Position-dependent power spectrum of the large-scale structure: a novel
  method to measure the squeezed-limit bispectrum
  The influence of large-scale density fluctuations on structure formation on
small scales is described by the three-point correlation function (bispectrum)
in the so-called "squeezed configurations," in which one wavenumber, say $k_3$,
is much smaller than the other two, i.e., $k_3\ll k_1\approx k_2$. This
bispectrum is generated by non-linear gravitational evolution and possibly also
by inflationary physics. In this paper, we use this fact to show that the
bispectrum in the squeezed configurations can be measured without employing
three-point function estimators. Specifically, we use the "position-dependent
power spectrum," i.e., the power spectrum measured in smaller subvolumes of the
survey (or simulation box), and correlate it with the mean overdensity of the
corresponding subvolume. This correlation directly measures an integral of the
bispectrum dominated by the squeezed configurations. Measuring this correlation
is only slightly more complex than measuring the power spectrum itself, and
sidesteps the considerable complexity of the full bispectrum estimation. We use
cosmological $N$-body simulations of collisionless particles with Gaussian
initial conditions to show that the measured correlation between the
position-dependent power spectrum and the long-wavelength overdensity agrees
with the theoretical expectation. The position-dependent power spectrum thus
provides a new, efficient, and promising way to measure the squeezed-limit
bispectrum from large-scale structure observations such as galaxy redshift
surveys.
