We present a new observable, position-dependent power spectrum, to measure
the large-scale structure bispectrum in the squeezed configuration, where one
wavenumber is much smaller than the other two. The squeezed-limit bispectrum
measures how the small-scale power spectrum is modulated by a long-wavelength
overdensity, which is due to gravitational evolution and possibly inflationary
physics. We divide a survey into small subvolumes, compute the local power
spectrum and the mean overdensity in each subvolume, and measure the
correlation between them. The correlation measures the integral of the
bispectrum, which is dominated by squeezed configurations if the scale of the
local power spectrum is much smaller than the subvolume size. We use the
separate universe approach to model how the small-scale power spectrum is
affected by a long-wavelength overdensity gravitationally. This models the
nonlinearity of the bispectrum better than the perturbation theory approach.
Not only the new observable is easy to interpret, but it sidesteps the
complexity of the full bispectrum estimation as both power spectrum and mean
overdensity are easier to estimate than the full bispectrum. We report on the
first measurement of the position-dependent correlation function from the
SDSS-III BOSS DR10 CMASS sample. We detect the bispectrum of the CMASS sample,
and constrain their nonlinear bias combining with anisotropic clustering and
weak lensing. We finally study the response of the small-scale power spectrum
to 1-3 long-wavelength overdensities. We compare the separate universe approach
to separate universe simulations to unprecedented accuracy. We test the
standard perturbation theory (SPT) hypothesis that the nonlinear n-point
function is fully predicted by the linear power spectrum at the same time. We
find discrepancies on small scales, which suggest that SPT fails even if it is
calculated to all orders.Comment: Ph.D. dissertation; 160 pages, 34 figures, 4 table
