New Result of Cosmological Constant From Quantum Cosmology and Inflation

The Quantum cosmology with Born-Infeld type scalar field is considered. The corresponding Wheeler-DeWitt equation can be solved analytically for both very large and small φ̇(i.e, very small or large cosmological scale factor respectively). In the extreme limits of small cosmological scale factor the wave function of the universe can also be obtained by applying the methods developed by Hartle-Hawking(H-H) and Vilenkin. H-H wave function predicts that most Probable cosmological constant Λ equals 1 η ( 1 2η is the critical kinetic energy of scalar field). The Vilenkin wave function predicts a nucleating unverse with largest possible cosmological constant, but it must be larger than 1/η. It is different from the original results of Hartle-Hawking and Vilenkin. According to the result of inflation with B-I type scalar field, we find that η depends on the amplitude of tensor perturbation δh.