On the adiabatic initial conditions for a particle gas in cosmology

TL;DR

The paper addresses how to define adiabatic initial conditions for a gas of relativistic particles in cosmology, clarifying the role of local momentum in the phase-space description and its impact on energy-density fluctuations, including a graviton gas. It identifies two broad classes—strong adiabatic, with momentum-independent fluctuations, and weak adiabatic, tied to internal isocurvature fluctuations that cancel only after momentum integration—and demonstrates that both are compatible with the separate-universe approach. By formulating the Boltzmann equation in terms of the local momentum, the authors show that δρ is directly linked to δf without spurious metric contributions, which resolves apparent non-adiabatic behavior for gravitons. The work has implications for the interpretation of primordial gravitational-wave backgrounds and lays groundwork for extending to interacting gases and concrete generation mechanisms, while highlighting gauge considerations at low frequencies as an area for future study.

Abstract

In view of recent interest in the role of "dark" radiation in cosmology, such as cosmic gravitational waves, sterile neutrinos, and dark photons, we clarify the definition of adiabatic initial conditions in the kinetic theory of gases in an expanding universe. Without assuming any form for the phase space distribution function, we identify two possibilities: a strong and a weak adiabatic initial condition. The strong one corresponds to the standard adiabatic initial conditions, while the weak one is related to the strong via internal isocurvature fluctuations. We show that both types of adiabatic initial conditions are consistent with the separate universe approach, although the latter requires initial internal isocurvature. In passing, we stress the importance of using the particle local momentum in the phase space to define the notion of adiabatic initial conditions. Doing so, we clarify that a gas of gravitons can have adiabatic initial conditions.