Extended General Relativity: (3+1)-anyons in a preinflationary cosmological model

Abstract

We propose an extended General Relativistic formalism with boundary terms included, that describes the dynamics of quantum spinor fields, which can take intermediate values, named (3 + 1) -anyons. In the approach here worked, we use an extended manifold in which the (3 + 1) -anyon fields can be expressed as a linear combination of bosons and fermions. We calculate the flow of these fields with self-interactions included in a preinflationary model that describes the birth of the universe from a null Hubble parameter, and we obtain the value of the cosmological parameter at this moment due to the flux of (3 + 1) -anyons through the 3d-closed hypersurface. The spectral indices at the end of preinflation are in very good agreement with observations. In particular the tensor to scalar ratio obtained at the end of preinflation is very small: r(ϕ∗) = 0.00336.