Non-minimal two-loop inflation

Abstract

We investigate the chaotic inflationary model using the two-loop effective potential of a self-interacting scalar field theory in curved spacetime. We use the potential which contains a non-minimal scalar curvature coupling and a quartic scalar self-interaction and which was found in Ref.[1]. We analyze the Lyapunov stability of de Sitter solution and show the stability bound. Calculating the inflationary parameters, we systematically explore the spectral index n s and the tensor-to-scalar ratio r, with varying the four parameters, the scalar-curvature coupling ξ 0 , the scalar quartic coupling λ 0 , the renormalization scale μ and the e-folding number N. It is found that the two-loop correction on n s is much larger than the leading-log correction, which has previously been studied in Ref. [2]. We show that the model is consistent with the observation by Planck with WMAP [3,4] and a recent joint analysis of BICEP2 [5].

Running non-minimal inflation with stabilized inflaton potential

“…The number of e-folds is given by 8) where φ I is the inflaton value at horizon exit corresponding to the scale k 0 , and φ e is the inflaton value at the end of inflation, which is defined by max[ (φ e ), |η(φ e )|] = 1. The value of N depends logarithmically on the energy scale during inflation as well as on the reheating temperature, and is typically around 50-60.…”

“…For recent, detailed computations of quantum corrections, see [47][48][49] and their results of 1-loop beta functions with the s-factor. 8) where I is the initial inflation scale and 0 is the scale such that λ( 0 ) = 0. So we require β λ ( I ) 16π 2 × λ( I ) to ensure that the potential is stable.…”

“…In order to avoid this instability, we impose not only the condition of β λ = 0 but also dβ λ /d > 0 at I . 8 From the 7 In this paper, we are interested in this case, otherwise the beta function is so small that the inflaton quartic coupling is almost RG invariant. Although the tree-level analysis is valid in this case, the gauge and Yukawa couplings are too small to yield any impacts in the experimental point of view.…”

“…Hence, the simple chaotic inflationary scenario with the inflaton potentials V ∝ φ 4 and V ∝ φ 2 are disfavored because their predictions for r are too large. Among many inflation models, λφ 4 inflation with non-minimal gravitational coupling (ξφ 2 R, where φ is inflaton, R is the scalar curvature, and ξ is a dimensionless coupling) is a very simple model, which can satisfy the constraints by the Planck 2015 with ξ 0.001 [6][7][8].…”

“…In fact, we see that quantum corrections most likely cause an instability of the effective inflaton potential. Note that unless the non-minimal coupling (ξ ) is very large, the quartic inflaton coupling is very small [6][7][8]. Hence, quantum corrections to the effective potential are dominated by the gauge and Yukawa interactions.…”