We consider an inflationary model motivated by quantum effects of gravitational and matter fields near the Planck scale. Our Lagrangian is a resummed version of the effective Lagrangian recently obtained by Demmel, Saueressig, and Zanusso [A proper fixed functional for four-dimensional quantum Einstein gravity, J. High Energy Phys. 08 (2015) 113.] in the context of gravity as an asymptotically safe theory. It represents a refined Starobinsky model, ${\mathcal{L}}_{\mathrm{eff}}=M_{\mathrm{P}}^{2}R/2+(a/2)R^2/[1+b\ln (R/{\mu }^2)]$, where $R$ is the Ricci scalar, $a$ and $b$ are constants, and $\mu$ is an energy scale. By implementing the COBE normalization and the Planck constraint on the scalar spectrum, we show that increasing $b$ leads to an increased value of both the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. Requiring $n_s$ to be consistent with the Planck Collaboration upper limit, we find that $r$ can be as large as $r\simeq 0.01$, the value possibly measurable by Stage IV CMB ground experiments and certainly from future dedicated space missions. The predicted running of the scalar spectral index $\alpha =d{n}_s/d\ln (k)$ is still of the order $-5\times {10}^{-4}$ (as in the Starobinsky model), about 1 order of magnitude smaller than the current observational bound.

• Received 18 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.043505