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We expect a detectable correlation between two seemingly unrelatedquantities: the four point function of the cosmic microwave background (CMB)and the amplitude of flux decrements in quasar (QSO) spectra. The amplitude ofCMB convergence in a given direction measures the projected surface density ofmatter. Measurements of QSO flux decrements trace the small-scale distributionof gas along a given line-of-sight. While the cross-correlation between thesetwo measurements is small for a single line-of-sight, upcoming large surveysshould enable its detection. This paper presents analytical estimates for thesignal to noise (S/N) for measurements of the cross-correlation between theflux decrement and the convergence and for measurements of thecross-correlation between the variance in flux decrement and the convergence.For the ongoing BOSS (SDSS III) and Planck surveys, we estimate an S/N of 30and 9.6 for these two correlations. For the proposed BigBOSS and ACTPOLsurveys, we estimate an S/N of 130 and 50 respectively. Since thecross-correlation between the variance in flux decrement and the convergence isproportional to the fourth power of $\sigma_8$, the amplitude of thesecross-correlations can potentially be used to measure the amplitude of$\sigma_8$ at z~2 to 2.5% with BOSS and Planck and even better with future datasets. These measurements have the potential to test alternative theories fordark energy and to constrain the mass of the neutrino. The large potentialsignal estimated in our analytical calculations motivate tests with non-linearhydrodynamical simulations and analyses of upcoming data sets.

astrophysical journal/the astrophysical journal

Cross-correlations of the Lyman-alpha forest with weak lensing  convergence I: Analytical Estimates of S/N and Implications for Neutrino Mass  and Dark Energy