Preinflationary spacetime dynamics: A topological phase transition driven by a nonlinear and noncommutative quantum geometry

We study a topological phase transition in spacetime through which the early universe evolved, growing exponentially due to quantum fluctuations of gravity, described as a geometric quantum field with a noncommutative, nonlinear, and nonlocal algebra. The fluctuations are considered in the boundary terms of the Einstein-Hilbert action and alter the Einstein´s equations through a variable cosmological parameter. By non-perturbatively incorporating quantum gravity effects into the metric tensor, it is possible to recover these effects in the relativistic dynamics of the inflaton field, which is a massive scalar field whose mass is altered by quantum gravitational effects, altering its power spectrum. The quantization of the quantum fields arises from an expression that connects the geometric fields, the physical fields, and the relativistic frame. Fil: Bellini, Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina