Gavriil Shchedrin, Department of Applied Mathematics, University of Colorado Boulder

Time evolution of the gravitational wave damping in the early Universe

A thorough analysis of cosmic microwave background (CMB) radiation provides a unique test of the inflationary cosmological model. While scalar fluctuations in the CMB serve as an invaluable source for exploring the density of matter and radiation, as well as the large-scale structure of the Universe, observations of tensor fluctuations of the CMB open a window for detecting signatures of gravitational waves in the early Universe. In this talk, we will examine the time evolution of gravitational waves in the early Universe. We will present an exact analytical solution for gravitational wave damping in the presence of freely streaming neutrinos. This solution is expressed as a convergent series of spherical Bessel functions of even order and was made possible with a help of a compact formula for the convolution of spherical Bessel functions of integer order.