tokens: configuration of the non-Gaussianity vs. the sound speed in a nonminimal derivative model in which both the nonminimal coupling and potential are E-model. The left panel corresponds to N = 60, and the right panel is for N = 70. The stars show the maximum values of the sound speed in each case. Table 3 Constraints on the Sound Speed and Tensor-to-scalar Ratio Obtained from 95% CL of Planck2015 TT, TE, EE+lowP Data Note. These constraints are corresponding to a nonminimal derivative model in which the nonminimal coupling is a constant and the potential is E-model. Table 4 Constraints on the Sound Speed and Tensor-to-scalar Ratio Obtained from 95% CL of Planck2015 TT, TE, EE+lowP Data Note. These constraints are corresponding to a nonminimal derivative model in which both the nonminimal coupling and potential are E-model. 5. Summary The aim of this paper was to study the nonminimal derivative model in the context of α -attractor. In this regard, we have considered a two-fields action in which both the fields and their derivatives are nonminimally coupled to the gravity. We have used the conformal gauge to convert the two-fields model into a one field, which its derivative (and not the field itself) is nonminimally coupled to the gravity. After obtaining the the background equations of this NMDC model, we have studied the linear perturbations theory. By adopting the ADM formalism, we have studied both the scalar and tensor perturbations in this setup and found some important perturbation parameters such as the power spectrum, scalar spectral index, and tensor-to-scalar ratio. After that, by introducing the types of the general functions and U ( ψ , φ ), and using the conformal gauge, the NMDC function and potential have been obtained. In this paper, two types of NMDC function have been considered: and . We have shown that in both cases, there is an attractor line in large N and small α limits that the r − n s trajectories tend to, while in the the single-field α -attractor model, there is an attractor point in these limits. In fact, the presence of attractor line instead of attractor point is due to the nonminimal derivatives coupling that causes the scalar spectral index of this model to be a functions of two parameters, α and M . In the limit , one recovers the attractor point as is usual in α -attractor models. We have numerically studied the linear perturbation in two cases with constant NMDC coupling and E-model NMDC coupling (in both cases the potential is considered to be E-model). With these choices, the power spectrum of the perturbations in NMDC model can get the observationally viable value (almost 2.4 × 10 −9 ) in some ranges of χ and α . Also, in this model, the r − n s plane lies in the background of Planck2015 TT, TE, EE+lowP data for all values of M (or χ ) and in some ranges of α , for both N = 60 and N = 70. We have obtained some constraints on the free parameter α which lead to the values of the scalar spectral index and
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