Cosmological parameter estimation and the spectral index from inflation

TL;DR

The paper investigates whether Planck-like CMB data can detect scale dependence in the primordial density perturbation spectrum and how allowing such scale dependence affects estimates of other cosmological parameters. Using a Fisher-matrix approach, it forecasts errors for a Standard CDM baseline while including up to the second derivative dn/dlnk and considering polarization. It shows that in slow-roll inflation, n = 1 − 6ε + 2η and dn/dlnk = −24ε^2 + 16εη − 2ξ^2 with r_ts ≈ 14ε, and that |dn/dlnk| ≈ 0.01 could be detectable with Planck polarization in many regions, particularly in hybrid models where tensor modes may be negligible. The study concludes that incorporating scale dependence modestly enlarges uncertainties for other parameters, with a notable exception that a detectable dn/dlnk in certain hybrid scenarios can provide extra constraints on the inflaton potential.

Abstract

Accurate estimation of cosmological parameters from microwave background anisotropies requires high-accuracy understanding of the cosmological model. Normally, a power-law spectrum of density perturbations is assumed, in which case the spectral index $n$ can be measured to around $\pm 0.004$ using microwave anisotropy satellites such as MAP and Planck. However, inflationary models generically predict that the spectral index $n$ of the density perturbation spectrum will be scale-dependent. We carry out a detailed investigation of the measurability of this scale dependence by Planck, including the influence of polarization on the parameter estimation. We also estimate the increase in the uncertainty in all other parameters if the scale dependence has to be included. This increase applies even if the scale dependence is too small to be measured unless it is assumed absent, but is shown to be a small effect. We study the implications for inflation models, beginning with a brief examination of the generic slow-roll inflation situation, and then move to a detailed examination of a recently-devised hybrid inflation model for which the scale dependence of $n$ may be observable.

Figures (1)

• Figure 1: This shows contours of constant $dn/d \ln k$, assuming $\xi^2 = 0$. Detection of the scale dependence at 95% confidence requires roughly $|dn/d \ln k| \ga 0.01$.