Unparticle inspired corrections to the Gravitational Quantum Well

We consider unparticle inspired corrections of the type ${(\frac{R_{G}}{r})}^\beta$ to the Newtonian potential in the context of the gravitational quantum well. The new energy spectrum is computed and bounds on the parameters of these corrections are obtained from the knowledge of the energy eigenvalues of the gravitational quantum well as measured by the GRANIT experiment.Comment: Revtex4 file, 4 pages, 2 figures and 1 table. Version to match the one published at Physical Review

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