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

TL;DR

The paper investigates null energy condition (NEC) violation as a mechanism to address cosmological singularities and its observational relevance in a DESI DR2-era universe with dynamical dark energy. It adopts a unified EFT for inflation and dark energy and employs a non-parametric reconstruction of the beyond-Horndeski operator $\tilde{m}_4^2(a)$, using five scale-factor nodes and Gaussian Process interpolation to remain model-agnostic. By combining DESI DR2 BAO with Planck CMB and SNIa data and enforcing ghost and gradient stability, the study finds a ~$2\sigma$ hint for a nonzero $\tilde{m}_4^2 \delta g^{00}R^{(3)}$ term, indicating that beyond-Horndeski physics can stabilize NEC violation without altering background or tensor dynamics at quadratic order. The work thus provides a model-independent avenue to test NEC-violating physics and suggests a conceptual link between NEC dynamics in the early universe and late-time cosmic acceleration, while acknowledging that the signal is not yet conclusive.

Abstract

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 $w_{\rm DE} < -1$ at redshift $z \lesssim 1$ to $w_{\rm DE} > -1$ 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.

Figures (2)

• Figure 1: Upper panel:$1\sigma$ and $2\sigma$ posterior constraints in the $w_0-w_a$ plane of the EFT models with only $\delta g^{00}R^{(3)}$ (red) and both $\delta g^{00}R^{(3)}$ and $(\delta g^{00})^2$ turned on. The gray region indicates the $w_0-w_a$ parameter space where phantom crossing happens. Lower panel: the reconstructed functional shape of $\tilde{m}_4^2(a)$, the EFT coefficient of $\delta g^{00}R^{(3)}$. The blue dotted lines mark the $1\sigma$ posterior of $\tilde{m}_4^2(a)$ at each $a$. The gray points are the reconstruction nodes $\{\tilde{m}_{4,i}\}$ with $2\sigma$ range marked by blue boxes and $3\sigma$ range indicated by error bars. Red line plots the mean function of $\tilde{m}_4^2(a)$. The horizontal black dashed line marks the general relativity limit $\tilde{m}_4^2=0$.
• Figure S1: The same model given by Eq. (13) in the main text, with both the $(\delta g^{00})^2$ and $\delta g^{00}R^{(3)}$ operators turned on, and the same plotting style as in Fig. 1, but replacing the SNIa dataset with Pantheon+.