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We present a new method for constructing maps of the secondary temperaturefluctuations imprinted on the cosmic microwave background (CMB) radiation byphotons propagating through the evolving cosmic gravitational potential. Largecosmological N-body simulations are used to calculate the complete non-linearevolution of the peculiar gravitational potential. Tracing light rays backthrough the past lightcone of a chosen observer accurately captures thetemperature perturbations generated by linear (the integrated Sachs-Wolfe orISW effect) and non-linear (the Rees-Sciama or RS effect) evolution. Theseeffects give rise to three kinds of non-linear features in the temperaturemaps. (a) In overdense regions, converging flows of matter induce cold spots oforder 100 Mpc in extent which can dominate over the ISW effect at highredshift, and are surrounded by hot rings. (b) In underdense regions, the RSeffect enhances ISW cold spots which can be surrounded by weak hot rings. (c)Transverse motions of large lumps of matter produce characteristic dipolefeatures, consisting of adjacent hot and cold spots separated by a few tens ofMegaparsecs. These non-linear features are not easily detectable; they modulatethe ISW sky maps at about the 10 percent level. The RS effect causes theangular power spectrum to deviate from linear theory at l~50 and generatesnon-Gaussianity, skewing the one-point distribution function to negativevalues. Cold spots of similar angular size, but much smaller amplitude than theCMB cold spot reported by Cruz et al. are produced. Joint analysis of our mapsand the corresponding galaxy distribution may enable techniques to be developedto detect these non-linear, non-Gaussian features. Our maps are available athttp://astro.dur.ac.uk/~cai/ISW

Full‐sky map of the ISW and Rees–Sciama effect from Gpc simulations