Probing the early universe with inflationary gravitational waves

Abstract

Near comoving wave number $k$, the gravitational-wave background (GWB) from inflation carries information about the physical conditions near two moments in cosmic history: the moment when $k$ ``left the horizon'' during inflation, and the moment when it ``re-entered the horizon'' after inflation. We investigate the extent to which this information can be extracted if the GWB is measured by a combination of cosmic-microwave-background polarization experiments on large scales and space-based laser-interferometer experiments on small scales. To disentangle this information, we derive a new gravitational-wave transfer function that incorporates a number of physical effects that were treated less accurately, less generally, or were missing altogether in previous treatments. In particular, it incorporates: (i) dark energy with time-varying equation of state $w(z)$; (ii) tensor anisotropic stress due to free-streaming relativistic particles in the early universe; and (iii) a variety of physical effects that cause deviations from the standard equation of state $w=1/3$ during the radiation era. Based on this transfer function, we consider the degree to which the GWB can be used to test inflation and to probe the ``primordial dark age'' between the end of inflation and the electroweak phase transition.