Quantum Gravity and Astrophysics: The Microwave Background and Other Thermal Sources

The problem of formulating a fully consistent quantum gravity theory (QGT) has not yet been solved. Even before we are able to work out the details of a complete theory, however, we do know some important qualitative features to be expected in any quantum theory. Fluctuations of the metric, for example, are expected and are associated with fluctuations of the lightcone. Lightcone fluctuations affect the arrival time of signals from distant sources in potentially measurable ways, broadening the spectra. In this paper, we start with a thermal spectrum and derive the form of spectral changes expected in a wide class of QGTs. We apply these results, valid for any thermal spectrum, to the cosmic microwave background (CMB). The CMB offers two advantages: (1) deviations from a thermal spectrum are well constrained, and (2) the radiation emanates from the most distant source of light, the surface of last scattering. We use existing CMB data to derive an upper bound on the value of $\Delta t,$ the mean spread in arrival times due to metric fluctuations: ${\Delta t} < 2.1 \times 10^{-14}$ s at the 95% confidence limit. This limit applies to a wide range of QGTs, and falsifies those predicting a larger spread in arrival times. We find this limit rules out at least one QGT, the 5-dimensional theory in which the "extra" dimension is flat. Tests of other models may also be possible, depending on the results of calculations to predict values of \Delta t,$ and also a second time scale, $\tau_c,$ the correlation time, which is the characteristic time scale of the metric fluctuations. We show that stronger limits on the value of $\Delta t,$ hence on lightcone fluctuations, can likely be derived through observations of of higher-T sources, e.g., in the X-ray and gamma-ray regimes.