Weakly Broken Galileon Symmetry

TL;DR

Weakly Broken Galileon invariance identifies a radiatively robust subset of Horndeski scalar-tensor theories in which the galileon symmetry is softly broken by gravity. By preserving the leading galileon quantum non-renormalization properties with two scales $\Lambda_3$ and $\Lambda_2=(M_{ m Pl}\Lambda_3^3)^{1/4}$, the framework yields (quasi-) de Sitter backgrounds that are stable against loops and supports novel inflationary dynamics and late-time acceleration. The construction generalizes the covariant galileon to a broader class of models, enabling kinetically driven or slow-roll–driven inflation with tunable sound speeds and potentially large non-Gaussianities, while maintaining a controlled EFT expansion. In the late universe, the theory maps onto a Horndeski description with time-dependent EFT parameters $\alpha_K,\alpha_B,\alpha_M,\alpha_T$, allowing screening via the Vainshtein mechanism and compatibility with current constraints. Overall, WBG invariance broadens the landscape of technically natural cosmological models and provides a structured path to testable predictions for inflation and dark energy.

Abstract

Effective theories of a scalar $φ$ invariant under the internal \textit{galileon symmetry} $φ\toφ+b_μx^μ$ have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of \textit{weakly broken galileon invariance}, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon's quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.

Figures (2)

• Figure 1: For every given vertex, a solid straight line corresponds to a possible external leg resulting in a scalar with at most one derivative acting on it. A dashed line corresponds to an external scalar with at least two derivatives, while a wiggly line denotes an external graviton.
• Figure 2: Single-graviton vertices, which can contribute two or three external scalars with one derivative ($(\partial\phi)^2$ or $(\partial\phi)^3$) to a 1PI vertex. The vertices from the second line exactly cancel for the unique (non-minimal) curved-space extension of the galileon that retains second-order equations of motion.