  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 $1/m_D$ 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 $t_{\rm QCD}
\sim 10^{-5}\,{\rm s}$. 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.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory