Talks

We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained in the model from the nonperturbative form of the spectral action are sensitive not only to the geometry (flat or positively curved) of the universe, but also to the different possible non-simply connected topologies. We show this by explicitly computing the nonperturbative spectral action for some candidate cosmic topologies, spherical space forms and flat ones given by Bieberbach manifolds and showing that the resulting inflation potential differs from that of the sphere or flat torus by a multiplicative factor. We then show that, while the slow-roll parameters differ between the spherical and flat manifolds but do not distinguish different topologies within each class, the power spectra detect the different scalings of the slow-roll potential and therefore distinguish between the various topologies, both in the spherical and in the flat case. (Based on joint work with Elena Pierpaoli and Kevin Teh)

There are good reasons to think that our understanding of particle physics is incomplete. The effective field theory describing the particles that we know about breaks down at the TeV scale, and new effective degrees of freedom must enter. In this talk I will discuss the role that strong dynamics might play in this new physics, focusing on the ways in which approximately scale-invariant dynamics could explain puzzling features of our low-energy Lagrangian. I will also describe recent theoretical and numerical results aimed at constraining the range of behavior that can occur in 4D conformal field theories.