Noncommutative inflation

In spite of the success of the inflationary Universe scenario [1] in solving some of the mysteries of standard cosmology and of providing a mechanism which explains the origin of density fluctuations on cosmological scales, a mechanism which to date has passed all of the observational challenges, we still do not have a convincing realization of inflation based on fundamental physics. Moreover, the usual realizations of inflation based on weakly coupled scalar matter fields (see e.g. [2] for a comprehensive review) are plagued by important conceptual problems [3]. Thus, it is of great interest to explore possible realizations of inflation based on new fundamental physics. In particular, since inflation may occur at energy scales close to the Planck scale, it is of interest to consider the implications of the recent developments in our understanding of physics at the Planck scale for inflation. Space-time non-commutativity is one of the key new ideas which follows from recent developments in string and matrix theory [4]. It is thus of great interest to explore the compatibility of non-commutative spacetime structure with inflation (see [5,6] for ideas on how to solve some of the problems of standard cosmology without inflation in non-commutative geometry). Noncommutativity, and space-time quantization, in general lead to deformed dispersion relations (see e.g. [7]). It has been shown [8–10] (see also [11,12]) that this can have important consequences for the predictions of inflation. These authors demonstrated that the short distance cutoff given by modifying the usual commutation relations