Model Independent Statistics in Cosmology

In this talk, I will discuss a few different techniques to reconstruct different cosmological functions, such as the primordial power spectrum and the expansion history. These model independent techniques are useful because they can discover surprising results in a way that nested modeling cannot. For instance, we can use the modified Richardson Lucy algorithm to reconstruct a novel primordial power spectra from the Planck data that can resolve the "Hubble tension". This novel primordial power spectrum has regular oscillatory features that would be difficult to find using parametric methods. Further, we can use Gaussian process regression to reconstruct the expansion history of the Universe from low-redshift distance datasets. We can also this technique to test if these datasets are consistent with one another, which essentially allows for this technique to serve as a systematics finder.