Active to absorbing state phase transition in the presence of a fluctuating environment: Feedback and universality

We construct and analyse a simple {\em reduced} model to study the effects of the interplay between a density undergoing an active-to-absorbing state phase transition (AAPT) and a fluctuating environment in the form of a broken symmetry mode coupled to the density field in any arbitrary dimension. We show, by using perturbative renormalisation group calculations, that {\em both} the effects of the environment on the density and the latter's feedback on the environment influence the ensuing universal scaling behaviour of the AAPT at its extinction transition. Phenomenological implications of our results in the context of more realistic natural examples are discussed.