Some time ago I started working on some non-local theories of the Universe (see** this post**). The idea is that at least some of the equations that govern the evolution of the Universe have a non-local form, i.e. they depend not just on the value of the fields at or near some given epoch/location but also on the entire past evolution and on distant regions. In fact, in many cases such models can be written in a local form in which everything becomes easier, but then one should include appropriate initial conditions.

This class of models was introduced ten years ago in cosmology by Woodard and Deser (and even earlier by Wetterich). Their model was particularly appealing since it does not contain any new dimensional parameters beside the ubiquitous Netwon’s constant but still can explain the main features of the comic expansion, and notably the accelerated expansion. The lack of new constants means that the epoch of acceleration does not have to be introduced “by hand” with some very special value of the constant (as in the standard cosmological constant scenario) but emerges more naturally. The Woodard-Deser model attracted a lot of attention but was eventually ruled out a few years ago when compared to some observations, the so-called redshift distortion. So the original model was replaced by other models with new dimensional parameters, losing some of its initial attractiveness.

**In this paper**, however, we demonstrated that the localized version of the theory is actually well compatible with the observations and fit them better that the standard cosmology with a cosmological constant. We are still uncertain whether this new result holds true in the original non-local formulation, although we believe it does. In any case, this means that at least a version of the original model works fine and fits the data. Moreover, it solves also another puzzle, namely the fact that the amplitude of the clustering as extrapolated with the standard scenario from the Planck satellite data and that one obtained by weak lensing observations differs significatively, if not dramatically. The Woodard-Deser model, in fact, seems to naturally reconcile the two sets of observations.

We are now in the process of further testing this idea and trying to simplify it in some way. Keep tuned!

UPDATE: it has now been clarified that the result holds true even in the original non-local formulation!