Gravitational Wave Production at the End of Inflation

We consider gravitational wave production due to parametric resonance at the end of inflation, or “preheating.” This leads to large inhomogeneities that source a stochastic background of gravitational waves at scales inside the comoving Hubble horizon at the end of inflation. We confirm that the present amplitude of these gravitational waves need not depend on the inflationary energy scale. We analyze an explicit model where the inflationary energy scale is $\sim {10}^9\mathrm{GeV}$, yielding a signal close to the sensitivity of Advanced Laser Interferometer Gravitational Wave Observatory and Big Bang Observer. This signal highlights the possibility of a new observational “window” into inflationary physics and provides significant motivation for searches for stochastic backgrounds of gravitational waves in the Hz to GHz range, with an amplitude on the order of ${\Omega }_{\mathrm{gw}}(k)h^2\sim {10}^{-11}$.

Figure 1

We plot the spectrum of gravitational radiation produced during resonance with $\mu ={10}^{-18}$ (left) through to ${10}^{-6}$ (right) in units where $m_{\mathrm{Pl}}\approx {10}^{19}\mathrm{GeV}=1$, where each spectrum has a value of $\mu {10}^3$ times larger than the one immediately to the left. The corresponding initial energy densities run from $(4.5\times {10}^9\mathrm{GeV}{)}^4$ to $(4.5\times {10}^{15}\mathrm{GeV}{)}^4$ for our choice of ${\varphi }_0$. The plots are made on ${128}^3$ grids, and the “feature” at high frequency is a numerical artifact.

Figure 2

We sketch the gravitational wave spectra obtained for the lowest and highest energy models computed here, relative to that of the Advanced LIGO goal, and the proposed LISA and BBO experiments. We see that inflationary models with lower energy scale may lead to a signal that is visible at LIGO scales if the sensitivity of LIGO is further improved, and with BBO. The tensor background generated by quantum fluctuations during GUT scale inflation is shown by the solid horizontal line. The dashed lines denote the inferred $k^3$ tails. The spectra generated by the inflationary scenarios considered in 5, 15 roughly overlap with the ${10}^{15}\mathrm{GeV}$ spectrum depicted above.