The Layzer-Irvine Equation for Scalar-Tensor Theories: A Test of Modified Gravity N-body Simulations

TL;DR

This paper derives a generalized Layzer-Irvine equation for scalar-tensor theories of gravity, providing new tools to test the accuracy of N-body simulations in modified gravity models.

Contribution

It introduces a new Layzer-Irvine equation for scalar field theories and demonstrates its application as a dynamical and static test for N-body simulation accuracy.

Findings

The new equation effectively tests the numerical implementation of scalar fields in simulations.

Application to N-body simulations shows the equation's utility in verifying energy conservation.

Provides a static test for matter distributions in modified gravity simulations.

Abstract

The Layzer-Irvine equation describes energy conservation for a pressure less fluid interacting though quasi-Newtonian gravity in an expanding Universe. We here derive a Layzer-Irvine equation for scalar field theories where the scalar field is coupled to the matter fields, and show applications of this equation by applying it to N-body simulations of modified gravity theories. There it can be used as both a dynamical test of the accuracy of the solution and the numerical implementation when solving the equation of motion. We also present an equation that can be used as a new static test for an arbitrary matter distribution. This allows us to test the N- body scalar field solver using a matter distribution which resembles what we actually encounter in numerical simulations.