Microwave background constraints on inflationary parameters

TL;DR

The paper addresses constraining inflationary physics from CMB data beyond simple power-law spectra by directly estimating slow-roll horizon-flow parameters. It develops a second-order slow-roll framework to predict scalar and tensor power spectra and embeds it in a CMB parameter estimation pipeline. Using a compilation of CMB data (including VSA, CBI, Archeops) and a HST prior on $h$, they obtain 2-σ bounds $11<{\cal P}_{\cal R}\times10^{10}<42$ and $\epsilon_1<0.057$, and place inflationary energy-scale limits $H_{\rm inf}/m_{\rm Pl}<1.5\times10^{-5}$ and $V_{\rm inf}^{1/4}<2.9\times10^{16}$ GeV. They show that current data permit a wide range of slow-roll models and that the approach is robust and potentially essential as data improve, with the potential to measure $\epsilon_3$ in the future and to test inflationary consistency relations.

Abstract

We use a compilation of cosmic microwave anisotropy data (including the recent VSA, CBI and Archeops results), supplemented with an additional constraint on the expansion rate, to directly constrain the parameters of slow-roll inflation models. We find good agreement with other papers concerning the cosmological parameters, and display constraints on the power spectrum amplitude from inflation and the first two slow-roll parameters, finding in particular that $ε_1 < 0.057$. The technique we use for parametrizing inflationary spectra may become essential once the data quality improves significantly.

Figures (4)

• Figure 1: Three views of the constraints on $\omega_{{\rm B}}$, $\omega_{\rm M}$ and $\omega_{\Lambda}$. The dashed lines show the constraints from the CMB alone, while the solid lines include the HST prior on the Hubble constant.
• Figure 2: Constraints on the amplitude ${\mathcal{P}}_{{\mathcal{R}}}$ and the first slow-roll parameter $\epsilon_1$, the solid lines again including the HST prior.
• Figure 3: Constraints on $\epsilon_1$ and $\epsilon_2$. The data are consistent with a scale-invariant, tensorless spectrum ($\epsilon_1<<1$, $|\epsilon_2|<<1$), but a significant tensor fraction and tilt are still permitted by the data. The dashed line, $\epsilon_1 = - \epsilon_2/2$, indicates inflationary models with a scale-invariant power spectrum. To the right the spectra are red, to the left they are blue.
• Figure 4: Constraints on ${\mathcal{P}}_{{\mathcal{R}}}$ and the optical depth $\tau$. The thick dashed curve is given by $10^{10}{\mathcal{P}}_{{\mathcal{R}}}e^{-2\tau}=15$.