# The general scalar-tensor Hamiltonian with deformed covariance

## TL;DR

This paper derives a generalized scalar-tensor Hamiltonian with deformed covariance, revealing how matter and gravity momenta combine to influence cosmological phenomena like bounces and singularities.

## Contribution

It provides a comprehensive derivation of the scalar-tensor Hamiltonian constraint with all-order momenta under deformed algebra, highlighting the role of matter and gravity in covariance deformation.

## Key findings

- Deformation functions can induce a big bounce at high densities.
- Some deformations lead to sudden cosmological singularities.
- The form of deformation affects the universe's early evolution.

## Abstract

We derive the scalar-tensor Hamiltonian constraint to all orders of momenta when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. We find that the momenta and spatial derivatives from gravity and matter fields must combine in a very specific form to maintain a deformed general covariance. This suggests that the deformation should be equally caused by matter field derivatives as it is by gravitational curvature. We demonstrate the cosmological consequences of a variety of deformation functions. Some cause a big bounce at high energy densities and others cause a sudden singularity.