Density perturbations in generalized Einstein scenarios and constraints on nonminimal couplings from the cosmic microwave background

Abstract

We study cosmological perturbations in generalized Einstein scenarios and show the equivalence of inflationary observables both in the Jordan frame and the Einstein frame. In particular the consistency relation relating the tensor-to-scalar ratio with the spectral index of tensor perturbations coincides with the one in Einstein gravity, which leads to the same likelihood results in terms of inflationary observables. We apply this formalism to nonminimally coupled chaotic inflationary scenarios with potential V = cφ p and place constraints on the strength of nonminimal couplings using a compilation of latest observational data. In the case of the quadratic potential (p = 2), the nonminimal coupling is constrained to be ξ > −7.0 × 10 −3 for negative ξ from the 1σ observational contour bound. Although the quartic potential (p = 4) is under a strong observational pressure for ξ = 0, this property is relaxed by taking into account negative nonminimal couplings. We find that inflationary observables are within the 1σ contour bound as long as ξ < −1.7 × 10 −3 . We also show that the p ≥ 6 cases are disfavoured even in the presence of nonminimal couplings.

Agravity

“…4 10 18 GeV is the reduced Planck mass. Special assumptions such as V (S) ∝ f (S) 2 make the Einstein-frame potential V E flat at S M Pl , with predictions compatible with present observations [7][8][9][10][11][12][13][14][15][16][17][18][19]. However this flattening is the result of a fine-tuning: in presence of generic Planck-suppressed operators V and f and thereby V E are generic functions of S/M Pl .…”

“…In the agravity context, such field must have a dimensionless logarithmic potential: this is why our predictions for r ≈ 8/N ≈ 0.13 differ from the tentative prediction r ≈ 12/N 2 ≈ 0.003 of a generic ξ-inflation model with mass parameters in the potential [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In the limit where h or χ feel the vacuum expectation value of s as a constant mass term, one obtains Starobinsky inflation and Higgs ξ-inflation [7][8][9][10][11][12][13][14][15][16][17][18][19]: agravity dictates how they can hold above the Planck scale. Leaving a full analysis to a future work, we here want to explore the possibility that the inflaton is the field s that dynamically generates the Planck scale, as discussed in section 3.…”

“…However, this is a quite unusual outcome of quantum field theory: it requires special models with flat potentials, and often field values above the Planck scale. Let us discuss this issue in the context of Starobinsky-like inflation models [7][8][9][10][11][12][13][14][15][16][17][18][19]: a class of inflation models favoured by Planck data [20]. Such models can be described in terms of one scalar S (possibly identified with the Higgs H) with a potential V (S) and a coupling to gravity − 1 2 f (S)R. Going to the Einstein frame (i.e.…”

Realizing scale-invariant density perturbations in low-energy effective string theory

“…Provided that L c = 0, this standard consistency relation holds even for scalar-tensor models characterized by the action (1) [24,28].…”