark energy models.

Findings

Scalar potential has a flat region for large field values.

The theory predicts a zero-energy true vacuum state.

It provides a mechanism for a decaying cosmological constant.

Abstract

Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first order formalism) is of the form $S = \int L_{1} \Phi d^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $\Phi$ is a density built out of degrees of freedom, the "measure fields" independent of $g_{\mu\nu}$ and matter fields appearing in $L_{1}$, $L_{2}$. If $L_{1}$ contains the curvature, scalar potential $V(\phi)$ and kinetic term for $\phi$, $L_{2}$ another potential for $\phi$, $U(\phi)$, then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), where the equations assume the Einstein form. Global Scale invariance is realized when $V(\phi)$ = $f_{1}e^{\alpha\phi}$ and $U(\phi)$ = $f_{2}e^{2\alpha\phi}$. In the CEF the scalar field potential energy $V_{eff}(\phi)$ has in, addition to a minimum at zero, a flat region for $\alpha\phi \to\infty$, with non zero vacuum energy, which is suitable for either a New Inflationary scenario for the Early Universe or for a slowly rolling decaying $\Lambda$-scenario for the late universe, where the smallness of the vacuum energy can be understood as a kind of see-saw mechanism.