Attractor cosmology from nonminimally coupled gravity

Abstract

By using a bottom-up reconstruction technique for non-minimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the Ω(φ)-Jordan frame. For our approach, what is needed for the reconstruction method to work is the functional form of the non-minimal coupling Ω(φ) and of the scalar-to-tensor ratio, and also the assumption of the slow-roll inflation in the Ω(φ)-Jordan frame. By appropriately choosing the scalar-to-tensor ratio, we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the Ω(φ)-Jordan frame. We investigate the special conditions that are required to hold true in for this realization to occur, and we provide the analytic form of the potential in the Ω(φ)-Jordan frame. Also, by performing a conformal transformation, we find the corresponding Einstein frame canonical scalartensor theory, and we calculate in detail the corresponding observational indices. The result indicates that although the spectral index of the primordial curvature perturbations is the same in the Jordan and Einstein frames, at leading order in the e-foldings number, the scalar-to-tensor ratio differs. We discuss the possible reasons behind this discrepancy, and we argue that the difference is due to some approximation we performed to the functional form of the potential in the Einstein frame, in order to obtain analytical results, and also due to the difference in the definition of the e-foldings number in the two frames, which is also pointed out in the related literature. Finally, we find the F (R) gravity corresponding to the Einstein frame canonical scalar-tensor theory.PACS numbers: 04.50. Kd, 95.36.+x, 98.80.Cq,

Beyond the poles in attractor models of inflation

“…We have seen that when the kinetic term of a single-field Lagrangian is singular, a canonical model is no longer sufficient for representing the entirety of the underlying theory. Poles may arise in various ways: common examples include the hyperbolic geometry of the manifold on which inflation occurs [20][21][22] and the modification of the gravity sector, such as via nonminimal couplings [23,24] or F (R) gravity [25]. No matter their origin, poles introduce subtleties in the picture painted in Figure 1 and in the previous section.…”

Pole inflation from non-minimal coupling to gravity

“…As reviewed in section 2, these models generate predictions that depend on the order and residue of the leading pole [7,8]. The pole in the kinetic term is usually introduced by hand, motivated from SUSY-induced hyperbolic geometry [9,10] or modified gravity [11,12]. However, an often overlooked way to motivate pole cosmology is through the inclusion of a vanishing conformal factor [13].…”

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