Current and future constraints on single-field α -attractor models

Physical review. D/Physical review. D., vol. 104

Abstract

We study the observational constraints on single-field inflationary models achievable with the next generation of cosmic microwave background (CMB) experiments. We focus on a Stage IV (S4)-like experiment and forecast its constraints on inflationary parameters in the context of $\ensuremath{\alpha}$-attractor inflation comprising a large class of single-field models. To tailor our forecasts, we use as a fiducial model the results obtained with current CMB and LSS data, assuming the $\ensuremath{\alpha}$ model a priori. We find that current CMB data are able to place a tight bound on the ratio of the tensor amplitude with the alpha parameter $r/\ensuremath{\alpha}=3.8{7}_{\ensuremath{-}0.94}^{+0.78}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and on the running of the scalar index ${\ensuremath{\alpha}}_{S}=\ensuremath{-}6.{4}_{\ensuremath{-}1.3}^{+1.6}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ with a value of the scalar index consistent with current constraints. These tight constraints are the result of the strong bound imposed on ${n}_{s}$ by the current cosmological data and the theoretical prior of $\ensuremath{\alpha}$-attractor models on inflationary observables. This bound can also be translated into an upper bound for $\ensuremath{\alpha}$. We find $\ensuremath{\alpha}<25$ and $\ensuremath{\alpha}<15$, given $r<0.1$ and $r<0.06$ for Planck 2018 and Planck 2018 and BICEP/Keck 2015 data, respectively. In the optimistic scenario of detection of primordial gravitational waves in the CMB $B$-mode polarization, CMB-S4 will be able to achieve a 15% bound on the value of the $\ensuremath{\alpha}$ parameter. This bound clearly shows the ability of CMB-S4 to constrain not only the energy scale of inflation but also the shape of its potential. Enlarging the baseline model to also include the neutrino sector merely reduces the accuracy on $\ensuremath{\alpha}$ by about 5%, and thus our main conclusions are still valid. Conversely, in the pessimistic scenario of no detection, a CMB-S4-like experiment will reduce the upper bound on $\ensuremath{\alpha}$ by around an order of magnitude, leading to a possible exclusion of the Starobinsky model at the level of 6 standard deviations.

Authors 2

1. G Cañas-Herrera Aachen Leiden Observatory Lorentz Institute for Theoretical Physics

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands

   Lorentz Institute for Theoretical Physics, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands

2. Fabrizio Renzi Aachen Lorentz Institute for Theoretical Physics

   Leiden University

   Affiliation as printed

   Lorentz Institute for Theoretical Physics, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands