Tensor to Scalar Ratio in Non-Minimal ϕ⁴ Inflation

Abstract

We reconsider nonminimal λϕ⁴ chaotic inflation which includes the gravitational coupling term ξRϕ², where ϕ denotes a gauge singlet inflaton field and R is the Ricci scalar. For ξ ≫ 1, we require, following recent discussions, that the energy scale λ¹/⁴mₚ/√ξ for inflation should not exceed the effective UV cutoff scale mₚ/ξ, where mₚ denotes the reduced Planck scale. The predictions for the tensor-to-scalar ratio r and the scalar spectral index nₛ are found to lie within the Wilkinson Microwave Anisotropy Probe 1−σ bounds for 10⁻¹² ≲ λ ≲ 10⁻⁴ and 10⁻³ ≲ ξ ≲ 10². In contrast, the corresponding predictions of minimal λϕ⁴ chaotic inflation lie outside the Wilkinson Microwave Anisotropy Probe 2−σ bounds. We also find that r ≳ 0.002, provided the scalar spectral index nₛ ≥ 0.96. In estimating the lower bound on r, we take into account possible modifications due to quantum corrections of the tree level inflationary potential.