A Fully Covariant Information Theoretic Ultraviolet Cutoff for Fields on Expanding FRW Spacetimes

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A covariant ultra-violet cutoff on the modes of physical fields on a given space-time can be achieved by cutting off the spectrum of the D'Alembertian of the manifold. This cutoff is a natural generalization of the naive ultra-violet cutoff inEuclidean space which is obtained by simply projecting out frequencies greater in magnitude than a given maximum frequency. Here it is shown that for flat spacetime and expanding FRW spacetimes thiscutoff manifests itself as a decrease in temporal degrees of freedom for large spatial modes. In a large class of expanding FRW spacetimes where the proper time co-ordinate ends at a finite value, it is shown how the numberof temporal degrees of freedom of a fixed spatial mode depends on the magnitude of the spatial mode. We further indicate how the effects of this ultra-violet cutoff on the dynamics of field theories can be studied, and how the resulting modifications to inflationary predictions of the CMB spectrum could be calculated. This talk is based on ongoing joint work with Prof. Achim Kempf (University of Waterloo) and Aidan Chatwin-Davies (UW).