Constraining $ \mathcal{N} $ = 1 supergravity inflationary framework with non-minimal Kähler operators

Abstract

In this paper we will illustrate how to constrain unavoidable Kähler corrections for N = 1 supergravity (SUGRA) inflation from the recent Planck data. We will show that the non-renormalizable Kähler operators will induce in general non-minimal kinetic term for the inflaton field, and two types of SUGRA corrections in the potential -the Hubbleinduced mass (c H ), and the Hubble-induced A-term (a H ) correction. The entire SUGRA inflationary framework can now be constrained from (i) the speed of sound, c s , and (ii) from the upper bound on the tensor to scalar ratio, r ⋆ . We will illustrate this by considering a heavy scalar degree of freedom at a scale, M s , 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 for the light field explicitly. As an example, we will consider a visible sector inflationary model of inflation where inflation occurs at the point of 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 the non-renormalizable Kähler operators, which we find them to be order O(1), consistent with physical arguments. While the scale of heavy physics is found to be bounded by the tensor-to scalar ratio, and the speed of sound, O 10 11 ≤ M s ≤ 10 16 GeV, for 0.02 ≤ c s ≤ 1 and 10 −22 ≤ r ⋆ ≤ 0.12.

Modulus stabilization in higher curvature dilaton gravity

“…Thus increasing the GB coupling beyond a value leads to instability. Hence, in the perturbative regime of the solution we can always obtain a stabilized modulus potential although these stabilized values of the modulus radius r c are not effective in resolving the gauge hierarchy or fine-tuning problem as k M r c ≪ O (12). We observe that as S goes beyond the value ∼ 0.9 the minimum of the potential disappears and we move to the region of instability.…”

“…Usually such corrections originate naturally in string theory where power expansion in terms of inverse of Regge slope (or string tension) yields the higher curvature corrections to pure Einstein's gravity. Supergravity, as the low energy limit [7][8][9][10][11][12][13][14][15][16][17][18] of heterotic string theory [19][20][21][22][23][24][25][26][27], yields the Gauss-Bonnet (GB) term along with dilaton coupling at the leading order correction. Consequently it became an active area of interest as a modified theory of gravity.…”

Possible resolution of the domain wall problem in the NMSSM

“…Such a mass term generically arises via a Plancksuppressed interaction in the framework of supergravity [32]; see also [3,[5][6][7]. Since the value of the coefficient c depends on the details of the Kähler terms [33], it is fair to treat it as a free parameter to keep the discussion model independent. According to its value, we may consider the following three possibilities:…”

Quantum gravity effect in torsion driven inflation and CP violation

“…However such quantum corrections are extremely hard to compute as it completely belongs to the hidden sector of the theory dominated by heavy fields [21,22]. In the trans-Planckian regime the classical gravity sector is corrected by incorporating the effect of higher derivative interactions appearing through the modifications to GR which plays significant role in this context [23][24][25][26][27][28].…”