Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat Friedmann-Robertson-Walker space-time. Two simple measurement prescriptions are given in order to remove the ambiguity associated with the short distance singularity of the correlation function. In some cases, it turns out that one is dealing with a quantum thermometer, recovering a proposal due to Buchholzet al. in order to determine local temperature in the framework of quantum field theory. In general, by arranging the detector so that it does not register for inertial motion in flat space, the regularized quantum fluctuation may be used as a probe of space-time geometry and, in particular, may provide informations on the Hubble parameter. As an aside, it is not possible in general to fully decouple the effect of the detector motion from the universe expansion, a fact that could be interpreted as a kind of Machian effect which can be traced back to the worldwide nature of the vacuum.