Probing the early universe with inflationary gravitational waves

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.