Signatures of Spatial Curvature on Growth of Structures

TL;DR

This paper investigates how spatial curvature influences the evolution of matter density and photon oscillations in the universe, revealing modifications to gravitational potential memory and Silk damping effects.

Contribution

It provides an analytical framework incorporating spatial curvature into Boltzmann equations for matter and photons, highlighting its impact on structure growth and damping phenomena.

Findings

Spatial curvature affects the memory of early gravitational potentials.

Oscillation frequencies and Silk damping are altered by curvature.

Modified damping influences the growth of matter density perturbations.

Abstract

We write down Boltzmann equation for massive particles in a spatially curved FRW universe and solve the approximate line-of-sight solution for evolution of matter density, including the effects of spatial curvature to the first order of approximation. It is shown that memory of early time gravitational potential is affected by presence of spatial curvature. Then we revisit Boltzmann equation for photons in the general FRW background. Using it, we show that how the frequency of oscillations and damping factor (known as Silk damping) changed in presence of spatial curvature. At last, using this modified damping factor in hydrodynamic regime of cosmological perturbations, we find our analytic solution which shows the effects of spatial curvature on growing mode of matter density.