Inflation in an effective gravitational model and asymptotic safety

Abstract

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.JHEPFG1029-847910.1007/JHEP08(2015)113] in the context of gravity as an asymptotically safe theory. It represents a refined Starobinsky model, Leff=MP2R/2+(a/2)R2/[1+bln(R/μ2)], where R is the Ricci scalar, a and b are constants, and μ 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 ns and the tensor-to-scalar ratio r. Requiring ns to be consistent with the Planck Collaboration upper limit, we find that r can be as large as r≃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 α=dns/dln(k) is still of the order -5×10-4 (as in the Starobinsky model), about 1 order of magnitude smaller than the current observational bound.