Prepared for submission to JCAP (Lack of) Cosmological evidence for dark radiation after Planck Licia Verde,a;b Stephen M. Feeney,c Daniel J. Mortlockd;e and Hiranya V. Peirisc;f aICREA & ICC, Institut de Ciencies del Cosmos, Universitat de Barcelona (IEEC-UB), Marti i Franques 1, Barcelona 08028, Spain bTheory Group, Physics Department, CERN, CH-1211, Geneva 23, Switzerland cDepartment of Physics and Astronomy, University College London, London WC1E 6BT, U.K. dAstrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, U.K. eDepartment of Mathematics, Imperial College London, London SW7 2AZ, U.K. f Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106, USA E-mail:
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[email protected] Abstract. We use Bayesian model comparison to determine whether extensions to Standard-Model neutrino physics { primarily additional effective numbers of neutrinos and/or massive neutrinos { are merited by the latest cosmological data. Given the significant advances in cosmic microwave back- ground (CMB) observations represented by the Planck data, we examine whether Planck temperature and CMB lensing data, in combination with lower redshift data, have strengthened (or weakened) the previous findings. We conclude that the state-of-the-art cosmological data do not show evidence for deviations from the standard (ΛCDM) cosmological model (which has three massless neutrino fami- lies). This does not mean that the model is necessarily correct { in fact we know it is incomplete as arXiv:1307.2904v2 [astro-ph.CO] 10 Sep 2013 neutrinos are not massless { but it does imply that deviations from the standard model (e.g., non-zero neutrino mass) are too small compared to the current experimental uncertainties to be inferred from cosmological data alone.