Lower bound on the cosmological constant from the classicality of the Early Universe

TL;DR

This paper uses quantum unimodular gravity to connect the value of the cosmological constant with the emergence of classicality in the early universe, deriving a lower bound on the energy scale of classicality based on cosmological parameters.

Contribution

It introduces a novel relation between the cosmological constant and the emergence of classicality using unimodular gravity, providing a lower bound on the classicality energy scale.

Findings

Classicality emerges at around 7 x 10^{11} GeV for the observed Λ.

The classicality scale depends on the size of the classical patch, potentially up to 4 x 10^{12} GeV.

The classicality scale is linked to the non-linearity scale of the primordial spectrum.

Abstract

We use the quantum unimodular theory of gravity to relate the value of the cosmological constant, $\Lambda$, and the energy scale for the emergence of cosmological classicality. The fact that $\Lambda$ and unimodular time are complementary quantum variables implies a perennially quantum Universe should $\Lambda$ be zero (or, indeed, fixed at any value). Likewise, the smallness of $\Lambda$ puts an upper bound on its uncertainty, and so a lower bound on the unimodular clock's uncertainty or the cosmic time for the emergence of classicality. Far from being the Planck scale, classicality arises at around $7 \times 10^{11}$ GeV for the observed $\Lambda$, and taking the region of classicality to be our Hubble volume. We confirm this argument with a direct evaluation of the wavefunction of the Universe in the connection representation for unimodular theory. Our argument is robust, with the only leeway being in the comoving volume of our cosmological classical patch, which should be bigger than that of the observed last scattering surface. Should it be taken to be the whole of a closed Universe, then the constraint depends weakly on $\Omega_k$: for $-\Omega_k < 10^{-3}$ classicality is reached at $ > 4 \times 10^{12}$ GeV. If it is infinite, then this energy scale is infinite, and the Universe is always classical within the minisuperspace approximation. It is a remarkable coincidence that the only way to render the Universe classical just below the Planck scale is to define the size of the classical patch as the scale of non-linearity for a red spectrum with the observed spectral index $n_s = 0.967(4)$ (about $10^{11}$ times the size of the current Hubble volume). In the context of holographic cosmology, we may interpret this size as the scale of confinement in the dual 3D quantum field theory, which may be probed (directly or indirectly) with future cosmological surveys.