http://arxiv.org/abs/1403.0852
The imprint of the cross-correlation of the Integrated Sachs-Wolfe effect (ISW) and lensing of the cosmic microwave background (CMB) radiation has recently been detected in the bispectrum of temperature maps. In this paper, we use the optimised skew-spectrum as well as skew-spectra associated with Minkowski Functionals (MFs) to test the possibility of using this signal 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 $\rB_0$ that denotes the the {\em Compton wavelength} of the scalaron at the present epoch, and both can be used to put stringent constraints on any departure from GR, or pinpoint any systematics in the data. 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. The performance of MFs can be improved by using Wiener-type filtering, but we find that the optimal skew-spectrum is much more powerful, giving $\rm B_0<0.071$ at $95\%$ CL and $\rm B_0<0.15$ at $99\%$ CL, which is a factor of six improvement compared to constraints derived from MF, and essentially identical to what can be achieved using the full bispectrum.
D. Munshi, B. Hu, A. Renzi, et. al.
Wed, 5 Mar 14
48/75