Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation

Together with holonomy corrections, inverse volume terms should be taken into account when studying the primordial universe in loop quantum cosmology. We investigate how the tensor power spectrum is modified with respect to the standard general relativistic prediction by those semiclassical corrections. Depending on the values of the free parameters of the model, it is shown that the spectrum can exhibit a very large deviation from its usual shape, in particular, with a very red slope and a strong running in the infrared limit.

Figure 1

Primordial tensor power spectrum as a function of the wave number. The solid line is the analytical calculation, whereas filled circles are the numerical results.

Figure 2

Primordial tensor power spectrum as a function of the wave number for different values of the slow-roll parameter $ϵ$.

Figure 3

Primordial tensor power spectrum as a function of the wave number for different values of the LQC parameters $\lambda$ (left panel) and $\kappa$ (right panel).

Figure 4

Primordial tensor power spectrum as a function of the wave number for different values of the parameter $H_0$.

Figure 5

Value of the critical wave number as a function of the inflationary parameters $ϵ$ (top-left panel) and $H_0$ (top-right panel) and as a function of the LQC parameters $\lambda$ (bottom-left panel) and $\kappa$ (bottom-right panel).