Discretuum versus Continuum Dark Energy

TL;DR

Dimopoulos and Thomas compare discretuum and continuum realizations of dark energy within multi-vacua theories. They show that a discretuum yields a constant vacuum energy with $w=-1$, while a continuum realized by a large-$Z$ modulus leads to a quantum-stable, long-range-force-free framework with a potentially evolving equation of state $w(z)$ governed by a one-parameter family. They model the continuum with a Lagrangian $L = \tfrac{1}{2} Z (∂ φ)^2 - V(φ)$, derive the equation of motion and the expression for $w_φ$, and discuss a potential form $V(φ)=m^2 M_p^2 f(φ/M_p)$ with a bound on the energy scale. The authors discuss technical naturalness, absence of fifth forces, and the testability of the predictions by future expansion-history probes, also noting connections to Z-inflation and broader cosmological implications.

Abstract

The dark energy equation of state for theories with either a discretuum or continuum distribution of vacua is investigated. In the discretuum case the equation of state is constant $w=p/ρ=-1$. The continuum case may be realized by an action with large wave function factor $Z$ for the dark energy modulus and generic potential. This form of the action is quantum mechanically stable and does not lead to measurable long range forces or violations of the equivalence principle. In addition, it has a special property which may be referred to as super-technical naturalness which results in a one-parameter family of predictions for the cosmological evolution of the dark energy equation of state as a function of redshift $w=w(z)$. The discretuum and continuum predictions will be tested by future high precision measurements of the expansion history of the universe. Application of large $Z$-moduli to a predictive theory of $Z$-inflation is also considered.