Effective field theory of gravitating continuum: solids, fluids, and aether unified

We investigate the relativistic effective field theory (EFT) describing a non -dissipative gravitating continuum. In addition to ordinary continua, namely solids and fluids, we find an extraordinary more symmetric continuum, aether. In particular, the symmetry of the aether concludes that a homogeneous and isotropic state behaves like a cosmological constant. We formulate the EFT in the unitary/comoving gauge in which the dynamical degrees of freedom of the continuum (phonons) are eaten by the spacetime metric. This gauge choice, which is interpreted as the Lagrangian description in hydrodynamics, offers a neat geometrical understanding of continua. We examine a thread-based spacetime decomposition with respect to the four-velocity of the continuum which is different from the foliation-based Arnowitt-Deser-Misner one. Our thread-based decomposition respects the symmetries of the continua and, therefore, makes it possible to systematically find invariant building blocks of the EFT for each continuum even at higher orders in the derivative expansion. We also discuss the linear dynamics of the system and show that both gravitons and phonons acquire masses in a gravitating background.

Automated summary

The study focuses on the relativistic effective field theory describing a non-dissipative gravitating continuum, uncovering the more symmetric continuum called aether and its behavior akin to a cosmological constant. Formulating the EFT in the unitary/comoving gauge offers a geometrical understanding of continua, while a thread-based spacetime decomposition allows for systematic identification of invariant building blocks at higher orders in the derivative expansion. Additionally, the linear dynamics analysis demonstrates the acquisition of mass by gravitons and phonons in a gravitating background.