Fisher matrix forecasts for astrophysical tests of the stability of the fine-structure constant

We use Fisher Matrix analysis techniques to forecast the cosmological impact of astrophysical tests of the stability of the fine-structure constant to be carried out by the forthcoming ESPRESSO spectrograph at the VLT (due for commissioning in late 2017), as well by the planned high-resolution spectrograph (currently in Phase A) for the European Extremely Large Telescope. Assuming a fiducial model without $\alpha$ variations, we show that ESPRESSO can improve current bounds on the E\"{o}tv\"{o}s parameter---which quantifies Weak Equivalence Principle violations---by up to two orders of magnitude, leading to stronger bounds than those expected from the ongoing tests with the MICROSCOPE satellite, while constraints from the E-ELT should be competitive with those of the proposed STEP satellite. Should an $\alpha$ variation be detected, these measurements will further constrain cosmological parameters, being particularly sensitive to the dynamics of dark energy.Comment: Phys. Lett. B (in press

A note on black hole entropy, area spectrum, and evaporation

We argue that a process where a fuzzy space splits in two others can be used to explain the origin of the black hole entropy, and why a "generalized second law of thermodynamics" appears to hold in the presence of black holes. We reach the Bekenstein-Hawking formula from the count of the microstates of a black hole modeled by a fuzzy space. In this approach, a discrete area spectrum for the black hole, which becomes increasingly spaced as the black hole approaches the Planck scale, is obtained. We show that, as a consequence of this, the black hole radiation becomes less and less entropic as the black hole evaporates, in a way that some information about its initial state could be recovered.Comment: 4 pages, 2 figure