The cosmic microwave background in a causal set universe

We discuss cosmic microwave background constraints on the causal set theory of quantum gravity, which has made testable predictions about the nature of dark energy. We flesh out previously discussed heuristic constraints by showing how the power spectrum of causal set dark energy fluctuations can be found from the overlap volumes of past light cones of points in the universe. Using a modified Boltzmann code we put constraints on the single parameter of the theory that are somewhat stronger than previous ones. We conclude that causal set theory cannot explain late-time acceleration without radical alterations to general relativity.

Figure 1

A schematic of the PLCs of two points. The big bang is at the bottom of the diagram; the dimensions are heavily distorted. The volumes of the light cones are $V_1=V_A+V_C$ and $V_2=V_B+V_C$.

Figure 2

The power spectra obtained from a standard cold dark matter parameter combination described above (red, dashed) and from the causal set fluctuations (black), in the case of zero velocity, for $\alpha ={10}^{-6}$.

Figure 3

The power spectra obtained from the standard CMB parameter combination (red, dashed) and from the causal set fluctuations (black, solid), in the case of zero shear, for $\alpha ={10}^{-7}$.