Constraining regularization ambiguities in Loop Quantum Cosmology via CMB

In order to investigate the potential observational signals of different regularization ambiguities in loop quantum cosmological models, we systematically compute and compare the primordial scalar power spectra and the resulting angular power spectra in the standard loop quantum cosmology (LQC) and its Thiemann regularized versions -- modified LQC-I/II (mLQC-I/II), using both the dressed metric and the hybrid approaches. All three loop quantum cosmological models yield a non-singular bounce with a post-bounce physics that converges rapidly in a few Planck seconds. Using Starobinsky potential and the initial conditions for the background dynamics chosen to yield the same inflationary e-foldings, which are fixed to be $65$ in all three LQC models, we require that all three models result in the same scale-invariant regime for the primordial power spectrum with a relative difference of less than one percent. This permits us to explore the differences resulting from the deep Planck regime in the angular power spectrum. For the adiabatic states, our results demonstrate that the angular power spectrum predicted by the hybrid approach has a smaller deviation from the angular power spectrum predicted by the standard $\Lambda$CDM cosmological model at large angles in comparison with the dressed metric approach for all three models. The angular power spectrum predicted by mLQC-I in both the hybrid and the dressed metric approaches shows the smallest deviation from the one predicted by the standard $\Lambda$CDM cosmological model at large angular scales, except for the case of fourth order adiabatic initial states in the hybrid approach. On the contrary, mLQC-II results in the largest deviations for the amplitude of the angular power spectrum at large angles and is most disfavored.