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We show that harmonically trapped Bose-Einstein condensates can be used toconstrain Planck scale physics. In particular we prove that a Planck-scaleinduced deformation of the Minkowski energy-momentum dispersion relation$\delta E \simeq \xi_1 mcp/2M_p$ produces a shift in the condensationtemperature $T_c$ of about $\Delta T_{c}/T_{c}^{0} \simeq 10^{-6} \xi_1 $ fortypical laboratory conditions. Such a shift allows to bound the deformationparameter up to $|\xi_1| \lesssim 10^4$. Moreover we show that it is possibleto enlarge $\Delta T_{c}/T_{c}^{0}$ and improve the bound on $\xi_1$ loweringthe frequency of the harmonic trap. Finally we compare the Planck-scale inducedshift in $T_c$ with similar effects due to interboson interactions and finitesize effects.

Trapped Bose-Einstein condensates with Planck-scale induced deformation of the energy-momentum dispersion relation