Loop quantum inflation with inverse volume corrections in light of ACT data

TL;DR

This work tests whether inverse volume corrections in loop quantum cosmology can reconcile low-scale SB SUSY and exponential inflation with high-precision CMB data. By deriving LQC-corrected expressions for the inflationary observables $n_{ m s}$ and $r$ and analyzing two representative potentials, the authors map the viable regions in the LQC parameter space $(\\sigma,\\delta)$ and, for the exponential case, dependences on the slope parameter $\\lambda$. They find that the dominant effect of the corrections is a negative shift in $n_{ m s}$ (via $c_{n_{ m s}}\\delta_{pl}$) which can move SB SUSY into the 68–95% CL regions, while the exponential potential becomes viable only for sufficiently small $\\lambda$ (roughly $\\lambda \lesssim 0.076$). These results demonstrate that quantum gravity-inspired inverse-volume effects can substantially alter inflationary predictions and provide concrete, data-driven bounds on LQC parameters using ACT/Planck observations.

Abstract

Within the framework of loop quantum cosmology (LQC), we investigate the effect of inverse volume corrections on the low scale spontaneously broken supersymmetric (SB SUSY) and exponential inflationary potentials. The LQC modifications to the Friedmann equations and cosmological perturbation parameters are employed to assess the observational viability of these models against recent data from the Atacama Cosmology Telescope (ACT). Our results indicate that in contrary to the standard model of inflation, in the presence of inverse volume corrections in LQC, the prediction of SB SUSY and exponential potentials in the $r-n_{\rm s}$ plane lie inside the 68\% confidence level interval of the ACT data.

Figures (4)

• Figure 1: The tensor-to-scalar ratio $r$ against the scalar spectral index $n_{\rm s}$ for the SUSY potential (\ref{['eq:susy_pot']}) with LQC inverse volume corrections. The dashed and solid green curves show the model predictions for $N=50$ and $N=60$ e-folds, respectively. For both cases, the parameters are fixed at $\alpha=0.005$ and $\sigma=2$, while $\delta$ is varied from $0$ to $3 \times 10^{-3}$.
• Figure 2: The allowed zones for the LQC inverse volume parameters $\sigma$ and $\delta$ in the phase space, for the SB SUSY potential (\ref{['eq:susy_pot']}), calculated for: (a) $N=50$ and (b) $N=60$. The plot is bounded by P-ACT-LB-BK18 data at 68% CL (dark purple) and 95% CL (light purple).
• Figure 3: The $r-n_{\rm s}$ diagram for the exponential potential (\ref{['eq:exp_potential']}) in the LQC framework with inverse volume corrections. (a) The parameter $\delta$ is varied over the range $[0, 10^{-2}]$ for a fixed $\sigma=1$. (b) The parameter $\sigma$ is varied over the range $[0, 3)$ for a fixed $\delta = 10^{-3}$. In both panels, the black arrows indicate the direction of increase for the varying parameters. The dashed line curves show the prediction of standard power law inflation (i.e. without inverse volume corrections).
• Figure 4: The allowed regions for the LQC parameters $\sigma$ and $\delta$ in the phase space for the exponential potential (\ref{['eq:exp_potential']}), constrained by P-ACT-LB-BK18 data at 68% (dark purple) and 95% (light purple) confidence levels. The panels show the results for different values of $\lambda$: (a) $\lambda=0.01$, (b) $\lambda=0.04$, (c) $\lambda=0.064$, and (d) $\lambda=0.076$.