Optimal CMB estimators for bispectra from excited states

We propose optimal estimators for bispectra from excited states. Two common properties of such bispectra are the enhancement in the collinear limit and the prediction of oscillating features. We review the physics behind excited states and some of the choices made in the literature. We show that the enfolded template is a good template in the collinear limit but does poorly elsewhere, establishing a strong case for an improved estimator. Although the detailed scale dependence of the bispectra differs depending on various assumptions, generally the predicted bispectra are either effectively one-or two-dimensional, and a simple Fourier basis suffices for accurate reconstruction. For an optimal CMB data analysis, combining all n-point functions, the choice for the excited state needs to be the same when computing power spectrum, bispectrum and higher-order correlation functions. This has not always been the case, which could lead to wrong conclusions. We calculate the bispectrum for different choices previously discussed for the power spectrum, setting up a consistent framework to search for evidence of excited states in the CMB data.