Einstein–Cartan–Dirac gravity with U(1) symmetry breaking

Abstract

Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein-Cartan-Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the U (1) gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).

Cosmological bounces, cyclic universes, and effective cosmological constant in Einstein-Cartan-Dirac-Maxwell theory

“…These imprints could be probed by cosmological GWs [25], neutrino [26], and radiation (CMB) [27] backgrounds. This may have a profound impact on scale-invariance regimes and its symmetry breaking, parity breaking [20][21][22], CP breaking and matter/antimatter asymmetries [28,29], Uð1Þ-gauge breaking [30], Higgs-like mechanisms, etc.…”

“…In a previous work [30], we considered an extension of the ECSK theory by adding a minimal coupling to fermionic (Dirac) and bosonic (Maxwell) fields in the RC geometry. The resulting Einstein-Cartan-Dirac-Maxwell (ECDM) model contains new nonlinear generalized Dirac-Hehl-Data and electromagnetic equations with nonminimal interactions between fermionic and bosonic fields.…”

“…Any new physics in extreme environments, linked to a Uð1Þ symmetry breaking phase transition induced by torsion is therefore unexplored, and as far as we know, there are no observational constraints in the literature, though we point out that ECSK leaves the vacuum dynamics unaffected, implying its consistency with Solar System experiments. In general, cosmological torsion effects are expected to dominate when Cartan's density, ρ C ∼ 10 54 g=cm 3 is approached, and therefore, the ECDM model allows us to implement a valid physical mechanism to generate cosmological phase transitions during the torsion era [30].…”

On the Mathematics of Coframe Formalism and Einstein–Cartan Theory—A Brief Review

“…We present here field equations for ECSK theory 22 . Thus, we will neither assume the possibility of a propagating torsion (and we will always keep non-identically vanishing Riemann curvature [14]) nor display a lagrangian for a totally independent torsion field; rather, we will only set the Palatini-Cartan lagrangian for gravity, as done in Reference [15], and a matter lagrangian as the source.…”

“…We will focus more on the geometrical side of these equations and we will not dwell on deepening matter interaction (couplings, symmetry breaking, etc. ), as done for instance in References [20,21,24,22,23].…”