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Evidences for late-time acceleration of the Universe are provided by multipleprobes, such as Type Ia supernovae, the cosmic microwave background (CMB) andlarge-scale structure (LSS). In this work, we focus on the integratedSachs--Wolfe (ISW) effect, i.e., secondary CMB fluctuations generated byevolving gravitational potentials due to the transition between, e.g., thematter and dark energy (DE) dominated phases. Therefore, assuming a flatuniverse, DE properties can be inferred from ISW detections. We present aBayesian approach to compute the CMB--LSS cross-correlation signal. The methodis based on the estimate of the likelihood for measuring a combined setconsisting of a CMB temperature and a galaxy contrast maps, provided that wehave some information on the statistical properties of the fluctuationsaffecting these maps. The likelihood is estimated by a sampling algorithm,therefore avoiding the computationally demanding techniques of directevaluation in either pixel or harmonic space. As local tracers of the matterdistribution at large scales, we used the Two Micron All Sky Survey (2MASS)galaxy catalog and, for the CMB temperature fluctuations, the ninth-year datarelease of the Wilkinson Microwave Anisotropy Probe (WMAP9). The results show adominance of cosmic variance over the weak recovered signal, due mainly to theshallowness of the catalog used, with systematics associated with the samplingalgorithm playing a secondary role as sources of uncertainty. When combinedwith other complementary probes, the method presented in this paper is expectedto be a useful tool to late-time acceleration studies in cosmology.

A Bayesian estimate of the CMB-large-scale structure cross-correlation