The Quest for the Inflationary Spectral Runnings in the Presence of Systematic Errors

Abstract

Cosmological inflation predicts that the scalar spectral index "runs" with scale. Constraints on the values of the spectral runnings, $\alpha_s\equiv \textrm{d} n_s/\textrm{d}\ln k$ and $\beta_s\equiv \textrm{d}\alpha_s/\textrm{d}\ln k$, therefore provide a fundamental test of the physics of inflation. Here we study the feasibility of measuring the runnings when information from upcoming large-volume galaxy surveys is used to supplement the information provided by a CMB-S4 experiment, particularly focusing on the effect of including high-$k$, nonlinear scales. Since these measurements will be sensitive to modeling uncertainties for the nonlinear power spectrum, we examine how three different ways of parameterizing those systematics---introducing zero, two, or several hundred nuisance parameters---affect constraints and protect against parameter biases. Considering statistical errors alone, we find that including strongly nonlinear scales can substantially tighten constraints. However, these constraints weaken to levels not much better than those from a CMB-S4 experiment alone when we limit our analysis to scales where estimates are not strongly affected by systematic biases. Given these considerations, near-future large-scale structure surveys are unlikely to add much information to the CMB-S4 measurement of the first running $\alpha_s$. There is more potential for improvement for the second running, $\beta_s$, for which large-scale structure information will allow constraints to be improved by a factor of 3--4 relative to using the CMB alone. Though these constraints are still above the value predicted by slow roll inflation, they do probe regions of parameter space relevant to nonstandard inflationary models with large runnings, for example those that can generate an appreciable abundance of primordial black holes.