Constraints on general primordial non-Gaussianity using wavelets for the Wilkinson Microwave anisotropy probe 7-year data

ABSTRACT We present constraints on the non-linear coupling parameter f nl with the Wilkinson Microwave Anisotropy Probe (WMAP) data. We use the method based on the spherical Mexican hat wavelet (SMHW) to measure the f nl parameter for three of the most interesting shapes of primordial non-Gaussianity: local, equilateral and orthogonal. Our results indicate that this parameter is compatible with a Gaussian distribution within the two sigma confidence level (CL) for the three shapes and the results are consistent with the values presented by the WMAP team. We have included in our analysis the impact on f nl due to contamination by unresolved point sources. The point sources add a positive contribution of ∆f loc nl = 2.5 ± 3.0, ∆f eq nl = 37 ± 18 and ∆f ort nl = 25 ± 14. As mentioned by the WMAP team, the contribution of the point sources to the orthogonal and equilateral form is expected to be larger than to the local one and thus it cannot be neglected in future constraints on these parameters. Taking into account this contamination, our best estimates for f nl are −16.0 f 34 at 95% CL. The three shapes are compatible with zero at 95% CL (2σ). Our conclusion is that the WMAP 7-year data are consistent with Gaussian primordial fluctuations within 2σ CL. We stress however the importance of taking into account the unresolved point sources in the measurement of f nl in future works, especially when using more precise data sets such as the forthcoming Planck data