We present projections for reconstruction of the inflationary potential expected from ESAs upcoming Planck Surveyor CMB mission. We focus on the effects that tensor perturbations and the presence of non-Gaussianities have on reconstruction efforts in
the context of non-canonical inflation models. We consider potential constraints for different combinations of detection/null-detection of tensors and non-Gaussianities. We perform Markov Chain Monte Carlo and flow analyses on a simulated Planck-precision data set to obtain constraints. We find that a failure to detect non-Gaussianities precludes a successful inversion of the primordial power spectrum, greatly affecting uncertainties, even in the presence of a tensor detection. In the absence of a tensor detection, while unable to determine the energy scale of inflation, an observable level of non-Gaussianities provides correlations between the errors of the potential parameters, suggesting that constraints might be improved for suitable combinations of parameters. Constraints are optimized for a positive detection of both tensors and non-Gaussianities.
We study a two-parameter family of exactly solvable inflation models with variable sound speed, and derive a corresponding exact expression for the spectrum of curvature perturbations. We generalize this expression to the slow roll case, and derive a
n approximate expression for the scalar spectral index valid to second order in slow roll. We apply the result to the case of DBI inflation, and show that for certain choices of slow roll parameters, the Bunch-Davies limit (a) does not exist, or (b) is sensitive to stringy physics in the bulk, which in principle can have observable signatures in the primordial power spectrum.
