- The paper introduces a novel class of scalar-tensor theories that extend Horndeski models by including higher-order terms while evading ghost instabilities.
- It employs the ADM formalism to demonstrate that these extended theories maintain only three physical degrees of freedom consistent with gravitational constraints.
- Disformal transformations validate their covariant formulation, indicating potential observable effects on cosmic acceleration and gravitational wave propagation.
Healthy Theories Beyond Horndeski: Exploring Novel Scalar-Tensor Theories
The paper "Healthy Theories Beyond Horndeski" by Gleyzes et al. presents a significant extension to the widely studied Horndeski scalar-tensor theories of gravity. These theories are traditionally invoked to account for cosmological phenomena such as the observed acceleration of the universe. The authors introduce a new class of scalar-tensor theories, exceeding the classical constraints imposed by Horndeski's framework, which has been regarded as exhaustive in accommodating second-order equations of motion while being free from Ostrogradski instabilities.
Theoretical Development
The paper builds upon the generalized Galileon models, transcending the original Horndeski framework. While Horndeski theories ensure second-order equations to avert the emergence of ghost-like degrees of freedom typically associated with higher-order derivatives, the present work reveals that such necessity may not be absolute. The proposed theories are demonstrated to include terms that lead to higher-order equations of motion; however, the true propagating degrees of freedom intrinsically maintain second-order dynamics in the absence of gravity, effectively circumventing the Ostrogradski instability issue.
The authors employ the Arnowitt-Deser-Misner (ADM) formalism to reformulate the proposed theories explicitly. This reformulation provides a transparent framework to perform a Hamiltonian analysis. Through this method, it becomes evident that the theories in question possess only the anticipated three degrees of freedom: a scalar degree akin to a cosmic scalar field and two tensor modes analogous to gravitational waves in General Relativity (GR). The ADM approach allows the identification and preservation of first-class constraints analogous to the momentum constraints in GR, ensuring the elimination of viably redundant gravitational degrees of freedom.
A noteworthy aspect of this research is its verification of the covariant formulation of these extensions beyond Horndeski. Through disformal transformations, the paper affirms that these newer models can be associated with Horndeski's class concerning covariant field equations. More specifically, through this transformation, the models maintain second-order behavior once projected onto a suitable metric, underscoring their legitimacy and "healthiness" even under complex configurations.
Implications and Phenomenological Prospects
A distinct and intriguing phenomenological implication of these non-Horndeski theories is the interaction between gravity and matter's speed of sound, independent of the nature of their coupling in traditional Horndeski configurations. Contrary to canonical expectations, these novel models provoke alterations in sound speed due to scalar degree interactions unmatched in typical cosmological perturbation theories. The mixing induced by the scalar fields loosely coupled with ordinary matter paves the way for an assortment of observational effects that could challenge, refine, or falsify these extensions through empirical data analysis.
Conclusion and Future Directions
The exploration of these expanded theories beyond Horndeski provides new vistas in scalar-tensor theories, urging further examination of their observational signatures. Future developments in this regard may lead to refined cosmological models that could offer deeper insights into the nature of dark energy, the mechanisms underlying cosmic acceleration, and potentially, new physics in gravitational theory.
This paper denotes a substantive step forward in theoretical cosmology, informing ongoing discussions and investigation paths within the gravitational theory domain, urging the scientific community to brainstorm novel testable predictions, particularly concentrating on potential observable discrepancies from GR in the cosmological setting.