[Paper Review] The Role of Longitudinal Polarizations in Horndeski and Macroscopic Gravity: Introducing Gravitational Plasmas

Fabio Moretti, Flavio Bombacigno+1 more|arXiv (Cornell University)|Dec 15, 2021

Cosmology and Gravitation TheoriesPhysics and Astronomy169 references11 citations

TL;DR

This paper investigates longitudinal gravitational modes in Horndeski gravity and their interaction with matter media, introducing the concept of 'gravitational plasma' where massive scalar modes in Horndeski theory exhibit Landau damping analogous to electromagnetic waves in plasma. Using a gauge-invariant formulation, it demonstrates that massive scalar and vector fields induce breathing, vector, and longitudinal polarizations, and shows that molecular media can induce effective massive gravitons with subluminal propagation, while free-falling particles in a gravitational field form a self-consistent medium supporting damped longitudinal modes.

ABSTRACT

We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation, we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector, and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to molecule deformation. Finally, we investigate the interaction of the massive mode in Horndeski gravity with a noncollisional medium, showing that Landau damping phenomenon can occur in the gravitational sector as well. That allows us to introduce the concept of “gravitational plasma”, where inertial forces associated with the background field play the role of cold ions in electromagnetic plasma.

Motivation & Objective

• To clarify the role of longitudinal gravitational polarizations in Horndeski gravity using a gauge-invariant formulation.
• To investigate how massive scalar and vector fields induce transverse and longitudinal excitations in the geodesic deviation equation.
• To explore the emergence of effective massive gravitons in molecular media due to induced quadrupole moments.
• To establish a formal and phenomenological analogy between electromagnetic plasmas and gravitational waves in noncollisional media.
• To introduce and analyze the concept of 'gravitational plasma' where inertial forces play the role of cold ions in plasma physics.

Proposed method

• Employing a gauge-invariant linearized formulation of Horndeski gravity to unambiguously identify physical degrees of freedom.
• Analyzing metric perturbations over Minkowski spacetime using hµν with |hµν| ≪ 1 to derive the geodesic deviation equation for test particles.
• Deriving the effective stress-energy tensor for molecular media to model induced quadrupole moments and effective massive graviton behavior.
• Formulating a kinetic description of a noncollisional medium of free-falling particles to model gravitational plasma.
• Applying Landau damping theory to the massive scalar mode in Horndeski gravity, analogous to electromagnetic Langmuir waves.
• Using a local inertial frame to model the gravitational field as a neutralizing background, analogous to cold ions in plasma.

Experimental results

Research questions

• RQ1 How do massive scalar and vector fields in Horndeski gravity generate longitudinal and transverse polarizations in gravitational waves?
• RQ2 What is the effective behavior of gravitational waves in molecular media, and how does it lead to the emergence of effective massive gravitons?
• RQ3 Can Landau damping occur in the gravitational sector, and if so, under what conditions in a noncollisional medium?
• RQ4 In what way does the gravitational field of a free-falling particle system play a role analogous to cold ions in electromagnetic plasma?
• RQ5 How does the gauge-invariant formulation clarify the physical degrees of freedom in Horndeski gravity beyond general relativity?

Key findings

• Massive scalar and vector fields in Horndeski gravity induce a superposition of transverse and longitudinal polarizations, with the latter being physically distinct and detectable.
• In molecular media, the net quadrupole moment due to molecular deformation leads to the emergence of effective massive gravitons with subluminal propagation and five degrees of freedom.
• The interaction of massive modes in Horndeski gravity with a noncollisional medium results in Landau damping, confirming the existence of damped longitudinal gravitational waves.
• The concept of 'gravitational plasma' is established, where the background gravitational field acts as a neutralizing medium analogous to cold ions in electromagnetic plasma.
• The gauge-invariant formulation provides a clear, unambiguous identification of physical degrees of freedom, offering a phenomenological signature for detecting anomalous polarizations in gravitational wave detectors.
• The formal analogy between electromagnetic plasmas and gravitational waves in matter media is validated, with Landau damping in the gravitational sector mirroring that in plasma physics.