Constraining the braneworld with gravitational wave observations

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, L, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining L via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain L at the ~1 micron level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of L <= 5 microns.Comment: 4 pages, replaced with version published in Phys. Rev. Lett

Improvements in Birch's theorem on forms in many variables

We show that a non-singular integral form of degree d is soluble non-trivially over the integers if and only if it is soluble non-trivially over the reals and the p-adic numbers, provided that the form has at least (d-\sqrt{d}/2)2^d variables. This improves on a longstanding result of Birch.Comment: 36 page

Is the Universe More Transparent to Gamma Rays Than Previously Thought?

The MAGIC collaboration has recently reported the detection of the strong gamma-ray blazar 3C279 during a 1-2 day flare. They have used their spectral observations to draw conclusions regarding upper limits on the opacity of the Universe to high energy gamma-rays and, by implication, upper limits on the extragalactic mid-infrared background radiation. In this paper we examine the effect of gamma-ray absorption by the extragalactic infrared radiation on intrinsic spectra for this blazar and compare our results with the observational data on 3C279. We find agreement with our previous results, contrary to the recent assertion of the MAGIC group that the Universe is more transparent to \gray s than our calculations indicate. Our analysis indicates that in the energy range between ~80 and ~500 GeV, 3C279 has a best-fit intrinsic spectrum with a spectral index ~1.78 using our fast evolution model and ~2.19 using our baseline model. However, we also find that spectral indices in the range of 0.0 to 3.0 are almost as equally acceptable as the best fit spectral indices. Assuming the same intrinsic spectral index for this flare as for the 1991 flare from 3C279 observed by EGRET, viz., 2.02, which lies between our best fit indices, we estimate that the MAGIC flare was ~3 times brighter than the EGRET flare observed 15 years earlier.Comment: version accepted for publication in ApJ Letter