The cosmological principle in theories with torsion: the case of Einstein-Cartan-Dirac-Maxwell gravity

Abstract

We address the implementation of the cosmological principle, that is, the assumption of homogeneity and isotropy in the spatial distribution of matter in the Universe, within the context of Einstein-Cartan theory including minimal couplings of both Dirac and Maxwell fields to torsion. This theory gives rise to new physical effects in environments of high spin densities while leaving the vacuum dynamics unaffected. Our approach is to impose the cosmological principle from the onset to the geometrical degrees of freedom (metric and torsion functions), which constrains the torsion components and the corresponding correction terms in the Friedmann-like equations and in the resulting fermionic and bosonic (non-linear) dynamics. We derive the corresponding cosmological dynamics for the geometrical and matter degrees of freedom and discuss the validity of this approach.

Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories

“…This is a vital part of the effort to understand the nature of spacetime and gravity in those regimes where the standard picture provided by GR may break down, challenging our current ideas on the spacetime paradigm. This article complements our previous works: an extension of the Einstein-Cartan-Dirac theory where an electromagnetic (Maxwell) contribution minimally coupled to torsion is introduced (which breaks the U(1) gauge symmetry [27]), and its extension to analyze in detail the physics of this model with Dirac and Maxwell fields minimally coupled to the spacetime torsion [28,29].…”

Quantum Cosmology with vector torsion

“…It is an interesting avenue to explore the evolution of different matter fields allowing such form of torsion and study its effect on structure formation. Recently possible Dirac and Maxwell fields allowing forms of torsion compatible with the cosmological constant has been discussed [24]. Also we have in a previous work considered the triad field in classical regime and it was shown to derive an exponential inflation [25].…”

Entanglement production in Einstein-Cartan theory

“…Given the high symmetry of such a spacetime, the torsion tensor has to satisfy certain constraints. We follow the ansatz of [32] and assume that the only non-zero components of the torsion tensor are 1…”

“…Accordingly, from the Lagrangian (10) we obtain the Dirac equation in a FRW spacetime with torsion [32]…”

“…In this respect, we investigate entanglement for Dirac and KG field within the EC theory. Thus, assuming the cosmological principle to hold, we adopt the Friedmann-Friedmann-Robertson-Walker (FRW) spacetime, fulfilling constraints for the torsion provided by recent observations [32] and we notice the effect of the torsion appears in the dependence of the particle density from momentum. Thus, invoking a generic torsion source, reinterpreted as an external geometrical source, we describe how Dirac field are minimally coupled to torsion and how a non-minimal coupling of torsion to KG field is plausible, both introducing significant curvature effects.…”