Palatini formulation of non-local gravity

We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have shown that, in some specific cases, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein's gravity are not removed.Comment: 10 page

Planck-scale effects on Bose-Einstein condensates

The effects of a Planck-scale deformation of the Minkowski energy-momentum dispersion relation on the phenomenology of non-trapped Bose-Einstein condensates (BECs) are examined. Such a deformation is shown to cause a shift in the condensation temperature $T_{c}$ of the BEC and, for a specific functional form of deformation, this shift can be as large as the current measured precision on $T_{c}$. For a $_{37}^{85}Rb$ cold-atom BEC with a particle density $n\simeq 10^{12}cm^{-3}$ we find a fractional shift of order $10^{-4}$, but this can be much larger for even more dilute BECs. We discuss the possibility of planning specific experiments with BECs that might provide phenomenological constraints on Planck-scale physics. These corrections to $T_{c}$ are found to be extremely small for ultrarelativistic BECs implying that, in some cases, Planck-scale effects may be more important in low- rather than high-energy processes.Comment: 5 pages, some references added, version published in EP

Study of stability of relativistic ideal Bose-Einstein condensates

A relativistic complex scalar boson field at finite temperature $T$ is examined below its critical Bose-Einstein condensation temperature. It is shown that at the same $T$ the state with antibosons has higher entropy, lower Helmholtz free energy and higher pressure than the state without antibosons, but the same Gibbs free energy as it should. This implies that the configuration without antibosons is metastable. Results are generalized for arbitrary $d$ spatial dimensions.Comment: Accepted for publication in Phys.Lett.