Loop quantum gravity effects on inflation and the CMB

TL;DR

The paper investigates how loop quantum cosmology provides a non-singular onset of inflation via a short super-inflation phase that pushes the inflaton up its potential hill, potentially setting suitable initial conditions for standard slow-roll inflation. It derives an effective dynamics with a quantum correction factor D(q) in the density and an adjusted Friedmann equation, showing the big-bang singularity is avoided and that a brief anti-friction phase can drive sufficient e-folds when phi_max reaches around a few times the Planck mass. It then analyzes cosmological perturbations generated after this quantum era, finding a modified curvature spectrum near the turning point where slow-roll is violated, including a potentially observable running of the spectral index and a suppression of power on the largest scales. The results suggest an indirect loop quantum gravity signature in the CMB under certain conditions, highlighting the need for a more complete treatment of perturbations within loop quantum gravity to make robust observational predictions.

Abstract

In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early and short super-inflation phase. During super-inflation, non-perturbative quantum corrections to the dynamics drive an inflaton field up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyze the cosmological perturbations generated when slow-roll is violated after super-inflation, and show that loop quantum effects can in principle leave an indirect signature on the largest scales in the CMB, with some loss of power and running of the spectral index.

Figures (3)

• Figure 1: Evolution of the inflaton (in Planck units). We set $\dot{\phi}_{i}/(m_\phi M_{\rm pl})=2$, with $m_\phi/M_{\rm pl}=10^{-6}$, and choose $\phi_i/M_{\rm pl}$ as the minimum value satisfying the uncertainty bound, Eq. (\ref{['up']}), i.e. $\phi_i/M_{\rm pl} \sim 10^{12}j^{-15/2}$. The solid curve has $j = 100$, the upper dashed curve has $j = 125$, and the lower dashed curve has $j = 75$. Inset: Evolution of the scale factor and Hubble rate (in units of $m_\phi$) with the same parameters as the solid curve for $\phi$.
• Figure 2: The maximum reached by $\phi$ (in Planck units) as a function of $j$. From top to bottom, the curves correspond to initial conditions $\dot{\phi}_i/(m_\phi M_{\rm pl}) = 5, 2.5, 1, 0.5, 0.25, 0.1$ and $\phi_i/M_{\rm pl}$ is taken as the minimum value satisfying the uncertainty bound, Eq. (\ref{['up']}). An increase (decrease) in $j$ and ${\dot \phi_i}$ leads to an increase (decrease) in the number of e-folds.
• Figure 3: The CMB angular power spectrum with loop quantum inflation effects. From top to bottom, the curves correspond to (i) no loop quantum era (standard slow-roll chaotic inflation), (ii) $\bar{\alpha}=-0.04$ for $k \le k_0=2 \times 10^{-3}\,{\rm Mpc}^{-1}$, (iii) $\bar{\alpha}=-0.1$ for $k \le k_0$, and (iv) $\bar{\alpha}=-0.3$ for $k \le k_0$. There is some suppression of power on large scales due to the running of the spectral index.