Tensor power spectrum with holonomy corrections in loop quantum cosmology

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In this paper we consider tensor perturbations produced at a bounce phase in the presence of holonomy corrections. Here, the bounce phase and holonomy corrections originate from loop quantum cosmology. We rederive formulas for the corrections of a model with scalar field content. Background dynamics with a free scalar field and multifluid potential are considered. Because the considerations are semiclassical, effects of quantum fluctuations of the background dynamics are not taken into account. Quantum and classical backreaction effects are also neglected. To find the spectrum of the gravitational waves, both analytical approximations and numerical investigations are performed. We have found analytical solutions on superhorizontal and subhorizontal regimes and derived the corresponding tensor power spectra. Also, the occupation number ${n}_{\mathbf{k}}$ and the parameter ${\ensuremath{\Omega}}_{\mathrm{gw}}$ were derived in the subhorizontal limit, leading to the extremely low present value of ${\ensuremath{\Omega}}_{\mathrm{gw}}$. The final results are the numerical power spectra of the gravitational waves produced in the presence of quantum holonomy corrections. The spectrum obtained has two UV and IR branches where ${\mathcal{P}}_{T}\ensuremath{\propto}{k}^{2}$; however, they have different prefactors. The spectrum connecting these regions is in the form of oscillations. We have found good agreement between the numerical spectrum and the spectrum obtained from the analytical model. The obtained spectrum can be directly applied as an initial condition for the inflationary modes. Based on our results, we discuss implications on the CMB radiation, in particular, on B-type polarization.