Limits on primordial power spectrum resolution: An inflationary flow analysis

TL;DR

This paper explores the range of primordial power spectra consistent with current CMB data, revealing that more complex spectra with strong running can fit the data as well as simple models, thus broadening the viable inflationary scenarios.

Contribution

It introduces a combined flow formalism and numerical mode integration to analyze a wide variety of inflationary spectra beyond standard parameterizations.

Findings

Current data poorly constrains spectra on large scales due to cosmic variance.

Spectra with strong running on large scales are statistically degenerate with simpler models.

Generalized spectra can predict tensor-to-scalar ratios outside traditional confidence intervals.

Abstract

We investigate the ability of current CMB data to reliably constrain the form of the primordial power spectrum generated during inflation. We attempt to identify more exotic power spectra that yield equally good fits to the data as simple power-law spectra. In order to test a wide variety of spectral shapes, we combine the flow formalism, which is a method of stochastic model generation, with a numerical integration of the mode equations of quantum fluctuations. This allows us to handle inflation models that yield spectra that are not well described by the standard spectral parameterization. Using the latest WMAP data-set, we find a high degree of variation in possible spectral shapes. In particular, we find strongly running spectra arising from fast-rolling inflaton fields providing equally good fits to the data as power-law spectra arising from slowly-rolling fields. Current data poorly constrains the spectrum on scales (k < 0.01 h{\rm Mpc}^{-1}), where the error due to cosmic variance is large. Among the statistically degenerate models, we identify spectra with strong running on these larger scales, but with reduced running at smaller scales. These models predict values for the tensor-to-scalar ratio, (r), that lie outside the 2-(\sigma) confidence interval obtained from SDSS+WMAP data for spectra that are parametrized as power-laws or spectra with constant running. By considering more generalized power spectra, we therefore open up regions of parameter space excluded for simpler models.