General Relativity & Quantum Cosmology

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The vacuum sector of the resulting gravitational theory exhibits local conformal symmetry. We allow for conventional matter coupled to the spacetime metric as well as matter coupled to the field that gauges special conformal transformations.  When the theory is linearized about flat space, we find there is a long range gravitational force in addition to Newton’s inverse square law.  Furthermore, the cosmological sector of the theory exhibits late time acceleration, an early time bounce, and a post-bounce quasi-de Sitter ``inflationary'' phase of arbitrary duration (without an inflaton).