Noncommutative Spacetime Effect on the Slow-Roll Period of Inflation

We study how the noncommutative spacetime affects inflation. First we obtain the noncommutative power spectrum of the curvature perturbations produced during inflation in the slow-roll approximation. This is the explicit k-dependent power spectrum up to first order in slow-roll parameters ɛ₁, δ₁ including the noncommutative parameter μ. In order to test the role of μ further, we calculate the noncommutative power spectrum using the slow-roll expansion. We find corrections which arise from the change of pivot scale and the slowly varying nature of μ. It turns out that the noncommutative parameter μ could be considered as a zero order slow-roll parameter and the noncommutative spacetime effect provides a negatively large running spectral index.