Trace-anomaly driven inflation in modified gravity and the BICEP2 result
  We explore conformal-anomaly driven inflation in $F(R)$ gravity without
invoking the scalar-tensor representation. We derive the stress-energy tensor
of the quantum anomaly in the flat homogeneous and isotropic universe. We
investigate a suitable toy model of exponential gravity plus the quantum
contribution due to the conformal anomaly, which leads to the de Sitter
solution. It is shown that in $F(R)$ gravity model, the curvature perturbations
with its enough amplitude consistent with the observations are generated during
inflation. We also evaluate the number of $e$-folds at the inflationary stage
and the spectral index $n_\mathrm{s}$ of scalar modes of the curvature
perturbations by analogy with scalar tensor theories, and compare them with the
observational data. As a result, it is found that the Ricci scalar decreases
during inflation and the standard evolution history of the universe is
recovered at the small curvature regime. Furthermore, it is demonstrated that
in our model, the tensor-to-scalar ratio of the curvature perturbations can be
a finite value within the $68\%\,\mathrm{CL}$ error of the very recent result
found by the BICEP2 experiment.
