  It is well known gravitational lensing, mainly via magnification bias,
modifies the observed galaxy/quasar clustering. Such discussions have largely
focused on the 2D angular correlation. Here and in a companion paper (Paper II)
we explore how magnification bias distorts the 3D correlation function and
power spectrum, as first considered by Matsubara. The interesting point is: the
distortion is anisotropic. Magnification bias preferentially enhances the
observed correlation in the line-of-sight (LOS) orientation, especially on
large scales. For example at LOS separation of ~100 Mpc/h, where the intrinsic
galaxy-galaxy correlation is rather weak, the observed correlation can be
enhanced by lensing by a factor of a few, even at a modest redshift of z ~
0.35. The opportunity: this lensing anisotropy is distinctive, making it
possible to separately measure the galaxy-galaxy, galaxy-magnification and
magnification-magnification correlations, without measuring galaxy shapes. The
anisotropy is distinguishable from the well known distortion due to peculiar
motions, as will be discussed in Paper II. The challenge: the magnification
distortion of the galaxy correlation must be accounted for in interpreting data
as precision improves. For instance, the ~100 Mpc/h baryon acoustic oscillation
scale in the correlation function is shifted by up to ~3% in the LOS
orientation, and up to ~0.6% in the monopole, depending on the galaxy bias,
redshift and number count slope. The corresponding shifts in the inferred
Hubble parameter and angular diameter distance, if ignored, could significantly
bias measurements of the dark energy equation of state. Lastly, magnification
distortion offers a plausible explanation for the well known excess
correlations seen in pencil beam surveys.
