Relic gravitons as the observable for Loop Quantum Cosmology

In this paper we investigate tensor modes of perturbations in the universe governed by Loop Quantum Cosmology. We derive the equation for tensor modes and investigate numerically effects of quantum corrections. This investigation reveals that the region of super-adiabatic amplification of tensor modes is smaller in comparison with the classical case. Neglecting quantum corrections to the equation for tensor modes and holding underlying loop dynamics we study analytically the creation of gravitons. We calculate the power spectrum of tensor perturbations during the super-inflationary phase induced by Loop Quantum Gravity. The main result obtained is the spectrum of gravitons, produced in the transition from the quantum to classical regime of the Universe. Obtained spectrum is characterized by a hard branch. The numerical investigation shows the strong dependence of $\nu_{\text{max}}$ frequency with respect to quantum numbers. The parameter $\Omega_{\text{gw}}(\nu_{\text{max}})$ approaches even to $\sim 10^{-1}$ for highest frequencies. We compare our results with recent constraints from the Laser Interferometer Gravitational-wave Observatory (LIGO) and find that it is possible to test the quantum effects in the early Universe.