Cosmology with a spin

Abstract

Using the chiral representation for spinors we present a particularly transparent way to generate the most general spinor dynamics in a theory where gravity is ruled by the Einstein-Cartan-Holst action. In such theories torsion need not vanish, but it can be re-interpreted as a 4-fermion self-interaction within a torsion-free theory. The self-interaction may or may not break parity invariance, and may contribute positively or negatively to the energy density, depending on the couplings considered. We then examine cosmological models ruled by a spinorial field within this theory. We find that while there are cases for which no significant cosmological novelties emerge, the self-interaction can also turn a mass potential into an upside-down Mexican hat potential. Then, as a general rule, the model leads to cosmologies with a bounce, for which there is a maximal energy density, and where the cosmic singularity has been removed. These solutions are stable, and range from the very simple to the very complex.Comment: Version published in Physical Review

f(T) teleparallel gravity and cosmology

“…The avoidance of the Big Bang singularity by using torsion arisen from a cosmic spinor field can be found in [420][421][422][423]. Moreover, it has been known for many years that the coupling between the torsion tensor and the cosmic spinor field can lead to interesting gravitational repulsion and thus avoid curvature singularities by violating the energy condition [424][425][426][427][428][429][430]. In this subsection, we are interested in searching for a non-singular bouncing solution in the early universe within the frame of f (T ) gravity.…”

Fermion condensate from torsion in the reheating era after inflation

“…Shifting the momentum operators to the right using 5) where the derivative ∂ µ = (∂ 0 , −∇) acts only on the next object to its right, we obtain the following quadratic and quartic terms…”

Emergent cosmos in Einstein–Cartan theory

“…For these cosmologies at the bounce point, we have H = 0, meaning that the attracting effect of usual prefect fluid is balanced by the repulsion effect of the spin/torsion fluid, leading to a bouncing solution for H . In this context, the time derivative of the Hubble parameter satisfies the conditionḢ > 0 at the bouncing point, so that the universe possesses the ability for transition from a contracting phase to an expanding one [173][174][175][176][177][178]. In such a scenario [175,176], as the universe contracts the total density ρ tot increases like 1/t 2 , as usual, but then torsion kicks in and the maximal density is reached.…”

“…In this context, the time derivative of the Hubble parameter satisfies the conditionḢ > 0 at the bouncing point, so that the universe possesses the ability for transition from a contracting phase to an expanding one [173][174][175][176][177][178]. In such a scenario [175,176], as the universe contracts the total density ρ tot increases like 1/t 2 , as usual, but then torsion kicks in and the maximal density is reached. Then, as the universe continues to contract further, the density decreases, due to the negative contribution of spin fluid, until it reaches zero and a bounce occurs at the corresponding non-zero scale factor a 0 .…”

“…(18) at early time if the spin fluid dominates to the usual perfect fluid. This issue is resolved in the context of the non-singular cosmological models such as bouncing [173][174][175][176][177][178] or emergent cosmologies [179]. For these cosmologies at the bounce point, we have H = 0, meaning that the attracting effect of usual prefect fluid is balanced by the repulsion effect of the spin/torsion fluid, leading to a bouncing solution for H .…”