Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (1602.08398v1)

Abstract: We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo conformal-disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to field redefinitions.

• The paper classifies degenerate higher-order scalar-tensor theories beyond Horndeski by using degeneracy criteria to avoid Ostrogradski instability.
• It derives explicit disformal transformation laws that preserve the quadratic structure of DHOST theories, ensuring no new degrees of freedom emerge.
• It connects DHOST subclasses to known frameworks like mimetic gravity, offering robust avenues for cosmological model building and gravitational research.

Insights into Degenerate Higher Order Scalar-Tensor Theories Beyond Horndeski and Disformal Transformations

The paper of modified gravity theories often pivots around scalar-tensor theories, which have gained prominence due to their capability of extending General Relativity while adhering to the principle of limiting unwanted instabilities such as the Ostrogradski instability. This paper embarks on an exploration of degenerate higher-order scalar-tensor (DHOST) theories which encompass quadratic dependencies on the second derivatives of a scalar field. A central theme is understanding how these theories are transformed and classified under general disformal transformations.

Core Contributions

The authors of the paper delve into the classification of scalar-tensor theories, emphasizing degeneracy as a criterion to ensure viable gravitational modifications without invoking the Ostrogradski instability. Here's a detailed look at the essential contributions:

• Classification and Stability: Scalar-tensor theories are classified beyond Horndeski, focusing on quadratic Lagrangians. The paper introduces a comprehensive classification of these theories, categorized into three broad classes, each stable under disformal transformations. The classification further narrows down into subclasses that are individually stable as well.
• Disformal Transformations: A significant analysis goes into determining how these scalar-tensor theories behave when subjected to disformal transformations. The authors derive explicit transformation laws, maintaining the quadratic nature of DHOST theories. This transformation is shown to preserve the degeneracy across different classes, signifying that these transformative processes won't introduce new dynamical degrees of freedom, upholding the theories’ original constraints.
• Intrinsic Link to Known Theories: Notably, certain subclasses of DHOST theories overlap with known frameworks such as Horndeski theories, mimetic gravity, and khronometric models. Through disformal transformations, the paper establishes connections, extending the understanding of how existing models fit within the broader DHOST spectrum.

Implications and Applications

This work produces several noteworthy implications for both theoretical physics and cosmological applications:

• Cosmological Insights: The classification and understanding of DHOST theories provide a refined toolkit for exploring cosmological models, particularly those diverging from General Relativity by introducing controlled modifications to gravitational dynamics. The interplay between disformal transformations and cosmological perturbations in DHOST frameworks is ripe for exploration, offering potential explanations for observed cosmic phenomena without relying on dark energy or other exotic components.
• Model Building and Future Exploration: The broader classification of DHOST theories presents a plethora of opportunities for model building. By linking these theories to existing frameworks like mimetic gravity, researchers can feasibly adapt these models to address specific cosmological or astrophysical challenges. The stability of these theories under disformal transformations underscores their robustness, making them attractive candidates for exploring gravity’s role in the universe.

Future Research Directions

The intricate relationship between DHOST theories and other gravitational models invites further investigative efforts. Future research could angle towards:

• Numerical Simulations: Utilizing numerical simulations to explore the cosmological evolution of universes described by these DHOST theories. Such simulations could provide insights into the observable consequences of DHOST-induced modifications on large-scale structures and cosmic background radiation.
• Observational Signatures: Examining the precise observational signatures of these theories. This entails crafting constraints from gravitational wave observations, galaxy rotation curves, or lensing phenomena to validate or constrain DHOST contributions.
• Exploration of New Theories: Digging deeper into subclasses not directly linked to existing models, potentially unearthing novel theories that could inform future gravitational research.

In summary, the presented work pushes the boundary of scalar-tensor theories, underlining the importance of degeneracy and disformal transformations in maintaining theoretical consistency and opening new avenues for research into modified gravity. The findings bolster ongoing efforts to unify various gravitational theories while ensuring stability and compatibility with established physical laws.