The Inflaton and Time in the Matter-Gravity System

TL;DR

This paper explores how the concept of time emerges in the matter-gravity system during inflation, using quantum cosmology and perturbation theory to derive an effective evolution equation for normal matter.

Contribution

It introduces a novel approach to deriving an effective time parameter from gravitational wave functions in quantum cosmology during inflation.

Findings

Normal matter evolution can be described by an effective Schrödinger equation.

A gravitational wave function's oscillations relate to a 'time density' concept.

The approach draws an analogy between time emergence and temperature in statistical mechanics.

Abstract

The emergence of time in the matter-gravity system is addressed within the context of the inflationary paradigm. A quantum minisuperspace-homogeneous minimally coupled inflaton system is studied with suitable initial conditions leading to inflation and the system is approximately solved in the limit for large scale factor. Subsequently normal matter (either non homogeneous inflaton modes or lighter matter) is introduced as a perturbation and it is seen that its presence requires the coarse averaging of a gravitational wave function (which oscillates at trans-Planckian frequencies) having suitable initial conditions. Such a wave function, which is common for all types of normal matter, is associated with a ``time density'' in the sense that its modulus is related to the amount of time spent in a given interval (or the rate of flow of time). One is then finally led to an effective evolution equation (Schroedinger Schwinger-Tomonaga) for ``normal'' matter. An analogy with the emergence of a temperature in statistical mechanics is also pointed out.