Non-local formulation of ghost-free bigravity theory

We study the ghost-free bimetric theory of Hassan and Rosen, with parameters $\beta_i$ such that a flat Minkowski solution exists for both metrics. We show that, expanding around this solution and eliminating one of the two metrics with its own equation of motion, the remaining metric is governed by the Einstein-Hilbert action plus a non-local term proportional to $W_{\mu\nu\rho\sigma} (\Box-m^2)^{-1}W^{\mu\nu\rho\sigma}$, where $W_{\mu\nu\rho\sigma}$ is the Weyl tensor. The result is valid to quadratic order in the metric perturbation and to all orders in the derivative expansion. This example shows, in a simple setting, how such non-local extensions of GR can emerge from an underlying consistent theory, at the purely classical level.Comment: 16 page

Measurement of the primordial helium abundance from the intergalactic medium

Almost every helium atom in the Universe was created just a few minutes after the Big Bang through a process commonly referred to as Big Bang nucleosynthesis1,2. The amount of helium that was made during Big Bang nucleosynthesis is determined by combining particle physics and cosmology3. The current leading measures of the primordial helium abundance (YP) are based on the relative strengths of H I and He I emission lines emanating from star-forming regions in local metal-poor galaxies4,5,6,7. As the statistical errors on these measurements improve, it is essential to test for systematics by developing independent techniques. Here we report a determination of the primordial helium abundance based on a near-pristine intergalactic gas cloud that is seen in absorption against the light of a background quasar. This gas cloud, observed when the Universe was just one-third of its present age (zabs = 1.724), has a metal content around 100 times less than that of the Sun, and at least 30% less metal content than the most metal-poor H II region currently known where a determination of the primordial helium abundance is possible. We conclude that the helium abundance of this intergalactic gas cloud is Y=0.250+0.033−0.025, which agrees with the standard model primordial value8,9,10, YP = 0.24672 ± 0.00017. Our determination of the primordial helium abundance is not yet as precise as that derived using metal-poor galaxies, but our method has the potential to offer a competitive test of physics beyond the standard model during Big Bang nucleosynthesis