Inflationary spectra from a near $\Omega$-deformed space-time transition point in Loop Quantum Cosmology

TL;DR

This paper investigates inflationary spectra in loop quantum cosmology with holonomy corrections, revealing how the spacetime structure affects vacuum states and perturbation spectra near a transition point, with implications for observable predictions.

Contribution

It introduces a new approach to defining initial vacuum states after the spacetime transition point in loop quantum cosmology, analyzing scalar and tensor spectra with holonomy corrections.

Findings

Vacuum states are well-defined when initial conditions are set after the transition point.

Scalar power spectrum can be significantly smaller than classical predictions.

Tensor perturbations may exhibit a blueshift under certain conditions.

Abstract

Anomaly-free perturbations of loop quantum cosmology with holonomy corrections reveal an $\Omega$ -deformed spacetime structure, $\Omega:=1-2\rho/\rho_c$, where $\Omega<0$ indicates a Euclidean-like space and $\Omega>0$ indicates a Lorentz-like space. It would be reasonable to give the initial value at the spacetime transition point, $\rho=\rho_c/2$, but we find that it is impossible to define a Minkowski-like vacuum even for large $k$ modes at that time. However, if we loosen the condition and give the initial value slightly after $\Omega=0$, e.g., $\Omega\simeq 0.2$, the vacuum state can be well defined and, furthermore the slow roll approximation also works well in that region. Both scalar and tensor spectra are considered in the framework of loop quantum cosmology with holonomy corrections. We find that if the energy density is not too small in relation to $\rho_c/2$ when the considered $k$ mode crossing the horizon, effective theory can give a much smaller scalar power spectrum than classical theory and the spectrum of tensor perturbations could blueshift. But when compared to other observations, since the energy densities when the modes crossed the horizon were significantly smaller than $\rho_c$,the results we get agree with previous work in the literature and with the classical inflation theory.