An extended Cheeger-Müller theorem for covering spaces

We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Müller theorem on Ray-Singer torsion and Reidemeister torsion, to the case of infinite Galois covering spaces. Our result is stated in the framework of extended cohomology, and generalizes in this case a recent result of Braverman-Carey-Farber-Mathai. It does not use the determinant class condition and thus also (potentially) generalizes several results on L2-torsions due to Burghelea, Friedlander, Kappeler and McDonald. We combine the framework developed by Braverman-Carey-Farber-Mathai on the determinant of extended cohomology with the heat kernel method developed in the original paper of Bismut-Zhang to prove our result.