Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 478, Issue 1, Pages 516-529Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/sty1081
Keywords
neutrinos; dark matter; large-scale structure of Universe; cosmology: theory
Categories
Funding
- National Aeronautics and Space Administration through Einstein Postdoctoral Fellowship Award by the Chandra X-ray Observatory Center [PF7-180167]
- National Aeronautics Space Administration [NAS8-03060]
- Chamberlain Fellowship at Lawrence Berkeley National Laboratory
- Berkeley Center for Cosmological Physics
- Natural Sciences and Engineering Research Council of Canada Postgraduate Scholarship
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We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w = 0) at late times. The equation of state smoothly transitions from the early- to late-time behaviour and exactly describes the evolution of a species with a Dirac delta function distribution in momentum magnitudes vertical bar p(0)vertical bar (i.e. all particles have the same vertical bar p(0)vertical bar). Such a component, here termed 'hot matter', is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of superhorizon perturbations in each case. The idealized model recovers t(a) to better than 1.5 per cent accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.
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