Crossing the phantom divide in scalar-tensor and vector-tensor theories

TL;DR

This paper investigates the theoretical challenges of achieving phantom-divide crossing in scalar-tensor and vector-tensor theories, proposing a specific model that accomplishes this transition without instabilities.

Contribution

It demonstrates that breaking shift symmetry in Horndeski theories enables phantom-divide crossing and constructs an explicit, stable model realizing this transition.

Findings

Phantom-divide crossing is difficult in shift-symmetric theories without pathologies.

Breaking shift symmetry allows for stable crossing in Horndeski models.

The constructed model achieves crossing without ghosts or Laplacian instabilities.

Abstract

DESI observations of baryon acoustic oscillations (BAOs), combined with cosmic microwave background (CMB) and type-Ia supernova (SN Ia) data, suggest that the dark energy equation of state $w_{\rm DE}$ crosses the phantom divide from $w_{\rm DE} < -1$ to $w_{\rm DE} > -1$ at low redshifts. In shift-symmetric Horndeski and generalized Proca theories with luminal gravitational-wave speed and no direct couplings to dark matter, we show that such a phantom-divide crossing is generically difficult without theoretical pathologies. Breaking the shift symmetry in Horndeski theories allows this transition. We construct an explicit model with broken shift symmetry, in which the scalar field has a potential in addition to a Galileon self-interaction and a quadratic kinetic term. This model realizes the desired phantom-divide crossing at low redshifts without introducing ghosts and Laplacian instabilities.