Cosmological Footprints of Loop Quantum Gravity

The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.

Figure 1

Primordial power spectrum, in Planck units, for power-law inflation with $\beta =-2.5$ and $H_0/M_{\mathrm{Pl}}={10}^{-4}$, ${10}^{-3}$, and ${10}^{-2}$ (from the left to the right). Dashed lines are for the numerical results, blue (darker) solid lines are for the IR limit, and red (lighter) solid lines are for the UV limit of the power spectrum. The UV approximation coincides with the primordial spectrum obtained without LQG correction.

Figure 2

Qualitative shape of the effective potential during inflation without LQG corrections, i.e., general relativistic (GR) potential (solid line), and with LQG corrections. The dashed line is for $p<2$ and the dotted one for $p>2$.