Effects of the inflaton mass on the pre-inflationary dynamics and primordial power spectra in loop quantum cosmology

Abstract

Considering the mass parameters as free phenomenological parameters, we investigate inflation driven by a canonical scalar field with different potentials in LQC. We find that a smaller mass value makes it easier to obtain a sufficient number of e-folds for the quadratic potential, while for the Starobinsky potential, more e-folds are obtained for larger mass values. By estimating the probability of slow-roll inflation, we find that it remains very close to unity for all considered cases. We compute the primordial power spectrum using three approaches: the dressed metric, the hybrid, and the alternative mass function approaches for the case that the kinetic energy dominated at bounce. The resulting power spectrum for both potentials and different mass values shows the same qualitative pattern in all three approaches. It is suppressed at small $k$, amplified and oscillating over an intermediate range, and nearly scale-invariant at large $k$. The approaches mainly differ in how fast the power spectrum converges to this regime, with the hybrid approach converging the fastest, followed by the alternative mass function and dressed metric approaches. We find that the pivot scale $k_\star$ is highly sensitive to the inflaton mass, changing by more than an order of magnitude for a mass variation of only a few percent. Using the tensor power spectrum at $k_\star$, we calculate the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, finding good agreement with current data. Finally, the scalar power spectra are fed into the CAMB code to obtain the angular power spectrum and compare with the Planck 2018 data and the best-fit $Λ$CDM model. All three approaches are consistent with data at high multipoles, while at low multipoles the hybrid approach gives the closest agreement and the dressed metric approach shows the largest deviation.

23 pages, 4 figures, 5 tables