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We compare the primordial scalar power spectra in the loop cosmological models using the effective dynamics of the hybrid approach to cosmological perturbations in which the background is loop quantized, but the perturbations are Fock quantized. The three loop cosmological models under consideration are the standard loop quantum cosmology (LQC), the modified LQC-I (mLQC-I) and the modified LQC-II (mLQC-II) in the spatially flat Friedmann-Lemaître-Robertson-Walker universe with a Starobinsky potential. These models arise from different regularizations of the classical Hamiltonian constraint in the symmetry reduced spacetimes and aim to capture certain features of quantization in loop quantum gravity. When applying the techniques in the hybrid approach to mLQC-I/II, we find the effective Mukhanov-Sasaki equations take the same form as in LQC. The difference among the three models is encoded in the unique expressions of the effective masses in each model. We find that the relative difference in the amplitude of power spectrum between LQC and mLQC-II is approximately 50% in the infrared and the oscillatory regimes, whereas this difference can be as large as 100% between mLQC-I and LQC/mLQC-II. Interestingly, in the infrared and the oscillatory regimes of mLQC-I, we obtain a suppressed power spectrum from the hybrid approach which is far below the Planck scale. This result is in a striking contrast to the one obtained from the dressed metric approach to perturbations where the corresponding amplitude in this regime is extremely large. Our analysis shows that while the phenomenological predictions are in agreement between the two approaches for LQC and mLQC-II, for mLQC-I the differences between the dressed and hybrid approaches can be quite significant. Our result provides the first robust evidence of difference in predictions between the dressed and hybrid approaches due to respective underlying constructions.

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Physical Review D