Chern-Simons gravity and PT Symmetry

This paper considers a string inspired effective axion anomalously coupled to Abelian gauge fields and gravity. By considering the renormalisation group flows in the flat space limit it is observed that a Hermitian parity symmetric phase of the theory can flow into a non-Hermitian parity-time symmetric phase. This behavior has implications for Chern-Simons gravity. The repulsive nature of gravity, usually attributed to the existence of a positive cosmological constant, is reinterpreted at large scales as a flow from a Hermitian (attractive) gravitational theory, to a PT-symmetric (repulsive) gravity in the infrared. The discussion here is presented in the context of a Chern-Simons gravitational theory but it may be valid 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 the cosmological evolution, thus avoiding their associated conceptual and technical complications.