New class of consistent scalar-tensor theories.

Area of Science:

• Theoretical Physics
• Gravitational Theory
• Cosmology

Background:

• Horndeski theory, also known as generalized Galileon models, is a prominent framework for scalar-tensor theories of gravity.
• Standard lore suggests that higher-order derivative equations of motion lead to Ostrogradski instabilities, rendering the theory unphysical.
• Understanding the stability and properties of modified gravity theories is crucial for cosmology and fundamental physics.

Purpose of the Study:

• To introduce a new class of scalar-tensor theories that extend Horndeski models.
• To demonstrate that these theories, despite higher-order equations of motion, are free from Ostrogradski instabilities.
• To explore the unique phenomenology arising from these extended theories, particularly the effect of scalar degrees of freedom on matter.

Main Methods:

• Formulation of a new class of scalar-tensor theories.
• Analysis of the equations of motion to identify propagating degrees of freedom.
• Demonstration of the absence of Ostrogradski instabilities in the physical sector.
• Investigation of the phenomenology, including the speed of sound for minimally coupled matter.

Main Results:

• A new class of scalar-tensor theories extending Horndeski models has been successfully introduced.
• The propagating degrees of freedom in these theories obey stable, second-order equations, contrary to standard expectations.
• Covariant Galileon Lagrangians are shown to be members of this new class.
• A novel phenomenon is observed: the scalar degree of freedom impacts the speed of sound of minimally coupled matter.

Conclusions:

• The developed scalar-tensor theories offer a stable extension to Horndeski models.
• These theories present a rich phenomenology with potential implications for understanding gravity and matter interactions.
• The findings challenge conventional wisdom regarding higher-order derivative theories and instabilities.