Tuning goodness-of-fit tests

As modern precision cosmological measurements continue to show agreement with the broad features of the standard A cold dark matter (Lambda CDM) cosmological model, we are increasingly motivated to look for small departures from the standard model's predictions that might not be detected with standard approaches. While searches for extensions and modifications of Lambda CDM have to date turned up no convincing evidence of beyond-the-standard-model cosmology, the list of models compared against Lambda CDM is by no means complete and is often governed by readily coded modifications to standard Boltzmann codes. Also, standard goodness-of-fit methods such as a naive chi(2) test fail to put strong pressure on the null hypothesis, since modern data sets have orders of magnitudes more degrees of freedom than the null hypothesis. Here we present a method of tuning goodness-of-fit tests to detect potential subdominant extra-Lambda CDM signals present in the data through compressing observations in a way that maximizes extra-Lambda CDM signal variation over noise and Lambda CDM variation. This method, based on a Karhunen-Loeve transformation of the data, is tuned to be maximally sensitive to particular types of variations characteristic of the tuning model, but unlike direct model comparison, the test is also sensitive to features that only partially mimic the tuning model. As an example of its use, we apply this method in the context of a non-standard primordial spectrum compared against the 2015 Planck cosmic microwave background temperature power spectrum. We find no evidence for extra-Lambda CDM physics.