  In this work we investigate the reflectivity of highly reflective multilayer
polymer foils used in the CRESST experiment. The CRESST experiment searches
directly for dark matter via operating scintillating CaWO$_4$ crystals as
targets for elastic dark matter-nucleon scattering. In order to suppress
background events, the experiment employs the so-called phonon-light technique
which is based on the simultaneous measurement of the heat signal in the main
CaWO$_4$ target crystal and of the emitted scintillation light with a separate
cryogenic light detector. Both detectors are surrounded by a highly reflective
and scintillating multilayer polymer foil to increase the light collection
efficiency and to veto surface backgrounds. While this study is motivated by
the CRESST experiment, the results are also relevant for other rare event
searches using scintillating cryogenic bolometers in the field of the search of
dark matter and neutrinoless double beta decay ($0\nu\beta\beta$). In this work
a dedicated experiment has been set up to determine the relative reflectivity
at 300 K and 20 K of three multilayer foils ("VM2000", "VM2002", "Vikuiti")
produced by the company 3M. The intensity of a light beam reflected off the
foil is measured with a CCD camera. The ratio of the intensities at 300 K and
20 K corresponds to the relative reflectivity change. The measurements
performed in this work show no significant change in the reflectivity with
temperature for all foils studied.
