- The paper presents a systematic derivation of generalized Galileon models that preserve second-order field equations and stress tensors in curved backgrounds.
- It employs nonminimal curvature couplings and Levi-Civita tensors to reformulate the Lagrangians, ensuring stability by eliminating higher-order derivatives.
- The study offers a scalable framework for extending modified gravity theories, paving the way for new insights into cosmological phenomena.
Generalized Galileons: Curved Background Scalar Models
The paper "Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors" by C. Deffayet, S. Deser, and G. Esposito-Farese, explores the extension of Galileon scalar field theories, originally formulated in flat spacetime, to curved backgrounds, while preserving key second-order properties of their field equations and stress tensors. The focus of this paper is the systematic derivation of these scalar models that encompass both field and metric second-order derivatives, maintaining consistency across arbitrary dimensions.
Summary of Contributions
The Galileon model, introduced as an intriguing scalar field theory in the context of the Dvali-Gabadadze-Porrati (DGP) model, provides the foundation for this paper. The essential property of the Galileon model is its reliance solely on second-order derivatives in the equations of motion. However, challenges arise when transitioning from flat to curved spacetime, as the straightforward covariantization of these models introduces higher-order derivatives, adversely impacting the stability and tractability of these equations.
This paper resolves these issues by devising nonminimal curvature coupling terms that extend the Galileon model to curved spaces without introducing third-order or higher derivatives. In particular, the paper establishes a uniform and transparent procedure applicable to any dimension D, systematically deriving extensions of the model in a manner that does not compromise the second-order nature of the original equations.
Numerical Results and Theoretical Claims
The paper provides explicit formulations and general expressions for the extended Lagrangians, ensuring that the nonminimal couplings introduced do not affect the Galileon model's essential properties. Equations like (9) for the flat background and (35) for a general background encapsulate the derived results. The authors assert that these new formulations not only maintain the desired mathematical properties but also exhibit a systematic scalability to higher-dimensional and differently curved backgrounds.
The derivation process employs Levi-Civita tensors, allowing reformulation of the Galileon Lagrangians into a form that naturally excludes higher derivatives. Importantly, these reformulations allow integrating by parts to handle surface terms effectively, ensuring no contribution from potentially harmful higher derivative terms.
Implications and Future Directions
The presented work potentially paves the way for new advancements in theoretical cosmology and gravitational physics. Practically, these models could enrich our understanding of modified gravity theories, offering paths to address unexplained cosmological phenomena without invoking higher-order differential equations that complicate these models.
For future exploration, understanding the phenomenological implications of these new scalar-tensor couplings in varied cosmological scenarios could provide valuable insights. Additionally, investigating the stability and perturbative behavior of these models in concrete astrophysical and cosmological settings could further clarify their utility and limitations.
In conclusion, this paper delivers a comprehensive framework for extending Galileon theories to curved spacetime, preserving their second-order nature across all dimensions, and setting the stage for future theoretical investigations in modified gravity models.
