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

We use the quantum unimodular theory of gravity to relate the value of the cosmological constant, A, and the energy scale for the emergence of cosmological classicality. The fact that A and unimodular time are complementary quantum variables implies a perennially quantum Universe should A be zero (or, indeed, fixed at any value). Likewise, the smallness of A puts an upper bound on its uncertainty, and thus 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 x 1011 GeV for the observed A, and taking the region of classicality to be our Hubble volume. We confirm this argument with a direct evaluation of the wave function 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 Elk: for -Elk < 10-3, classicality is reached at > 4 x 1012 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 nonlinearity for a red spectrum with the observed spectral index Its 1/4 0.967o4 thorn (about 1011 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.

Automated summary

In this study, the researchers use the quantum unimodular theory of gravity to investigate the relationship between the cosmological constant and the energy scale for the emergence of cosmological classicality. The findings suggest that a perennially quantum Universe would occur if the cosmological constant is zero. The study also establishes a lower bound on the uncertainty of the unimodular clock or the cosmic time for the emergence of classicality based on the smallness of the cosmological constant. Classicality arises at around 7 x 1011 GeV for the observed value of the cosmological constant, highlighting the importance of understanding the classicality and quantum nature of the Universe.