# Spacetime Deformation Effect on the Early Universe and the PTOLEMY Experiment

## TL;DR

This paper investigates how spacetime noncommutativity affects relic neutrino detection in the early universe and at the PTOLEMY experiment, revealing a maximal noncommutativity scale that influences neutrino interactions and detection prospects.

## Contribution

It introduces a nonperturbative gauge field theory framework to analyze the impact of spacetime noncommutativity on relic neutrino physics and detection, establishing an upper bound on the noncommutativity scale.

## Key findings

- Noncommutative background induces vector-like photon coupling for neutrinos.
- Right-handed neutrinos can be thermally produced due to noncommutativity.
- Maximum noncommutativity scale is approximately 10^{-4} times the Planck mass.

## Abstract

Using a fully-fledged formulation of gauge field theory deformed by the spacetime noncommutativity, we study its impact on relic neutrino direct detection, as proposed recently by the PTOLEMY experiment. The noncommutative background tends to influence the propagating neutrinos by providing them with a tree-level vector-like coupling to photons, enabling thus otherwise right-handed (RH) neutrinos to be thermally produced in the early universe. Such a new component in the universe's background radiation has been switched today to the almost fully active sea of non-relativistic neutrinos, exerting consequently some impact on the capture on tritium at PTOLEMY. The peculiarities of our nonperturbative approach tend to reflect in the cosmology as well, upon the appearances of the coupling temperature, above which RH neutrinos stay permanently decoupled from thermal environment. This entails the maximal scale of noncommutativity as well, being of order of $10^{-4} M_{Pl}$, above which there is no impact whatsoever on the capture rates at PTOLEMY. The latter represents an exceptional upper bound on the scale of noncommutativity coming from phenomenology.