Imperfect Dark Energy from Kinetic Gravity Braiding

TL;DR

The paper develops a broad class of scalar-tensor theories with second-derivative interactions, formulated as $\mathcal{L}=K(\phi,X)+G(\phi,X)\Box\phi$, which introduce kinetic braiding between the scalar and gravity. This braiding yields an imperfect-fluid behavior for the scalar and a novel effective metric for perturbations, while preserving second-order equations of motion and avoiding extra degrees of freedom. Cosmological analysis reveals attractor solutions in which the scalar tracks external matter, often yielding a phantom equation of state on the attractor and a de Sitter end state, with stable perturbations ($D>0$, $c_s^2>0$) even when crossing the phantom divide. The Imperfect Dark Energy example demonstrates a simple, viable instantiation with Early Dark Energy signatures, a phantom attractor, and concrete observationally allowed parameter ranges, highlighting a new, testable dark energy framework built on kinetic braiding.

Abstract

We introduce a large class of scalar-tensor models with interactions containing the second derivatives of the scalar field but not leading to additional degrees of freedom. These models exhibit peculiar features, such as an essential mixing of scalar and tensor kinetic terms, which we have named kinetic braiding. This braiding causes the scalar stress tensor to deviate from the perfect-fluid form. Cosmology in these models possesses a rich phenomenology, even in the limit where the scalar is an exact Goldstone boson. Generically, there are attractor solutions where the scalar monitors the behaviour of external matter. Because of the kinetic braiding, the position of the attractor depends both on the form of the Lagrangian and on the external energy density. The late-time asymptotic of these cosmologies is a de Sitter state. The scalar can exhibit phantom behaviour and is able to cross the phantom divide with neither ghosts nor gradient instabilities. These features provide a new class of models for Dark Energy. As an example, we study in detail a simple one-parameter model. The possible observational signatures of this model include a sizeable Early Dark Energy and a specific equation of state evolving into the final de-Sitter state from a healthy phantom regime.