Tadpole Cosmology: Milne Solution as a Cosmological Constant Hideout

TL;DR

This paper introduces a new self-tuning mechanism via an exact Milne solution in a scalar-tensor theory, exploring its stability, generalizations to FLRW spacetimes, and potential for vacuum energy mitigation.

Contribution

It presents a novel Milne solution in tadpole plus cubic-Galileon models and explores its stability, generalizations, and implications for vacuum energy screening.

Findings

Milne solution exists as an exact vacuum solution in the model.

The Milne solution is not an attractor and can lead to diverse asymptotic behaviors.

The model admits generalizations to FLRW spacetimes with matter presence.

Abstract

Dynamical cancellation frameworks present a potential means of mitigating the effect of a large vacuum energy, that would otherwise ruin the late-time, low energy dynamics of the Universe. Certain models in the literature, such as the Fab Four and Well Tempering, realize this idea by introducing some degeneracy in the dynamical equations. In this paper, we introduce a third potential route to self-tuning, and infer the existence of a new, exact Milne solution in the simplest tadpole plus cubic-Galileon scalar-tensor theory. We study the dynamics of the scalar field and metric in the vicinity of the Milne coordinate singularity, and find that the vacuum solution belongs to a more general family of Milne-like metrics. By numerically evolving the field equations for a range of initial conditions, we show that the Milne solution is not an attractor, and varying the initial scalar field data can lead to completely different asymptotic states; exponential growth of the scale factor, a static non-spatially flat metric or a severe finite-time instability in the scalar field and metric. We generalise the Milne solution to a class of FLRW spacetimes, finding that the tadpole-cubic Galileon model admits perfect-fluid-like solutions in the presence of matter. Finally, we present a second Horndeski model which also admits an exact Milne solution, hinting at the existence of a larger undiscovered model space containing vacuum-energy-screened solutions.