# Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology

## TL;DR

This paper critically reviews the semiclassical interpretation of quantum cosmology, demonstrating that gauge fixing of the time coordinate can reproduce key results without requiring a classical gravitational background, and discusses the implications for wave function interpretation.

## Contribution

It shows that gauge fixing at classical and quantum levels reproduces semiclassical results, challenging the notion that time emerges only in a classical gravitational context.

## Key findings

- Gauge fixing reproduces semiclassical quantum cosmology results.
- A positive-definite inner product is defined via an iterative procedure.
- Wave function interpreted as a state vector with unitary evolution.

## Abstract

We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that a concept of time emerges only when the gravitational field is (semi)classical. We show that the usual results of the semiclassical interpretation, and its generalisation known as the Born-Oppenheimer approach to quantum cosmology, can be obtained by gauge fixing, both at the classical and quantum levels. By `gauge fixing' we mean a particular choice of the time coordinate, which determines the arbitrary Lagrange multiplier that appears in Hamilton's equations. In the quantum theory, we adopt a tentative definition of the (Klein-Gordon) inner product, which is positive definite for solutions of the quantum constraint equation found via an iterative procedure that corresponds to a weak coupling expansion in powers of the inverse Planck mass. We conclude that the wave function should be interpreted as a state vector for both gravitational and matter degrees of freedom, the dynamics of which is unitary with respect to the chosen inner product and time variable.