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While a natural ultraviolet cutoff, presumably at the Planck length, iswidely assumed to exist in nature, it has proven difficult to implement aminimum length scale covariantly. A key reason is that the presence of a fixedminimum length would seem to contradict the ability of Lorentz transformationsto contract lengths. In this paper, we implement a fully covariant Planck scalecutoff by cutting off the spectrum of the d'Alembertian. In this scenario,consistent with Lorentz contractions, wavelengths that are arbitrarily smallerthan the Planck length continue to exist. However, the dynamics of modes ofwavelengths that are significantly smaller than the Planck length possess avery small bandwidth. This has the effect of freezing the dynamics of suchmodes. While both, wavelengths and bandwidths, are frame dependent, Lorentzcontraction and time dilation conspire to make the freezing of modes oftransplanckian wavelengths covariant. In particular, we show that thisultraviolet cutoff can be implemented covariantly also in curved spacetimes. Wefocus on Friedmann Robertson Walker (FRW) spacetimes and their much-discussedtransplanckian question: The physical wavelength of each comoving mode wassmaller than the Planck scale at sufficiently early times. What was the mode'sdynamics then? Here, we show that in the presence of the covariant UV cutoff,the dynamical bandwidth of a comoving mode is essentially zero up until itsphysical wavelength starts exceeding the Planck length. In particular, we showthat under general assumptions, the number of dynamical degrees of freedom ofeach comoving mode all the way up to some arbitrary finite time is actuallyfinite. Our results also open the way to calculating the impact of this naturalUV cutoff on inflationary predictions for the CMB.

A fully covariant information-theoretic ultraviolet cutoff for scalar fields in expanding FRW spacetimes