Debye Screening of Non-Abelian Plasmas in Curved Spacetimes

Decades of analytic and computational work have demonstrated that a charge immersed in a hot plasma is screened. For both Abelian and non-Abelian interactions, the characteristic screening length $1\mathrm{/}{m}_D$ is set by the so-called Debye mass $m_D\sim g_{s}T$, proportional to the plasma temperature $T$ and the dimensionless gauge coupling $g_s$. One of the most interesting naturally occurring examples is the quark-gluon plasma (QGP) that filled the early universe prior to the QCD confinement phase transition at $t_{\mathrm{Q}\mathrm{C}\mathrm{D}}\sim {10}^{-5}\mathrm{s}$. During this early epoch, regimes of strong spacetime curvature are of significant cosmological interest, such as near primordial black holes (PBHs). However, the typical description of Debye screening only applies within Minkowski spacetime, and is therefore insufficient to describe the dynamics of charged plasmas near PBHs or other primordial features. We construct an effective field theory for soft modes of the gauge field $A_{\mu }^a$ to give a full description of Debye screening in non-Abelian plasmas within arbitrary curved spacetimes, recovering a temperature-dependent Debye mass that exhibits gravitational redshift. We then apply our results to some scenarios of cosmological interest: an expanding FLRW universe and the vicinity of a PBH immersed in a hot QGP.