Scale invariance, unimodular gravity and dark energy

TL;DR

The paper couples a scale-invariant Standard Model extended by a massless dilaton to unimodular gravity, arguing that all dimensionful parameters originate from a single source and that the cosmological constant emerges as an integration constant. Classically, unimodular gravity with scale invariance yields a zero $\Lambda$ and a flat direction in the scalar sector when $\beta=0$, producing an exactly massless dilaton and a Planck scale fixed by non-minimal couplings, with the Einstein-frame potential $U_E(h,\chi)$. In cosmology, Higgs-driven inflation arises from a large non-minimal coupling $\xi_h$, followed by reheating; the late-time acceleration is driven by the dilaton via an exponential potential $U_\eta$ that leads to thawing quintessence with $w$ near, but above, $-1$, constrained by observations to $0<\xi_\chi<0.07$. The quantum discussion emphasizes that maintaining a massless dilaton and scale invariance requires $\beta=0$, with radiative corrections treated through a field-dependent cutoff; if $\beta>0$ the flat direction lifts and a vacuum energy could re-emerge, making the quantum completion of the theory an open issue.

Abstract

We demonstrate that the combination of the ideas of unimodular gravity, scale invariance, and the existence of an exactly massless dilaton leads to the evolution of the universe supported by present observations: inflation in the past, followed by the radiation and matter dominated stages and accelerated expansion at present. All mass scales in this type of theories come from one and the same source.

Figures (1)

• Figure 1: Potential for the Higgs field and dilaton in the Einstein frame. Left: $\Lambda=0$, middle: $\Lambda>0$, right $\Lambda<0$.