Tuning goodness-of-fit tests†. Issue 2 (9th January 2019) - Arrasmith, A; Follin, B; Anderes, E; Knox, L
ABSTRACT: As modern precision cosmological measurements continue to show agreement with the broad features of the standard Λ cold dark matter (ΛCDM) 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 ΛCDM have to date turned up no convincing evidence of beyond-the-standard-model cosmology, the list of models compared against ΛCDM 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 χ 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-ΛCDM signals present in the data through compressing observations in a way that maximizes extra-ΛCDM signal variation over noise and ΛCDM variation. This method, based on a Karhunen–Loève 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-ΛCDM physics.