  This paper considers the possibility that, starting from a relativistic
Hermitian quantum field theory in the ultraviolet (UV) regime, and applying a
non-perturbative renormalization-group (RG) flow, we arrive at a situation
where there are infrared (IR) singularities in the RG flow of couplings. The
latter can be resolved by assuming that the theory can have a phase described
by a related non-Hermitian PT-symmetric modification in the IR. The UV-to-IR
(Hermitian-to-PT-symmetric) transition can occur in a single
renormalization-group flow of the pertinent couplings, as demonstrated in
concrete examples. When embedded in a gravitational setting such a transition
can lead to a repulsive gravity phase. If there is a RG flow to a repulsive PT
-symmetric gravity, then this would be an alternative to dark energy. The
discussion here is presented in the context of a string-inspired Chern-Simons
gravitational effective action, which involves a pseudoscalar (axion-like)
field coupled to Abelian gauge fields and gravity; it may also hold more
generally in gravity with torsion. The validity of such a scenario in realistic
theories might alleviate the need for de Sitter phases in the current epoch of
cosmological evolution, thus avoiding their associated conceptual and technical
complications.
