On the possible mathematical connections between the Hartle-Hawking no boundary proposal concerning the Randall-Sundrum cosmological scenario, Hartle-Hawking wave-function in the mini-superspace sector of physical superstring theory, p-adic Hartle-Hawking wave function and some sectors of Number Theory.

摘要

In this paper we have described the Hartle-Hawking no boundary proposal concerning the Randall-Sundrum cosmological scenario, nonlocal braneworld action in the two-brane Randall-Sundrum model, Hartle-Hawking wave-function in the mini-superspace sector of physical superstring theory, p-adic models in the Hartle-Hawking proposal and p-adic and adelic wave functions of the universe. Furthermore, we have showed some possible mathematical connections between some equations of these arguments and, in conclusion, we have also described some mathematical connections between some equations of arguments above mentioned and some equations concerning the Riemann zeta function, the Ramanujan’s modular equations and the Palumbo-Nardelli model. In the section 1, we have described the Hartle-Hawking “no boundary” proposal applied to Randall-Sundrum cosmological scenario. In the section 2, we have described nonlocal braneworld action in the two-brane Randall-Sundrum model. In the section 3, we have described the compactifications of type IIB strings on a Calabi-Yau three-fold and Hartle-Hawking wave-function in the mini-superspace sector of physical superstring theory. In the section 4, we have described the p-Adic models in the Hartle-Hawking proposal. In the section 5, we have described the p-Adic and Adelic wave functions of the Universe. In the section 6, we have described some equations concerning the Riemann zeta function, specifically, the Goldston-Montgomery Theorem, the study of the behaviour of the argument of the Riemann function with the condition that s lies on the critical line s=1/2+it, where t is real, the P-N Model (Palumbo-Nardelli model) and the Ramanujan identities. In conclusion, in the section 7, we have described some possible mathematical connections between some equations of arguments above discussed and some equations concerning the Riemann zeta-function, the Ramanujan’s modular equations and the Palumbo-Nardelli model.