Cosmological perturbation theory in a matter-time gauge

Abstract

This work examines cosmological perturbations in a Hamiltonian framework with a matter-time gauge. Einstein's field equations are written in a matter-time gauge. The perturbed three-metric of cosmology, its conjugate momentum and the shift are substituted in these equations. The equations of motion of the perturbations to linear order are derived. These equations are expanded in terms of spatial Fourier modes and are then decomposed into scalar, vector and tensor components. After fixing gauges and solving constraints we find that the scalar mode is ultralocal and that the vector modes vanish. We also see that the traceless transverse tensor modes give the known propagation equation for gravitational waves in an expanding, spatially at, homogeneous and isotropic background.