Null energy condition violation and beyond Horndeski physics in light of DESI DR2 data

Inflation and dark energy (DE), both featuring accelerated expansion, are crucial components of modern cosmology. As indicated by singularity theorems, null energy condition (NEC) violation is essential for resolving the initial singularity of inflation. The latest DESI DR2 results show that the DE equation of state evolves from $w_{\mathrm{D}\mathrm{E}}<-1$ at redshift $z\lesssim 1$ to $w_{\mathrm{D}\mathrm{E}}>-1$ today, reinforcing interest in testing NEC violation in the observable Universe. Within a unified effective field theory framework that applies to both inflation and DE, we use DESI DR2 data and a non-parametric reconstruction approach to test, for the first time, the ``beyond Horndeski’’ physics known to support fully stable NEC violation in nonsingular cosmology. Therefore, our work provides a novel avenue to constrain the physics underlying NEC violation in a model agnostic way. It also highlights the potential relevance of NEC violation to both the primordial Universe and late-time cosmic acceleration.