Current and Future constraints on single-field $\alpha$-Attractor model

Abstract

We study here the observational constraints on single-field inflationary models achievable with the next generation of CMB experiments. We particularly focus on a Stage-IV like experiment and forecasts its constraints on inflationary parameters in the context of $\alpha$-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 $\alpha$-model a priori. We found that current CMB data are able to place a tight bound on the ratio of the tensor-to-scalar ratio with the alpha parameter $r/\alpha =3.87_{-0.94}^{+0.78}\cdot 10^{-3}$ and on the running of the scalar index ${\alpha }_S=-6.4_{-1.3}^{+1.6}\cdot 10^{-4}$ with a value of the scalar index consistent with current constraints. In the optimistic scenario of detection of primordial gravitational waves in the CMB B-mode polarization power spectra, we found that CMB-S4 will be able to achieve a $15\%$ bound on the value of the parameter $\alpha =1.01_{-0.18}^{+0.14}$. This bound clearly show 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 reduce the accuracy of $5\%$ leading to $\alpha =1.07_{-0.23}^{+0.18}$ so that our main conclusions are still valid.

arXiv comment8 pages, 5 figures. Comments are welcome

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