Abstract
Large-scale magnetogenesis is analyzed within the Palatini approach when the gravitational action is supplemented by a contribution that is nonlinear in the Einstein-Hilbert term. While the addition of the nonlinear terms does not affect the scalar modes of the geometry during the inflationary phase, the tensor-to-scalar ratio is nonetheless suppressed. In this context it is plausible to have a stiff phase following the standard inflationary stage provided the potential has a quintessential form. The large-scale magnetic fields can even be a fraction of the nG over typical length scales of the order of the Mpc prior to the gravitational collapse of the protogalaxy.
Highlights
Higher-order actions are a recurrent theme in various areas of physics and are often invoked as a short-scale modifications of the underlying theory
In single-field inflationary models the conventional scalar-tensor action can be regarded as the first term of a generic effective field theory where the higher derivatives are suppressed by the negative powers of a large mass-scale associated with the fundamental theory that underlies the effective description [8]
Showing that for the typical scales relevant for the magnetogenesis problem k/(a1H1) < O(10−23) since β < 1/2 and ξr 1; this happens for the same reason already mentioned in connection with Eq (4.9) where we argued that the existence of a stiff phase affects the determination of the maximal number of e-folds presently accessible to large-scale observations [39, 40]
Summary
Higher-order actions are a recurrent theme in various areas of physics and are often invoked as a short-scale modifications of the underlying theory. If the inflaton is minimally coupled in the presence of a higher-order gravity action various classes of inflationary models that are currently under pressure because of an excessive tensor to scalar ratio [23, 24, 25] become viable again within the Palatini approach [14, 15] This idea has been developed in various frameworks by changing both the matter contribution and the nonlinear gravitational action [16, 18, 19, 20, 21].
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