Cosmological constraints on Galileon dark energy with broken shift symmetry

TL;DR

The paper investigates whether a dynamical dark energy model based on a cubic Galileon/kinetic-braiding scalar field with a shift-symmetry-breaking potential can reproduce phantom-crossing behavior suggested by data. Framed within an EFT/Horndeski context, the model is implemented with hi_class and confronted with a comprehensive data set including DESI BAO, DES-Y5/Pantheon+, Union3, Planck, and ACT. The analysis yields strong statistical support for the Galileon+potential scenario over ΛCDM (e.g., $\log B \approx 6.5$) and finds a present-day equation of state around $w_0 \approx -0.75$ with a past phantom phase crossing near $z \approx 0.5$. However, the model predicts nontrivial gravitational modifications (e.g., $\mu(z)>1$) and faces significant ancillary constraints from fifth forces, screening viability, and EFT consistency, highlighting that cosmological data alone cannot pin down the dark energy microphysics and pointing to growth, GW, and ISW tests as crucial future probes.

Abstract

Current cosmological data seem to show that dark energy is evolving in time and that it possibly crossed the phantom divide in the past. So far the only theories that lead to such a behavior involve a non-trivial coupling between dark energy, in the form of a scalar field, and the gravitational or matter sector. We show that there is another possibility involving both a non-trivial kinetic sector in a cubic Galileon theory and a scalar field potential that breaks the Galileon shift symmetry, which can lead to a similar phenomenology on large scales. We perform a full Bayesian analysis using the latest cosmological data, including DESI DR2 BAO measurements, type Ia SNe measurements from DESY5, Union3, and Pantheon+, and CMB data from Planck and ACT. We find that it is statistically strongly favored over a Universe dominated by a cosmological constant (with a Bayes factor of $\log B\simeq 6.5$). Yet, as with other non-minimally coupled theories, it has severe ancillary gravitational effects. These can be mitigated to some extent, but as with other viable theories, the penalty is ever more elaborate scalar field models of dark energy.

Figures (7)

• Figure 1: (Left) Equation of state evolution $w(z)$ for a cubic Galileon model with and without a potential. (Right) Phase-space wedge structure for various dark energy models where their theory priors are compared to the data posteriors.
• Figure 2: 68% and 95% C.L. posterior distributions for the cubic Galileon/kinetic braiding dark energy model parameters with a broken shift symmetry.
• Figure 3: Posterior constraints on $w(z)$ for the non-minimally coupled dark energy model Wolf:2025jed and the cubic Galileon dark energy model considered here. Both dark energy constructs produce similar equations of state which explains their similar success in fitting the expansion history data.
• Figure 4: Posterior constraints on $\mu(z)$ (Left) and f$\sigma_8$ (Right) for the non-minimally coupled dark energy model Wolf:2025jed and cubic Galileon dark energy model considered here. While both models predict similar phenomenology for the dark energy equation of state and fit the expansion history data remarkably well, the models predict very different modified gravity effects which will show up in their predictions for growth.
• Figure 5: