Carbonyl oxides ("Criegee intermediates"), formed in the ozonolysis of alkenes, are key species in tropospheric oxidation of organic molecules and their decomposition provides a non-photolytic source of OH in the atmosphere (Johnson and Marston, Chem. Soc. Rev., 2008, 37, 699, Harrison et al, Sci, Total Environ., 2006, 360, 5, Gäb et al., Nature, 1985, 316, 535, ref. 1-3). Recently it was shown that small Criegee intermediates, C.I.'s, react far more rapidly with SO2 than typically represented in tropospheric models, (Welz, Science, 2012, 335, 204, ref. 4) which suggested that carbonyl oxides could have a substantial influence on the atmospheric oxidation of SO2. Oxidation of 502 is the main atmospheric source of sulphuric acid (H2SO4), which is a critical contributor to aerosol formation, although questions remain about the fundamental nucleation mechanism (Sipilä et al., Science, 2010, 327, 1243, Metzger et al., Proc. Natl. Acad. Sci. U. S. A., 2010 107, 6646, Kirkby et al., Nature, 2011, 476, 429, ref. 5-7). Non-absorbing atmospheric aerosols, by scattering incoming solar radiation and acting as cloud condensation nuclei, have a cooling effect on climate (Intergovernmental Panel on Climate Change (IPCC), Climate Change 2007: The Physical Science Basis, Cambridge University Press, 2007, ref. 8). Here we explore the effect of the Criegees on atmospheric chemistry, and demonstrate that ozonolysis of alkenes via the reaction of Criegee intermediates potentially has a large impact on atmospheric sulphuric acid concentrations and consequently the first steps in aerosol production. Reactions of Criegee intermediates with SO2 will compete with and in places dominate over the reaction of OH with SO2 (the only other known gas-phase source of H2SO4) in many areas of the Earth's surface. In the case that the products of Criegee intermediate reactions predominantly result in H2SO4 formation, modelled particle nucleation rates can be substantially increased by the improved experimentally obtained estimates of the rate coefficients of Criegee intermediate reactions. Using both regional and global scale modelling, we show that this enhancement is likely to be highly variable spatially with local hot-spots in e.g. urban outflows. This conclusion is however contingent on a number of remaining uncertainties in Criegee intermediate chemistry.