Planck constraints on inflation in auxiliary vector modified f (R ) theories

Abstract

We show that the universal α -attractor models of inflation can be realized by including an auxiliary vector field A_μ for the Starobinsky model with the Lagrangian f (R )=R +R²/(6 M²) . If the same procedure is applied to general modified f (R ) theories in which the Ricci scalar R is replaced by R +A_μA^μ+β ∇_μA^μ with constant β , we obtain the Brans-Dicke theory with a scalar potential and the Brans-Dicke parameter ω_BD=β²/4 . We also place observational constraints on inflationary models based on auxiliary vector modified f (R ) theories from the latest Planck measurements of the cosmic microwave background anisotropies in both temperature and polarization. In the modified Starobinsky model, we find that the parameter β is constrained to be β <25 (68% confidence level) from the bounds of the scalar spectral index and the tensor-to-scalar ratio.