Probing Modified Gravity Theories with ISW and CMB Lensing
  We use the optimised skew-spectrum as well as the skew-spectra associated
with the Minkowski Functionals (MFs) to test the possibility of using the
cross-correlation of the Integrated Sachs-Wolfe effect (ISW) and lensing of the
cosmic microwave background (CMB) radiation to detect deviations in the theory
of gravity away from General Relativity (GR). We find that the although both
statistics can put constraints on modified gravity, the optimised skew-spectra
are especially sensitive to the parameter $\rm B_0$ that denotes the the {\em
Compton wavelength} of the scalaron at the present epoch. We investigate three
modified gravity theories, namely: the Post-Parametrised Friedmanian (PPF)
formalism; the Hu-Sawicki (HS) model; and the Bertschinger-Zukin (BZ)
formalism. Employing a likelihood analysis for an experimental setup similar to
ESA's Planck mission, we find that, assuming GR to be the correct model, we
expect the constraints from the first two skew-spectra, $S_{\ell}^{(0)}$ and
$S_{\ell}^{(1)}$, to be the same: $\rm B_0<0.45$ at $95%$ confidence level
(CL), and $\rm B_0<0.67$ at $99%$ CL in the BZ model. The third skew-spectrum
does not give any meaningful constraint. We find that the optimal skew-spectrum
provides much more powerful constraint, giving $\rm B_0<0.071$ at $95%$ CL and
$\rm B_0<0.15$ at $99%$ CL, which is essentially identical to what can be
achieved using the full bispectrum.
