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.
Highlights
In the standard big-bang cosmology, inflation has successfully solved various problems, such as the flatness, horizon and monopole problems
If the kinetic term of the scalar field is non-minimal coupled to Einstein tensor, the tensor-to-scalar ratio r could be reduced to being consistent with the observational data, and the effective Higgs self-coupling λ could be the order of 1 [6,7]
This inflation model with non-minimal derivative coupling belongs to the subclass of the Horndeski theory [8], which is a general scalar–tensor theory, with field equations that are at most of the second-order derivatives of both the metric gμν and scalar field φ in four dimensions [9]
Summary
In the standard big-bang cosmology, inflation has successfully solved various problems, such as the flatness, horizon and monopole problems. If the kinetic term of the scalar field is non-minimal coupled to Einstein tensor, the tensor-to-scalar ratio r could be reduced to being consistent with the observational data, and the effective Higgs self-coupling λ could be the order of 1 [6,7]. We consider the non-minimal derivative coupling inflation models to investigate this α-attractors issue by reconstructing the potential. The model parameters can be constrained and the reconstructed potential would always be consistent with the observational data [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47] After the inflation, it is followed by the reheating phase, which may give additional constraints on the inflation phase [46,48].
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