The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

Abstract

We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio r, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parameterization r=8α/(N+β)γ, which is a general form of the α-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose γ=2 and α≪1. We also discuss the constraints from the reheating phase by assuming the parameter wre of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put an upper limit on ns if wre=2/3 and a low limit on ns if wre=1/6.

Inflationary attractors from a non-canonical kinetic term

“…According to the observational data, the simplest form of the spectral index may be n s = 1 − 2/N with the e-folds N = 60. If the form of the spectral index n s or other slow-roll parameters is given, we can reconstruct the inflationary potentials in the slow-roll regime [7][8][9][10][11][12][13][14][15][16][17][18][19]. In this way, a wide range of inflation models that consistent with the observational data can be found.…”

Editorial to the Special Issue “Inflation, Black Holes and Gravitational Waves”

“…By parameterizing the slow-roll parameters or observables n s and r with N, we can reconstruct inflationary potentials. In [2], discus the reconstruction procedure for inflation models with the non-minimal derivative coupling term is discussed, and the study reconstructed the non-minimal derivative coupling inflationary potential by parameterizing the tensor-to-scalar ratio r. Because the observational data only probes large scales, the reconstructed potentials approximate the inflationary potential in the slow-roll regime only at large scales.…”