Evolving laws and cosmological energy

TL;DR

This paper explores how evolving physical laws, modeled through variable fundamental constants and Lorentz invariance violation, can lead to energy conservation violations and provide new cosmological insights like the Big Bang and signature change.

Contribution

It introduces a novel framework coupling evolving laws with energy violations, utilizing clocks dual to constants and Lorentz invariance violation inspired by Horava-Lifshitz theories.

Findings

Variability in laws leads to energy violations under certain conditions.

The framework can reproduce early universe solutions like VSL and address cosmological problems.

Models include signature change and classical realization of the no-boundary proposal.

Abstract

We couple the issue of evolution in the laws of physics with that of violations of energy conservation. We define evolution in terms of time variables canonically dual to ``constants'' (such as $\Lambda$, the Planck mass or the gravitational coupling), mimicking a procedure associated with one formulation of unimodular gravity. We then introduce variability via a dependence of {\it other} fundamental ``constants'' on these clocks. Although this is not needed, sharper results are obtained if this procedure violates local Lorentz invariance, which we define in the spirit of Horava-Lifshitz theories (modifying a $3+1$ split action, so that a Lorentz invariant 4D reassembly is no longer possible). We find that variability in the ``laws of physics'' generically leads to violations of energy conservation if either a matter parameter varies as a function of a gravitational clock, or a gravity parameter depends on a matter clock, with the other combinations sterile. We illustrate this with a variety of clocks (associated with matter, the speed of light, the Ricci scalar, etc) and parameters (mainly the gravitational and matter speed of light, but also the cosmological constant). We can accommodate in this construction (and improve) several early Varying Speed of Light solutions to the flatness and cosmological constant problem, allowing for variability effects related to the spatial curvature and $\Lambda$ to cause creation of radiation and a Hot Big Bang. But we can also go well beyond, for example modelling signature change by a change in the sign of $c^2$, thereby obtaining a {\it classical} realization of the Hartle-Hawking no-boundary proposal, among other developments.