Quantum Cosmology

The cosmology conference at Perimeter finished with a very interesting series of talks, the new consensus definitely tending towards a quantum explanation for the Dark Force. Although nobody mentioned Louise Riofrio's work, Starkman's results were displayed, the WMAP guy said primordial black holes were consistent with some difficult tests of dark matter theories, and even the string theorists seemed keen to move away from a cosmological constant.

Particularly enjoyable was the talk of Raphael Sorkin, who predicted an apparent cosmic acceleration from quantum causal set theory 20 years ago! He started the talk with a few entertaining jokes, before settling on the title Everpresent Lambda, referring to this paper. This model assumes that fluctuations are nonlocal and due to quantum discreteness.

A causal set is a network of atoms of spacetime with a partial order. Assuming an effective gravitational path integral one considers the uncertainty relation

$\Delta \Lambda \Delta V \simeq \hbar$

and under the assumption that the expectation value for $\Lambda$ is zero one finds that $\Lambda$ should be related to $\sqrt{V}^{-1}$. The model lets the volume $V$ be the volume to the past of some event. Although Sorkin did not discuss it, one could also rearrange the uncertainty relation to obtain

$c \simeq \frac{\sqrt{V}}{\Delta V}$

using $\hbar c = 1$. In this form it more closely resembles Riofrio's observationally successful quantum cosmology rule $R=ct$, since a time parameter is related to the number of nodes in the network which measures the volume.