Gravitational wave background from superinflation in loop quantum cosmology

We investigate the behavior of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbations, and find a strong blue tilt in the power spectrum with $n_t\approx 2$. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where $n_t\approx 0$.

Figure 1

Schematic illustration of the evolution of modes $k$ which exit the horizon (thick solid line) during superinflation and reenter during the standard radiation or matter era. $k_0^{-1}$ is the scale corresponding to the size of the observable universe.

Figure 2

Predicted present abundance of gravitational waves produced during the superinflationary phase of LQC with inverse volume corrections assuming that $H_{\mathrm{e}}={10}^{-6}$ in Planck units. The solid line corresponds to the standard inflation abundance ($n=r=0$). Also indicated are the present bounds and future sensitivities.

Figure 3

Predicted present abundance of gravitational waves produced during the superinflationary phase of LQC with holonomy corrections. The solid line corresponds to the standard inflation abundance. Also indicated are the present bounds and future sensitivities.