Quantum Spacetime and the Universe at the Big Bang, vanishing interactions and fading degrees of freedom

TL;DR

This paper explores how near the Big Bang, quantum spacetime may effectively reduce to a point with vanishing interactions, supported by mathematical convergence results in quantum field theories on quantum spacetime.

Contribution

It introduces a novel approach to quantum field theory on quantum spacetime that maintains ultraviolet finiteness and demonstrates convergence of interacting fields to zero at the origin of time.

Findings

Interacting quantum fields vanish at the quantum point near the Big Bang.

Perturbative expansions remain ultraviolet finite and converge in the adiabatic limit.

The S matrix may converge to unity in the limit of diverging Planck length.

Abstract

As discussed in arXiv:1501.03298, Physics suggests that, close to cosmological singularities, the effective Planck length diverges, hence a "quantum point" becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This last point is supported by converging evidences in two different approaches to interacting quantum fiedls on Quantum Spacetime: the field operators evaluated at a "quantum point" converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach, while, at all orders we find convergence to zero of the interacting field operators obtained adapting methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, with a novel picture of the effective Lagrangian introduced in arXiv:1906.05855. This novel picture mantains the ultraviolet finiteness of the perturbation expansion but allows us to prove also the convergence in the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.