Cosmological time and the constants of nature

TL;DR

This paper explores the idea that cosmological time is conjugate to the constants of nature, leading to a quantum framework where different definitions of time emerge and classical limits are recovered, with implications for new phenomenology.

Contribution

It introduces a novel approach linking cosmological time to constants of nature, solving the Hamiltonian constraint as a Schrodinger equation in a generalized connection space.

Findings

Normalizable superpositions of states exist.

Classical limits are recovered with coherent states.

Potential for new phenomenological insights through entangled constants.

Abstract

We propose that cosmological time is {\it effectively} the conjugate of the constants of nature. Different definitions of time arise, with the most relevant related to the constant controlling the dynamics in each epoch. The Hamiltonian constraint then becomes a Schrodinger equation. In the connection representation, it is solved by monochromatic plane waves moving in a space generalizing the Chern-Simons functional. Normalizable superpositions exist and for factorizable coherent states we recover the classical limit and a seamless handover between potentially disparate times. There is also a rich structure of alternative states, including entangled constants, opening up the doors to new phenomenology.