The Inflationary Perturbation Spectrum

Motivated by the prospect of testing inflation from precision cosmic microwave background observations, we present analytic results for scalar and tensor perturbations in single-field inflation models, based on the application of uniform approximations. This technique is systematically improvable, possesses controlled error bounds, and does not rely on assuming the slow-roll parameters to be constant. We provide closed form expressions for the power spectra and the corresponding scalar and tensor spectral indices.

Figure 1

Comparison of $\zeta$ for a ${\phi }^2$ chaotic inflation model calculated using the uniform approximation (crosses) and a numerical solution of the exact equations (solid line).