- The paper generalizes Horndeski theories by introducing degenerate cubic scalar-tensor models that maintain three degrees of freedom.
- It establishes precise degeneracy conditions using Hessian analysis to exclude Ostrogradsky ghosts and ensure theoretical stability.
- The work classifies new minimally and non-minimally coupled frameworks, providing fresh avenues for exploring cosmological dynamics.
Overview of Scalar-Tensor Theories Beyond Horndeski
The paper, "Degenerate Higher Order Scalar-Tensor Theories Beyond Horndeski up to Cubic Order" presented by J. Ben Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui, and G. Tasinato, provides a comprehensive paper of scalar-tensor theories in the context of gravitational dynamics that allows for higher order derivatives without the onset of Ostrogradsky instabilities. This work builds on Horndeski’s foundational theory, which delineates the most general scalar-tensor actions producing second-order equations of motion, ensuring stability and consistency in gravitational models.
Main Contributions
- Generalization of Scalar-Tensor Theories: The authors focus on extending the landscape of Horndeski theories by introducing and classifying degenerate theories up to cubic order beyond Horndeski’s original formulations. These theories are structured to maintain at most three degrees of freedom through the degeneracy of the associated Lagrangians.
- Degeneracy Conditions: By leveraging the degeneracy criterion, a systematic method to identify viable scalar-tensor theories, the paper meticulously investigates scenarios where the Hessian matrix of the Lagrangian is degenerate. This ensures the exclusion of higher-order Ostrogradsky ghost modes, vital for maintaining theoretical coherence and practical applicability.
- Classification of New Theories: The research classifies seven frameworks of minimally coupled cubic theories and two classes of non-minimally coupled cubic theories, expanding the catalog of consistent higher-order scalar-tensor theories. The authors explore how these new classes relate to existing frameworks via conformal and disformal transformations, linking them to classical scalar-tensor theories.
- Implications for Cosmology: These newly identified theories provide fertile ground for exploration in cosmological applications, possibly impacting the theoretical models of the universe's acceleration and modifying the structure of astrophysical bodies. Their formulation can also influence the screening mechanisms such as the Vainshtein mechanism, potentially explaining deviations from GR under extreme conditions.
- Merging Quadratic and Cubic Theories: The paper explores the integration of quadratic and cubic terms within the theories. It outlines the criteria under which these combinations remain viable, maintaining degeneracy and stability.
Future Directions
The work sets the stage for further exploration into the phenomenological aspects of these theories, particularly their implications on cosmological scales. The authors propose studying stable cosmological solutions and examining their potential to describe dark energy dynamics consistently. Also, the extension to theories beyond cubic orders presents an avenue for future theoretical developments.
Additionally, further research could advance the understanding of the modified screening effects in scalar-tensor theories, enhancing our ability to test these predictions against high-precision cosmological and astrophysical observations.
Conclusion
The paper is a significant leap towards understanding degenerate scalar-tensor theories, contributing to the broader framework of modified gravity. By providing a systematic classification and examining the theoretical and practical viability of these models, the authors enhance the repository of stable gravitational models beyond General Relativity and Horndeski’s initial scope, thus pushing the boundaries of current theoretical physics in addressing fundamental cosmological questions.