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

Understand

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.