Abstract
We study the dynamics of a generalized inflationary model in which both the scalar field and its derivatives are coupled with the gravity. We consider a general form of the nonminimal derivative coupling in order to have a complete treatment of the model. By expanding the action up to the second order in perturbation, we study the spectrum of the primordial modes of the perturbations. Also, by expanding the action up to the third order and considering the three-point correlation functions, the amplitude of the non-Gaussianity of the primordial perturbations is studied in both equilateral and orthogonal configurations. Finally, by adopting some sort of potentials, we compare the model in hand with the Planck 2015 released observational data and obtain some constraints on the model’s parameters space. As an important result, we show that the nonminimal couplings help to make models of chaotic inflation that would otherwise be in tension with Planck data, in better agreement with the data. This model is consistent with observation at weak coupling limit.
Highlights
Another extension of the inflation theory arises from considering a nonminimal coupling between the derivatives of the scalar field and the curvature, which leads to the interesting cosmological behaviors [53]
We have found that an inflationary model with a nonminimal coupling between the scalar filed and Ricci scalar and a nonminimal derivative coupling, in some ranges of nonminimal coupling parameter ξ is consistent with Planck2015 dataset
We have studied the dynamics of a generalized inflationary model in which both the scalar field and its derivatives are nonminimally coupled to gravity
Summary
The four-dimensional action for a cosmological model where a scalar field is nonminimally coupled to the Ricci scalar, in the presence of a nonminimal derivative coupling between the scalar field and gravity, is given by the following expression. In the nonminimal derivative term of the action (2.1), Gμν. In some papers there is a coefficient κ∗ 2 in front of the nonminimal derivative term, where the constant parameter κ∗ has dimension of length-squared. Where, a dot refers to a time derivative of the parameter and a prime denotes a derivative with respect to the scalar field. By varying the action (2.1) with respect to the scalar field we get the following equation of motion φ − 1 + 6F ′H2 + 12F ′HH + 18F ′H3 − 3H φ + 3F ′′H2φ2 + 6f ′R − V ′ = 0
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