Analytic Correlation of Inflationary Potential to Power Spectrum Shape: Limits of Validity, and `No-Go' for Small Field Model Analytics

Understand

The primordial power spectrum informs the possible inflationary histories of our universe.

• Given a power spectrum, the ensuing cosmic microwave background is calculated and compared to the observed one.
• Thus, one focus of modern cosmology is building well-motivated inflationary models that predict the primordial power spectrum observables.
• The common practice uses analytic terms for the scalar spectral index $n_s$ and the index running $\alpha$, forgoing the effort required to evaluate the model numerically.