Revisiting Witten-O'Raifeartaigh inflation for a non-minimally coupled scalar field

Abstract

In this work, we revisit the Witten-O'Raifeartaigh model of inflation, in which the potential takes a log2(ϕ/M) form, when the scalar field is non-minimally coupled to gravity. We investigate the impact of the coupling in the prediction of the inflationary parameters, thereby affecting the viability of the model. We find that a small coupling of order ξ ∼ 10-3 is preferred by data at the ns-r plane level, and that the presence of a non-zero ξ allows for a large interval of the mass scale M, in which it is possible to achieve a low tensor-to-scalar ratio. We also establish constraints imposed by a subsequent reheating era, in which its duration and temperature can be related to CMB observables, which in return, restricts the possible values for the ns and r parameters.

Constraints on the non-minimally coupled Witten-O'Raifeartaigh inflation

“…This motivates the consideration of extended scenarios, particularly the presence of a nonminimal coupling of the inflaton with gravity. An initial analysis was made in [32], and it was found that a small value of the parameter ξ was enough to drive the predictions of n s and r to values well into the 1σ confidence region of Planck data. Moreover, the range of the non-minimal coupling parameter is shown to be very restricted, in a way that it becomes interesting to know whether the CMB data indicates the presence of a non-zero ξ, at the same time that one can check if the value is consistent with the n s − r plane.…”

“…context to arrive at the same model through a different construction, where the mass scale associated is not theoretically constrained a priori [36]. A discussion of the model in the context of a non-minimally coupled field to gravity was done [32], whereby following previous works [13], a wide range of the mass M was considered. The main result is that in order for the model to have a good concordance with the recent CMB constraints on the n s − r parameters, the strength of the non-minimal coupling must be of the order of ξ ∼ 10 −3 .…”

“…where V 0 represents the amplitude of the potential, while M is a mass scale that controls its minimum value. The model was investigated in detail for ξ ≥ 0 in [32], where the Einstein frame potential is given by eq. ( 2.4) and we revise the main results on the predictions regarding the n s − r plane.…”

“…In this particular work, we seek to establish constraints on non-minimally coupled models by extending the analysis done in [32], in which the Witten-O'Raifeartaigh (WR) model of inflation [12,33] was investigated in the context of a non-minimally coupled scalar field. In the original picture, the model emerges from supergravity [33][34][35], in an attempt to solve the hierarchy problem, such that the mass scale associated with the model is estimated to be of the order of Planck mass.…”