Testing string theory with cosmic microwave background

Future detection/non-detection of tensor modes from inflation in cosmic microwave background observations presents a unique way to test certain features of string theory. The current limit on the ratio of tensor to scalar perturbations, r = T/S, is r less than or similar to 0.3; future detection may take place for r greater than or similar to 10(-2)-10(-3) At present all known string theory inflation models predict tensor modes well below the level of detection. Therefore a possible experimental discovery of tensor modes may present a challenge to string cosmology. The strongest bound on r in string inflation follows from the observation that in most of the models based on the Kachru-Kallosh-Linde-Trivedi construction, the value of the Hubble constant H during inflation must be smaller than the gravitino mass. For the gravitino mass in the usual range, m(3/2) less than or similar to O(1) TeV, this leads to an extremely strong bound r less than or similar to 10(-24). A discovery of tensor perturbations with r greater than or similar to 10(-3) would imply that the gravitinos in this class of models are superheavy, m(3/2) greater than or similar to 10(13) GeV. This would have important implications for particle phenomenology based on string theory.