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 left( 3+1right) -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(phi _*) = 0.00336.
Highlights
A very important question is how to construct a nonperturbative and covariant string formalism on a curved background which can be explained from a globally hyperbolic non-commutative quantum spacetime
An important fact in such description is that quantum spinor fields are considered on an extended manifold on which the variation of the metric tensor is nonzero, and the norma associated to vector and tensor fields is not conserved
Such thatα is a quantum spinor field and b is a parameter to be determined by the gauge we choose to describe its dynamics
Summary
A very important question is how to construct a nonperturbative and covariant string formalism on a curved background which can be explained from a globally hyperbolic non-commutative quantum spacetime. An important fact in such description is that quantum spinor fields are considered on an extended manifold on which the variation of the metric tensor is nonzero, and the norma associated to vector and tensor fields is not conserved. This is a key to can describe these fields in a background dynamical spacetime which can be expanding [20,21] or collapsing.
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