# The scalar field and gravity combined variable in ADM theory

## TL;DR

This paper reformulates the canonical theory of gravity coupled with a scalar field into a combined variable framework within ADM formalism, applicable to both classical and quantum contexts, and applies it to flat FLRW cosmology.

## Contribution

It introduces a unified variable approach to ADM gravity with scalar fields, extending the formalism to quantum theory and cosmological models.

## Key findings

- Unified ADM scalar field and gravity variables.
- Application to flat FLRW cosmology.
- Framework for classical and quantum gravity analysis.

## Abstract

The canonical theory of gravity together with the scalar field is written as a combined variable theory in ADM form, in the classical and quantum theory. FLRW $\kappa = 0$ cosmology is rewritten in the combined variable theory.