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Alexei Starobinsky Geometric inflationary models based on higherderivative gravity
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QGRAV2021 • International Workshop on Quantum Gravity, Higher Derivatives Nonlocality • 8th to 12th March 2021 • https://www.qgrav2021.com/ • https://www.qgrav2021.inpcs.net/ • Abstract: Contrary to widespread opinion, local higher-derivative gravity models need not always have difficulties due to the presence of ghosts. I consider f(R) higher-derivative and purely geometric gravity in which ghosts are absent at the classical level and which is renormalizable in the scalar • sector. At the quantum level, when the squared Weyl tensor have to added to it for renormalizability in the tensor sector, the tensor ghost appears, as is well known. However, if there exists a hierarchy in this theory due to the dimensionless coefficient in front of the R^2 term being much more than • both unity and the similar coefficient in front of the C^2 term, then such theory can be used at high curvatures when the R^2 term in the action density exceeds the Einstein one (though not up to arbitrarily large curvatures, of course). Indeed, the most remarkable application of this gravity theory to actual cosmology - the R+R^2 inflationary model (1980) – leads to the result that the coefficient of the R^2 term should be about 5\\times 10^8. Moreover, it can be shown that another inflationary model having formally the same observational predictions for the primordial scalar and tensor perturbation spectra - the Higgs one - can be approximately described by the R+R^2 model during inflation in the same Jordan frame, i.e., without a conformal transformation. Due to renormalizabity of this model in the scalar sector, one-loop quantum gravitational corrections to this model can (and should) be taken into account. It follows from observational data on the primordial scalar (matter density) perturbation spectrum that running of the coefficient in front of the R^2 term with curvature due to one-loop quantum-gravitational corrections is small and does not exceed a few percent. The same refers to the R\\Box R correction considered perturbatively, without increasing the number of degrees of freedom, and to the correction from the GaussBonnet-like non local term in the conformal anomaly which becomes local in a conformally flat space-time. On the other hand, one-loop quantum-gravitational corrections become crucial after the end of inflation when they provide the decay of scalarons (quanta of the scalar degree of freedom in f(R) gravity) into particle-antiparticle pairs of all quantum fields of matter, but not to gravitons.
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