Cosmological Parameters from Angular Correlations between Qsos and Galaxies

The angular two-point correlation function between background QSOs and foreground galaxies induced by gravitational lensing is derived. It is shown that the shape of this correlation function depends sensitively on the spectrum of the density fluctuations in the Universe, thus providing a possibility to distinguish between different models for the spectrum. Using numerical large-scale structure simulations, I estimate that the QSO-galaxy correlation function can be measured from galaxy counts down to $\simeq21^{\rm st}\ldots22^{\rm nd}$ magnitude in fields with radius $\la25'$ around $50\ldots100$ QSOs with redshift $z\ge1$. Since the QSO-galaxy correlation function is proportional to $(-a-1)b$, where $b$ is the biasing factor of galaxy formation and $a$ is the effective slope of the QSO number counts, steep number counts are favorable for this kind of analysis. I show that $a=-4\ldots-5$ can be achieved with the 1-Jansky sample of radio-loud QSOs when the double-waveband magnification bias is employed. Moreover, the cross-correlation analysis allows to determine the galaxy-formation bias factor $b$.