- The paper systematically reviews DHOST theories that extend Horndeski models to bypass Ostrogradsky instabilities.
- It rigorously classifies quadratic and cubic-order degenerate theories to model cosmic acceleration and modified gravity.
- Observational constraints from gravitational waves, such as GW170817, narrow the viable parameter space for these models.
Dark Energy and Modified Gravity in DHOST Theories: An Overview
The paper, authored by David Langlois, provides a comprehensive review of Degenerate Higher-Order Scalar-Tensor (DHOST) theories. This framework extends traditional scalar-tensor theories in an effort to address significant unresolved issues in cosmology, particularly the phenomena of dark energy and modified gravity. DHOST theories emerge as a promising avenue since they propagate a single scalar degree of freedom, thereby circumventing the problematic Ostrodradsky instability typically associated with theories involving higher-order derivatives. These theories have been thoroughly classified up to the cubic order in derivatives, and they include the well-known Horndeski and Beyond Horndeski theories as subsets.
Core Concepts and Methodologies
The key distinguishing feature of DHOST theories lies in the degeneracy of their Lagrangian, which ensures the absence of the Ostrodradsky instability by allowing only one scalar degree of freedom to propagate. This review begins with an exploration of scalars with second-order derivatives, elaborating on how classical theories such as Horndeski and Beyond Horndeski fit into this broader framework. Horndeski's work, identified by second-order Euler-Lagrange equations, and Beyond Horndeski theories, known for their third-order equations stabilized via degeneracy constraints, were early explorations into this field.
DHOST theories push these boundaries further by employing degeneracy conditions to systematically categorize theories at quadratic and cubic orders. The review highlights an exhaustive classification system for DHOST theories that encompasses a variety of subclasses, each defined by specific degeneracy constraints. Such classification serves as a foundation to explore their applicability in cosmological and astrophysical settings.
Implications and Observational Viability
The cosmological and astrophysical implications of DHOST theories are profound. The paper scrutinizes how these theories are expressible within the context of an effective field theory approach to dark energy, leveraging the ADM formalism for decomposing spacetime. This approach facilitates an elucidation of the potential cosmological dynamics induced by DHOST theories, offering refined models for cosmic acceleration without invoking an explicit cosmological constant.
One notable advance within this research domain is the consideration of DHOST theories post observations of gravitational waves, such as those from the GW170817 event. Such events strongly constrain the speed of gravitational wave propagation, thereby significantly restricting the parameter space of viable DHOST models. Langlois' paper explores the ramifications of these constraints, underscoring how certain parameter classes within DHOST theories remain consistent with the observed parity between gravitational wave and light velocities.
Future Directions
The exploration of DHOST theories opens up avenues for further inquiry into their consistency with cosmological observations and their integration into broader frameworks such as quantum gravity. Key future directions hinted at in the paper include the scrutiny of their robustness against quantum corrections and the development of a consistent initialization for cosmological scenarios within these frameworks. Furthermore, the ramifications of DHOST theories on compact objects, particularly neutron stars and black holes, remain a fertile ground for testing the viability of these models under extreme conditions.
In summary, DHOST theories represent a sophisticated extension of scalar-tensor models contributing to our understanding of dark energy and modified gravity. Langlois' review not only systematically categorizes these theories but also highlights their potential significances and the observational frontiers they are yet to grapple with. The insights provided set the stage for future explorations into the foundational principles of cosmology and the gravitational dynamics of the universe.