Small cosmological constant from a peculiar inflaton potential

We propose a novel scenario to explain the small cosmological constant (CC) by a peculiar inflaton potential. The shape almost satisfies the following conditions: The inflation is eternal if the CC is positive and not eternal if the CC is negative. Although realizing the peculiar shape has a similar amount of fine-tuning as the CC, the shape can be made stable under radiative corrections in the effective theory. By introducing a slowly varying CC from a positive value to a negative value, the dominant volume of the Universe after the inflation turns out to have a vanishingly small CC. The scenario does not require eternal inflation, but the e-folding number is exponentially large, and the inflation scale is low. The Hubble parameter during inflation, Hinf, is required to be smaller than the present CC scale, and, thus, the CC relaxed during inflation with the low renormalization scale, ∼Hinf, is safe from the radiative corrections from the standard model particles. The scenario can have a consistent thermal history, but the present equation of state of the Universe is predicted to slightly differ from the one for the ΛCDM model. In a time-varying CC model, CC can be relaxed from (103 GeV)4, and in a model with a light scalar field scanning the CC during inflation, CC can be relaxed from (10 MeV)4.