Inflation inR 2 cosmology with massless conformal scalar field and adiabatic regularization

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A cosmology described by a Robertson-Walker metric with Lagrangian √-g(@#@R+σR 2) and a massless conformal scalar field as matter content is considered. It is shown that, when the adiabatic regularization is performed, there is, in the spatially flat case, an inflationary solution which is not stable in the future, at first perturbative order, if the condition σ>t{p/2}/2160π (t p Planck time) is fulfilled and stable in the opposite case.

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