Cyclic universe and uniform rate inflation in loop quantum cosmology

TL;DR

The paper addresses whether a uniformly rolling inflaton can be realized in loop quantum cosmology and what the implications are. By enforcing a uniform-rate evolution in the LQC effective dynamics, it derives a polymerized-like potential and a modified Friedmann equation $H^2 = (rho/3) (1 - rho/rho_c)$, producing a cyclic background. Using the delta-N formalism, it fixes the amplitude to constrain the rate lambda and finds a viable n_s for lambda around 5.19e-6, while the initial r is large unless the end of inflation is shifted; quantum corrections remain negligible during inflation, giving CMB predictions close to GR. The study reveals a novel link between uniform rate inflation, polymer quantization of matter, and hybrid natural inflation within a loop-quantized spacetime, suggesting a unified picture of early-universe dynamics.

Abstract

We investigate uniform rate inflationary universe in the framework of loop quantum cosmology (LQC) and find that this seemingly simple inflationary model is interlinked with various concepts such as cyclic evolution, HNI inflation and polymer quantized scalar fields, when the background spacetime is loop quantized. The potential for an \textit{exactly} uniform rate inflation in a loop quantized FRW spacetime turns out to be a polymerized version of the corresponding potential in general relativity, which mimics the potentials for a polymerized scalar field and that for hybrid natural inflation (HNI). There is also a radical modification of the background spacetime, leading to a cyclic universe with identical epochs separated by quantum bounces which replace the classical singularity. The energy density and Hubble rate are bounded. The predictions for cosmological perturbations depend on the value of the field at the end of inflation. The parameter space is explored to compare the results for spectral index and tensor-to-scalar ratio with observational constraints.

Figures (3)

• Figure 1: The evolution of the scale factor $a$, the Hubble rate $H$, the energy density $\rho$ and the equation of state $w$ with respect to the rescaled scalar field $\tilde{\phi} =\sqrt{\frac{3\lambda^2}{\rho_c}} \phi$ is shown, where $a_0=50$. We have chosen $\lambda=0.1$ for better viewing.
• Figure 2: The cyclic evolution of the universe with respect to the rescaled scalar field $\tilde{\phi} =\sqrt{\frac{3\lambda^2}{\rho_c}} \phi$. As the scalar field is evolving backwards in our model, the evolution in the above figure is clockwise.
• Figure 3: The tensor-to-scalar ratio and the spectral index. The constraints are from Planck data Planck. The solid black line represents the values of tensor-to-scalar ratio and spectral index that are possible to obtain from LQC.