Introduction

Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to provide a deeper explanation for some aspect of our models (in this case, the standard model of cosmology) that seem unnatural or fine tuned. In particular, I will consider how cosmologists can test the multiverse using observations of this universe.

Cosmologists will only ever get one horizon-full of data. Our telescopes will see so far, and no further. At any particular time, particle accelerators reach to a finite energy scale and no higher. And yet, it would be an unnatural constraint on our theories for them to fall silent beyond the edge of the observable universe and above a certain energy. Natural, simple theories need not confine themselves to the observable. How do we speculate beyond current data?

In particular, how do we evaluate (what I will call) theory extensions? That is, physical

theories whose main attraction is that they provide a deeper, more natural understanding of some effective theory. For example, the appeal of cosmic inflation is its natural explanation of some of the “initial conditions” of the standard model of cosmology. The postulates of the standard model – a homogeneous and isotropic Robertson–Walker (RW) spacetime, a set of energy components and their densities (matter, radiation and a cosmological constant), and an initial set of adiabatic, Gaussian density and tensor perturbations – can explain all (or almost all) the cosmological data at our disposal: the expansion of the universe, big bang nucleosynthesis, the angular power spectrum of the cosmic microwave background (CMB), the galaxy and Lyman alpha forest power spectra, the baryon acoustic oscillation (BAO) scale, the luminosity distance-redshift relation of type Ia supernovae, and more.

So, why not simply declare cosmology to be finished? We have a model that explains all the data. Consider the following kind of reason for extending our cosmological theory. In the standard model of cosmology, photons in the CMB that are separated in the sky by more than∼1 degree were scattered by patches of gas that have never been in causal contact with each other. And yet the entire CMB is at the same temperature, to one part in 100,000.