Violation of the PT-symmetry and structure formation in the dark matter-gravitational wave interaction

TL;DR

This paper explores how PT-symmetry breaking in dark matter interacting with gravitational waves leads to damping and amplification effects, resulting in structure formation without cosmic expansion, highlighting novel quantum-gravitational phenomena.

Contribution

It demonstrates the role of PT-symmetry breaking in dark matter-gravitational wave interactions and its impact on structure formation in a flat spacetime context.

Findings

Gravitational waves are damped for wavelengths larger than the Jeans length.

Energy from damping is transferred to Bogoliubov modes, which become unstable and grow.

The process indicates a discrete PT-symmetry-breaking signature in the system.

Abstract

In flat spacetime, quantum fluctuations in dark matter, as described as a Bose-Einstein condensate, are stable and display a relativistic Bogoliubov dispersion relation. In the weak gravitational field limit, both relativistic and nonrelativistic models self-gravitating dark matter suggest the formation of structures as the result of a dynamical (Jeans) instability. Here, we show that in the presence of spontaneous symmetry breaking of the dark matter field, the gravitational wave is damped for wave-lengths larger than the Jeans length. Such energy is converted to the Bogoliubov modes of the BEC that in their turn become unstable and grow, leading to the formation of structures even in the absence of expansion. Remarkably, this compensated attenuation/amplification mechanism is the signature of a discrete PT-symmetry-breaking of the system.