Energy density of relic gravity waves from inflation

We evaluate both the spectral energy density and the total energy density for relic gravity waves produced during the transition from an early inflationary phase to a matter-dominated Friedmann-Robertson-Walker-type expansion: $a\sim t^c \mathrm{}(c<\mathrm{}1\mathrm{})\mathrm{}$. We find that for power-law inflation the spectral energy density for gravity waves has more power on larger scales than for purely exponential inflation. Evaluating the energy density of created massless particles (both gravitons and massless scalars) we find that in the case of exponential inflation the ratio of the density of created particles to the total density of matter is a constant, if $c\ge \frac{1}{2}$. This unusual behavior is a consequence of the fact that the equation of state for created particles mimics the equation of state for matter driving the expansion of the Universe. As a result, self-consistent solutions of the Einstein equations can be found, in which the expansion of the Universe is sustained solely by the ongoing production of massless particles, so that $G_{\mu \nu }=8\mathrm{}\pi G〈T_{\mu \nu }〉$. In the case of power-law and quasiexponential inflation we find that the ratio of the energy density of gravity waves to the background matter density increases with time, as gravity waves with longer wavelengths and larger amplitudes enter the horizon at successively later epochs. This could lead to the energy density of gravity waves becoming comparable to the energy density of matter at late times, if inflation commenced at Planckian energies.