Brans-Dicke inflation in light of the Planck 2015 data

Abstract

We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity.We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentials can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.

Anisotropic inflation in Brans–Dicke gravity

“…f → 0, and σ → 0 (i.e. spatially flat Friedmann-Robertson-Walker (FRW) universe), the model is reduced to that of the [54], [55] and [56]. Moreover, in the limit F (R, φ) = R and ω(φ) = 1 it is reduced to [41].…”

Generalized Brans–Dicke inflation with a quartic potential

“…We need just to have b > 0 due to having the end of inflation. Figure 5 shows that, in contrary to the result of quartic potential in both the Einstein [19] and standard BD gravity [20], the result of the model (22) for 0.09 ≤ ω 0 ≤ 1.2 lies inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data [19]. Also the running of the scalar spectral index predicted by the model (22) is favored by the Planck 2015 data, see Fig.…”

“…Also, the prediction of quartic potential in the standard BD gravity is disfavored by the Planck 2015 results [20]. In [36], it was shown that in the context of standard BD theory, the potential (20) can justify the late-time accelerated phase of the universe. It was pointed out that the scalar field ϕ in BD gravity can play the role of the dynamical Λ and describe the missing energy.…”

“…The result of the quartic potential(20) for the model(21) in r − n s plane. The marginalized joint 68% and 95% CL regions of Planck 2013, Planck 2015 TT+lowP and Planck 2015 TT,TE,EE+lowP data [19] are specified by gray, red and blue, respectively.…”

Induced affine inflation

“…A remarkable feature of this induced affine inflation is that, in addition to the nearly scale invariant spectrum of perturbations, it predicts a unique spectral index due to the existence of a unique frame set by a unique metric tensor. This feature is an important advantage compared to the induced inflation based on action (1), which suffers from Jordan-Einstein frame ambiguity (see the old and recent works [4][5][6][7][8][9][10][11][12][13]). Nevertheless, here we emphasize that, as in the induced gravity inflation, the observable quantities, namely the spectral index and the tensor-to-scalar ratio, are both sensitive to the nonminimal coupling parameter and can hardly stay in the observational bounds.…”