# Strong Planck constraints on braneworld and non-commutative inflation [CEA]

We place observational constraints on braneworld and non-commutative inflation for a number of inflaton potentials. In the Randall-Sundrum braneworld scenario, where the quadratic density dominates the Friedmann equation, the power-law potential $V(\phi) \propto \phi^p$ ($p \geq 2$) is outside the 95 % confidence-level (CL) observational contour constrained by Planck+WP+BAO+high-$\ell$ data, whereas in natural inflation and small-field inflation (including the Starobinsky model) some parameter values are allowed inside the 95 % CL region. If the contribution from the Gauss–Bonnet term dominates over the quadratic density term, the power-law potential is outside the 95 % CL boundary for any positive $p$. In the infrared limit of non-commutative inflation, the power-law potential with $p>0$ is disfavored by the data at more than 99 % CL due to a large scalar spectral index. In natural inflation, the non-commutative model can be inside the 68 % CL contour, but the symmetry-breaking scale is of order of the Planck mass. The small-field non-commutative model is viable provided that inflation occurs in the nearly flat regime away from the potential minimum, which includes the Starobinsky model as a specific case. We conclude that both braneworld and non-commutative scenarios of the kind considered here are limited by the most recent data even more severely than standard general-relativity models.

Date added: Tue, 22 Oct 13