Quantum Gravity Constraints on Inflation

TL;DR

The paper introduces entropy-based quantum gravity bounds on inflation by requiring that the entropy associated with the inflaton sector be less than the de Sitter horizon entropy $S_{dS}$. It develops two prescriptions—bits-per-area and entanglement entropy—to quantify the inflationary entropy and shows that trans-Planckian flat directions cannot be realized by aggregating many sub-Planckian fields. The authors apply the bounds to string constructions, finding that racetrack inflation and KKLT vacua generally conflict with the entropy limit, whereas the Large Volume Scenario (LVS) can be compatible in a parametric sense via bulk KK modes. The work connects quantum gravity to inflation model-building and has implications for observable tensor modes in the CMB, while highlighting the need for explicit UV-complete calculations.

Abstract

We study quantum gravity constraints on inflationary model building. Our approach is based on requiring the entropy associated to a given inflationary model to be less than that of the de Sitter entropy. We give two prescriptions for determining the inflationary entropy, based on either `bits per unit area' or entanglement entropy. The existence of transPlanckian flat directions, necessary for large tensor modes in the CMB, correlates with an inflationary entropy greater than that allowed by de Sitter space. Independently these techniques also constrain or exclude de Sitter models with large-rank gauge groups and high UV cutoffs, such as racetrack inflation or the KKLT construction.

Figures (4)

• Figure 1: The realisation of de Sitter space in string theory: de Sitter space exists as a metastable object with a barrier between it and the 10-dimensional decompactification solution.
• Figure 2: The shaded area shows the comoving horizon together with an observer at the origin and the initial field profile $\phi(x)$. The future evolution of the shown observer leads to asymptotic de Sitter space. We associate the entropy of this quantum object 'asymptotic de Sitter space' to the number of initial field configurations $\phi(x)$ that evolve in the far future to this object.
• Figure 3: A wavepacket delocalised across the horizon. From the viewpoint of an observer whose horizon encompasses this wavepacket, this is just a conventional delocalised quantum mechanical state.
• Figure 4: The horizon field configurations, set by the vev of $\Phi$ in each fundamental box. This is shown for an axion field where the fundamental box size is $f_a^{-1}$.