Vacuum energy as dark matter

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We consider the vacuum energy of massive quantum fields in an expanding universe. We define a conserved renormalized energy-momentum tensor by means of a comoving cutoff regularization. Using exact solutions for de Sitter space-time, we show that in a certain range of mass and renormalization scales there is a contribution to the vacuum energy density that scales as nonrelativistic matter and that such a contribution becomes dominant at late times. By means of the WKB approximation, we find that these results can be extended to arbitrary Robertson-Walker geometries. We study the range of parameters in which the vacuum energy density would be compatible with current limits on dark matter abundance. Finally, by calculating the vacuum energy in a perturbed Robertson-Walker background, we obtain the speed of sound of density perturbations and show that the vacuum energy density contrast can grow on sub-Hubble scales as in standard cold dark matter scenarios.
© 2014 American Physical Society. This work has been supported by MICINN (Spain) Projects No. FIS2011-23000, No. FPA2011-27853-01 and Consolider-Ingenio MULTIDARK No. CSD2009- 00064. F. D. A. acknowledges financial support from the UAM+CSIC Campus of International Excellence (Spain) and the kind hospitality of the Instituto de Astrofísica de Canarias (IAC) while writing the manuscript.
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