Imperfect Dark Energy from Kinetic Gravity Braiding (1008.0048v2)

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.

• The paper introduces kinetic gravity braiding that modifies scalar field dynamics to mimic imperfect fluid behavior in dark energy models.
• It demonstrates phantom-like behavior and attractor solutions while avoiding instabilities through a carefully constructed Lagrangian.
• The models naturally evolve to a de Sitter phase at late times, offering significant insights into cosmic acceleration and modified gravity.

Imperfect Dark Energy from Kinetic Gravity Braiding

The paper presents a substantial extension to the framework of scalar-tensor theories through the introduction of a class of models characterized by a unique form of interaction known as kinetic gravity braiding. This approach involves scalar fields with second derivatives in their interactions, resulting in a distinctive mixing of scalar and tensor kinetic terms. This kinetic braiding modifies the stress-energy tensor of the scalar field beyond the perfect-fluid form, leading to rich phenomenological features.

The primary contribution of this work lies in formulating a broad spectrum of scalar-tensor models that avoid additional degrees of freedom despite including second derivatives. This is achieved through carefully constructed Lagrangian terms of the form $\mathcal{L} = K(\phi,X) + G(\phi,X)\Box\phi$, where $K$ and $G$ are generic functions, and $X$ is the kinetic term of the scalar field. A significant theoretical advance is enabling the scalar field to mimic imperfect fluid dynamics, offering a novel perspective on dark energy modeling.

The paper highlights several intriguing properties and theoretical implications:

1. Attractor Solutions: These models feature cosmological solutions where the scalar field acts as a monitor for external matter behavior. The position of such attractors is sensitive to both the form of the Lagrangian and the external energy density.
2. Phantom Dynamics without Instabilities: The scalar can assume phantom-like behavior and cross the phantom divide without introducing ghosts or gradient instabilities. This is achieved without invoking explicit scalar potential terms or nonminimal gravitational couplings.
3. Late-time Cosmological Behavior: The models naturally evolve to a de Sitter state as an asymptotic late-time behavior, making them suitable candidates for describing current cosmic acceleration attributed to dark energy.

From a phenomenological standpoint, the work explores the observational signatures of simple scalar-tensor models and proposes a comprehensive method to paper early dark energy behaviors and evolving equations of state that transition towards a de Sitter-like phase dominated by healthy phantom dynamics.

Theoretical implications extend to providing an alternative to existing dark energy frameworks, such as quintessence or k-essence, and exploring the potential to resolve persistent cosmological issues like the null energy condition violation, previously thought to be plagued by instabilities.

Looking forward, the framework establishes a fertile ground for further exploration into cosmological perturbations and their relevance to structure formation, likely impacting the broader understanding of cosmic acceleration and the role of modified gravity theories. This paper forms a critical building block in extending the theoretical machinery for dark energy and invites additional research focusing on specific cosmological scenarios, potential coupling with matter, and implications for high-energy physics and cosmology.