Abstract
A massive, nonrelativistic scalar field in an expanding spacetime is usually approximated by a pressureless perfect fluid, which leads to the standard conclusion that such a field can play the role of cold dark matter. In this paper, we systematically study these approximations, incorporating subleading corrections. We provide two equivalent effective descriptions of the system, each of which offers its own advantages and insights: (i) A nonrelativistic effective field theory (EFT) with which we show that the relativistic corrections induce an effective self-interaction for the nonrelativistic field. As a byproduct, our EFT also allows one to construct the exact solution, including oscillatory behavior, which is often difficult to achieve from the exact equations. (ii) An effective (imperfect) fluid description, with which we demonstrate that, for a perturbed Friedmann-Lemaître- Robertson-Walker (FLRW) universe: (a) The pressure is small but nonzero (and positive), even for a free theory with no tree-level self-interactions. (b) The sound speed of small fluctuations is also nonzero (and positive), reproducing already known leading-order results, correcting a subdominant term, and identifying a new contribution that had been omitted in previous analyses. (c) The fluctuations experience a negative effective bulk viscosity. The positive sound speed and the negative bulk viscosity act in favor of and against the growth of overdensities, respectively. The net effect may be considered a smoking gun for ultra-light dark matter.
Highlights
In this paper we study the dynamics of a massive scalar field φ minimally coupled to gravity
A massive, nonrelativistic scalar field in an expanding spacetime is usually approximated by a pressureless perfect fluid, which leads to the standard conclusion that such a field can play the role of cold dark matter
We provide two equivalent effective descriptions of the system, each of which offers its own advantages and insights: (i) A nonrelativistic effective field theory (EFT) with which we show that the relativistic corrections induce an effective self-interaction for the nonrelativistic field
Summary
Taking the nonrelativistic limit of a scalar field theory is usually done by starting with an appropriate field redefinition, which is the subject of this section. We note that in terms of the original field φ, the conjugate momentum differs from φin a curved spacetime, leaving more freedom for an appropriate field redefinition Given these considerations, in this paper we follow a different approach compared to ref. In the original theory in terms of φ, we introduce a new field by the relation χ = φ (at the level of equations of motion); we replace φwith χ in the Lagrangian and add a Lagrange multiplier to guarantee the equivalence of the two theories: Lφ(φ, χ) = Lφ(φ, χ, ∂iφ) + π(φ − χ) Note that at this stage, the field π is only a Lagrange multiplier and not the momentum conjugate of φ. To avoid clutter we do not write out Tμν(ψ, ψ∗) explicitly here
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
