Logarithmic inflation?

Abstract

We consider a scalar–tensor action model, both simple and peculiar at the same time, with a boundary term added that it is form-invariant both under the conformal transformation of the metric as well as under the reparametrization of the scalar field. Under this assumption, the boundary term proposed matches (except factors) with the Gibbons–Hawking–York term proposed in such a way it cancels the term(s) involving [Formula: see text]. A matter term is added to the action also. In the Jordan frame, the pure gravitational action becomes the Einstein–Hilbert action with a cosmological constant when the scalar field takes the constant value of their vev, [Formula: see text], which is no otherwise but the only stable minimum of the classical potential chosen which is logarithmic type. This potential presents a large plateau in which it is almost fully flat and the decay of the field from its initial value (assumed to be close to [Formula: see text]) to vacuum draws a Low Field (or New Inflation) scenario. The model fits very well with the current paradigm of the universe and, under some assumptions, gives a good account of the value of the Higgs mass, the current value of the cosmological constant, e-folding, the Hubble parameter, the spectral index of scalar perturbations, etc. The model is not studied in Einstein’s frame. In this, only the expressions of the field and the potential, for a simple case, are achieved. As a result, we get that the nature of the decay of the initial value to its ground state for the scalar field, in this frame, should be by quantum tunneling and not by slow rolling.