Abstract
We discuss how the non-minimal coupling ξϕ2R between the inflaton and the Ricci scalar affects the predictions of single field inflation models in the Palatini formalism. The inflaton field ϕ must interact with matter fields at the end of inflation in order to make a transition to the radiation dominated era. Interactions of the inflaton with other fields lead to radiative corrections to the inflationary potential. These radiative corrections can be explained at leading order by Coleman-Weinberg (CW) one-loop corrections. In this work, the effect of radiative corrections to the potential has been examined using two different prescriptions debated in the literature. Prescription I and Prescription II examine the coupling of the inflaton to bosons and fermions. We analyze the range of these coupling parameters for which the spectral index ns and the tensor-to-scalar ratio r are compatible with data taken by the Keck Array/BICEP2 and Planck collaborations. Finally, we show for all the considered potentials the behavior of the running of the spectral index α=dns/dlnk as a function of κ for selected ξ values.
Highlights
By taking into account the Palatini formulation is not an additional assumption about the theory, only a different parametrisation of the gravitational degrees of freedom
In this paper aims to extend the previous work of non-minimal coupling in Palatini formulation, presenting a non-minimally coupled radiatively corrected quartic inflation potential in Palatini approach
It is clear from the figures that for ξ 1 values, linear inflation predictions are lost because r values are very tiny and in Palatini formulation, r is much smaller than the Metric formulation for the inflaton coupling to bosons for ξ 1, the inflaton coupling to bosons results in Metric formulation was shown in ref
Summary
The Jordan frame Lagrangian density with non-minimally coupled scalar field φ with a canonical kinetic term and a potential VJ (φ):. We obtain the Lagrangian density for a minimally coupled scalar field σ with a canonical kinetic term. For the Palatini formulation, the field redefinition is induced just by the rescaling of the inflaton kinetic term indicated as eq (2.7) It does not depend on Jordan frame Ricci scalar. Using eq (2.8), inflationary potential can be defined in terms of canonical scalar field σ, in one can be obtained slow-roll parameters in the Palatini formulation in large field limit according to σ. As long as the Einstein frame potential is obtained in terms of the canonical scalar field σ, observational parameters for inflation can be obtained using the slow-roll parameters [50]. The calculation is replicated over the entire grid, with self-coupling constant λ solutions for every point used as initial values of their neighbours
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