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

Journal of High Energy Physics, Apr 2014

Abstract In this paper we will illustrate how to constrain unavoidable Kähler corrections for \( \mathcal{N} \) = 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 Hubble-induced 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 \( \mathcal{O} \)(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, (\( \mathcal{O} \)1011 ≤ M s ≤ 1016) GeV, for 0.02 ≤ c s ≤ 1 and 10−22 ≤ r ⋆ ≤ 0.12.

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

Sayantan Choudhury 1 Anupam Mazumdar 0 Ernestas Pukartas 0 0 Consortium for Fundamental Physics, Physics Department, Lancaster University , LA1 4YB, Bailrigg, Lancaster, U.K 1 Physics and Applied Mathematics Unit, Indian Statistical Institute , 203 B.T. Road, Kolkata 700 108, India In this paper we will illustrate how to constrain unavoidable Kahler corrections for N = 1 supergravity (SUGRA) inflation from the recent Planck data. We will show that the non-renormalizable Kahler 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 (cH ), and the Hubble-induced A-term (aH ) correction. The entire SUGRA inflationary framework can now be constrained from (i) the speed of sound, cs, 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, Ms, 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 Kahler 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 1011 Ms 1016 GeV, for 0.02 cs 1 and 1022 r 0.12. ArXiv ePrint: 1402.1227 Open Access, c The Authors. Article funded by SCOAP3. Contents 1 Introduction 2 4 5 3 Inflationary setup within N = 1 SUGRA Non-minimal Kahler potential and non-canonical kinetic terms 5.1 Heavy field is dynamically frozen 5.2 Heavy field is oscillating during the onset of inflation 5.3 Constraining non-renormalizable operators, i.e. a, b, c, d, and Ms B Case -1, 2, 3, 4 C Expression for aH Introduction The success of primordial inflation [14], for a review, see [5], can be gauged by the current observations arising from the comic microwave background (CMB) radiation [68]. The observations from Planck have put interestingly tight bounds on a number of unknown parameters of a generic inflationary model [6], in particular the speed of sound, cs, of the perturbations, which also determines any departure from the Gaussian perturbations, the local type of non-Gaussianity, f NloLcal, and the constraint on tensor-to-scalar ratio, r, which can potentially unearth the scale of New Physics within any given effective field theory set-up. The N = 1 supergravity (SUGRA) [9, 10], for a review, see [11], is an excellent welldefined set-up where we can address some of the key questions about the physics of the new scale for instance. The Kahler metric determines the kinetic term for the inflaton potential, and one particular choice is the minimal Kinetic term for the inflaton field. However, quantum corrections to the Kahler potential is not very well-known. Generically corrections to the Kahler potential arise from integrating out the heavy physics, and due to lack of concrete knowledge on the details of the heavy physics, many times computing these corrections can be very challenging, see [12]. The aim of this paper is to place a generic bound on the Planck suppressed corrections to the Kahler potential on top of the minimal Kahler potential. We will consider dimensional 3 and dimensional 4 gauge invariant non-renormalizable Kahler operators in this paper. Since these correction will lead to a departure from the minimal kinetic term for the inflationary potential, such corrections can now be bounded from the Planck data, especially from the speed of sound of the primordial perturbations. In fact the Kahler potential within N = 1 SUGRA can induce corrections to the inflationary potential which can yield large Hubble-induced mass correction to the inflaton field [1317], some times known as the SUGRA- problem, and the Hubble-induced SUGRA A-term for the potential. In the context of N = 1 SUGRA hybrid inflation [1820], some of the Kahler corrections were constrained by the tensor to scalar ratio, r, and the spectral tilt, nS, of the power spectrum. In this paper we will be constraining these Kahler corrections systematically from the interaction of the heavy physics to the light inflaton field from the recent Planck data. Let us consider the scale of New Physics, Ms, to be within Mp Ms Hinf , where Hinf is the Hubble parameter during inflation, and Mp = 2.4 1018 GeV. In order to constrain Ms, we would require to consider at least 2 fields, one which is heavy at the relevant scale, Ms, and the other which is light. We will assume that these two fields are coupled gravi (...truncated)


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Sayantan Choudhury, Anupam Mazumdar, Ernestas Pukartas. Constraining \( \mathcal{N} \) = 1 supergravity inflationary framework with non-minimal Kähler operators, Journal of High Energy Physics, 2014, pp. 77, Volume 2014, Issue 4, DOI: 10.1007/JHEP04(2014)077