Constraining N=1 supergravity inflationary framework with non-minimal Kähler operators (original) (raw)

In this paper we will illustrate how to constrain unavoidable K\"ahler corrections for calN=1{\cal N}=1calN=1 supergravity (SUGRA) inflation from the recent Planck data. We will show that non-renormalizable K\"ahler operators will induce in general {\it non-minimal kinetic} term for the inflaton field, and two types of SUGRA corrections in the potential - the {\it Hubble-induced mass} ($c_{H}$), and the {\it Hubble-induced A-term} ($a_{H}$) correction. The entire SUGRA inflationary framework can now be constrained from (i) {\it speed of sound}, csc_scs, and (ii) from the upper bound on the {\it tensor to scalar ratio}, rstarr_{\star}rstar. We will illustrate this by considering a heavy scalar degree of freedom at a scale, MsM_sMs, and a light inflationary field which is responsible for a slow-roll inflation. We will compute the corrections to the kinetic term and the potential explicitly. As an example we will consider a visible sector inflationary model of inflation where inflation occurs at the point of {\it inflection}, which can match the density perturbations for the cosmic microwave background radiation, and also explain why the universe is filled with the Standard Model degrees of freedom. We will scan the parameter space of non-renormalizable K\"ahler operators, which we find them to be order calO(1){\cal O}(1)calO(1), as expected from physical arguments. While the scale of heavy physics is found to be bounded by the tensor-to scalar ratio and the speed of sound, this high scale comes out to be varying within a range, $ {\cal O}(10^{11}\leq M_s\leq 10^{16})$~GeV, for the speed of sound varying from 0.02leqcsleq10.02\leq c_s\leq 10.02leqcsleq1, and tensor to scalar ratio varying from 10−22leqrstarleq0.1210^{-22} \leq r_{\star} \leq 0.1210−22leqrstarleq0.12.

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