Non-minimal coupling inflation and dark matter under the ℤ3 symmetry

Abstract

We study the cosmological inflation and dark matter (DM) in a unified way within a ℤ3 complex scalar model. The real and imaginary parts of the complex scalar act as the inflaton and DM respectively. The slow-rolling inflation with non-minimal coupling in both the metric and Palatini formalisms can be realized.We examine the whole parameters space by fully considering the theoretical and experimental constraints.We find that in the low-energy scale,the DM relic density and the DM-nucleon direct scattering experiments favor the mixing angle |θ| ≲ 0.25, the DM mass mχ ≳ 80 GeV, and the mass of Higgs-like scalar mh 2 ≳ 300 GeV.In the high-energy scale, after further considering the cosmological constraints of the scalar spectral index and the tensor-to-scalar ratio for the two forms of inflation,the scalar spectral indices are both ∼ 0.965, the non-minimum coupling coefficients are ∼ 104 and ∼ 109, and the tensor-to-scalar ratios are ∼ 10-3 and ≲ 10-11 respectively, which suggests that the inflation under the two formalisms can be distinguished by measuring the tensor-to-scalar ratio with higher precision.