Nonlinear operations on distributions and application to cosmology of very early universe

In classical theory of distributions (Schwartz–Sobolov theory), nonlinear operations such as multiplication of distributions are forbidden (Schwartz impossibility theorem). Colombeau’s theory of new generalized functions provides a consistent framework to perform such operations. In this paper, using Colombeau algebra, we construct a signature changing cosmological model for beginning of the universe. Our model considers two different manifolds with a common signature changing boundary in which creation of the universe occurs as a quantum mechanical tunneling effect at this boundary. As an important result, we find a geometric interpretation of cosmological constant.