Extended Scalar-Tensor Theories of Gravity

Abstract: We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.

• The paper classifies novel scalar-tensor theories by imposing conditions that limit propagating degrees of freedom beyond traditional Horndeski models.
• It employs generalized conformal and disformal transformations to rigorously generate higher-order Lagrangians and maintain theoretical consistency.
• The study explores new effective field theory operators with implications for dark energy, suggesting experimental pathways in cosmological surveys.

Overview of Extended Scalar-Tensor Theories of Gravity

The paper "Extended Scalar-Tensor Theories of Gravity" by Marco Crisostomi, Kazuya Koyama, and Gianmassimo Tasinato introduces new scalar-tensor theories of gravity that extend current models beyond Horndeski, with particular focus on their cosmological significance. Key to this study is the objective to maintain three propagating degrees of freedom by controlling the order of derivatives, while extending the formalism through conformal and disformal transformations.

Scalar-tensor theories are vital in modeling cosmic phenomena such as inflation and dark energy. Traditionally, these are represented by the Horndeski theory, which supports second-order equations of motion. However, recent advancements have embraced theories labeled as "beyond Horndeski," which also adhere to the aforementioned criteria but extend the theoretical framework by supporting higher-order equations of motion.

Main Contributions

1. Classification of Theories: The authors rigorously derive conditions and classify consistent scalar-tensor theories that are quadratic in the second derivatives of the scalar field. Building on this groundwork, they identify distinct subclasses within the broader category of Extended Scalar-Tensor (EST) theories. This classification is pivotal for constructing models that align with observed cosmic dynamics.
2. Conformal and Disformal Transformations: The paper explores the connections between EST theories and both Horndeski and beyond Horndeski theories. This is achieved through generalised conformal and disformal transformations, which provide valuable methodologies for generating higher-order Lagrangians.
3. Phenomenological Implications: The work investigates the observational consequences of EST theories, particularly for dark energy. A noteworthy development is the introduction of novel EFT operators arising from EST theories, absent in existing Horndeski models. This suggests potential new avenues for experimental validation through cosmological surveys.
4. Minkowski Limit: Emphasis is placed on assessing which EST theories maintain a stable Minkowski limit, a critical condition when contemplating practical applications to weakly interacting gravitational systems and ensuring theoretical consistency.

Relevance and Future Directions

The discussions on effective field theory (EFT) of dark energy positions EST theories within a practical context, linking abstract theoretical insights to directly observable cosmic phenomena. By introducing non-traditional operators in the EFT framework, the authors suggest that these theories might reveal new facets of dark energy dynamics unexplored by current paradigms.

The classification and constraints derived in the paper offer a structured pathway for formulating new theories that harmonize with the foundational principles of scalar-tensor gravitation while pushing the boundaries toward understanding higher-order systems. Future investigations could leverage these insights to explore further extensions, particularly those integrating cubic or even higher powers of scalar derivatives, potentially leading to comprehensive models addressing unexplained cosmic phenomena.

In conclusion, while reaffirming the foundational elements of scalar-tensor gravity, this study provides an innovative expansion with profound implications for cosmological theory, offering structured methodologies for future theoretical advancements and observational tests.