Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-04-15
Nucl.Phys. B674 (2003) 434-458
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 26 pages, 3 eps figures; (V2) Expanded version: added section 2.1, comments and references; more detailed derivation in
Scientific paper
10.1016/j.nuclphysb.2003.09.041
There are good indications that fundamental physics gives rise to a modified space-momentum uncertainty relation that implies the existence of a minimum length scale. We implement this idea in the scalar field theory that describes density perturbations in flat Robertson-Walker space-time. This leads to a non-linear time-dependent dispersion relation that encodes the effects of Planck scale physics in the inflationary epoch. Unruh type dispersion relations naturally emerge in this approach, while unbounded ones are excluded by the minimum length principle. We also find red-shift induced modifications of the field theory, due to the reduction of degrees of freedom at high energies, that tend to dampen the fluctuations at trans-Planckian momenta. In the specific example considered, this feature helps determine the initial state of the fluctuations, leading to a flat power spectrum.
Hassan S. F.
Sloth Martin S.
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