D. Transplanckian Physics and Cosmology

Quantum effects during inflation may be the origin of the temperature fluctuations observed today in the CMB. If so, then scales observed today in large scale structure originated at smaller than Planck scales at the beginning of inflation. Thus, cosmological observations may reveal the structure of physics at sub-Planckian distances. The problem arises because, since there are typically many more than 60 e-foldings in inflationary models, we must extrapolate the weakly-coupled field theories we understand into regimes in which the approximation is no longer valid in order to extract information about the fluctuations. Although we should not trust this procedure, there is at present no way to calculate the expected dispersion relation of fluctuation modes from first principles in any fundamental theory. To make progress, several authors [Martin and Brandenberger(2001), Brandenberger and Martin(2001), Niemeyer(2001), Niemeyer and Parentani(2001), Kempf(2001), Kempf and Niemeyer(2001), Easther et al.(2001a), Hui and Kinney(2001), Easther et al.(2001b)] have adopted a phenomenological approach, trying different modifications to the dispersion relation at small scales and studying the effects on the expected spectrum of fluctuations.

In general, it proves quite difficult to make short-scale modifications that lead to large effects in cosmological observables. However, this may prove to be a useful technique for testing fundamental physics. In particular, the effects of transPlanckian physics are expected to alter the ratio of the spectrum of scalar to tensor perturbations generated during inflation. In a large class of inflationary models the evolution is dominated by a single field. In that case this ratio is a fixed known number, and deviations from it must signal some departure from the standard picture. Whether the specific signals predicted from short-scale modifications of the dispersion relation can be isolated from other possible effects remains to be seen. Nevertheless, we consider any possible cosmological tests of our most fundamental theories an interesting avenue to pursue.

Acknowledgments

MT thanks Toni Riotto for useful discussions on baryogenesis. AA is supported by DOE grant DE-FG03-91ER40674. The work of MT is supported by the NSF under grant PHY-0094122