Erratum: Cosmological Bardeen-Cooper-Schrieffer condensate as dark energy [Phys. Rev. D81, 043511 (2010)]

Abstract

We argue that the occurrence of late-time acceleration can conveniently be described by firstorder general relativity covariantly coupled to fermions. Dark energy arises as a Bardeen-CooperSchrieffer condensate of fermions which forms in the early universe. At late times, the gap and chemical potential evolve to have an equation of state with effective negative pressure, thus naturally leading to acceleration.

Four-fermion interaction from torsion as dark energy

“…That scenario does not relate the cosmic acceleration to the quark-gluon/hadron phase transition in the early Universe, as in [1], but introduces an auxiliary field (gap) ∆ ∼ψψ and derives a gap equation by integrating out the fermionic degrees of freedom. A nonzero solution ∆ to this equation signals a condensate that drives cosmic acceleration at late times [23,24]. Although that mean-field-approximation approach does not predict the scale at which the condensation occurs, it shows that fermions coupled to torsion condense.…”

“…Such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe, where 0|ψψ|0 ∼ λ 3 QCD [22]. The resulting torsion-induced cosmological constant, 0|Λ|0 , is positive and its energy scale is only about 8 times larger than the observed value [1].Alexander et al have proposed that dark energy is generated by a Bardeen-Cooper-Schrieffer condensation of fermions coupled to torsion, which forms in the early Universe [23,24]. They have considered the scalar part of the four-fermion interaction, (ψψ) 2 (originating from decomposing this interaction with the Fierz identity), and computed the conditions for such a condensation due to a covariant attractive channel.…”

“…Alexander et al have proposed that dark energy is generated by a Bardeen-Cooper-Schrieffer condensation of fermions coupled to torsion, which forms in the early Universe [23,24]. They have considered the scalar part of the four-fermion interaction, (ψψ) 2 (originating from decomposing this interaction with the Fierz identity), and computed the conditions for such a condensation due to a covariant attractive channel.…”

Cosmological constant from quarks and torsion

“…It is possible that the huge value of a cosmological constant from the zero-point energy of vacuum may be cancelled out by an effective cosmological term arising from spinning fluids in the Riemann-Cartan spacetime [5] or reduced through some dynamical processes [6]. It is also possible that the observed osmological constant is simply another fundamental constant of Nature [7].A model of a cosmological constant caused by the vacuum expectation value in quantum chromodynamics (QCD) through QCD trace anomaly from gluonic and quark condensates gives ρ Λ ∼ Hλ The cosmic acceleration could also arise from a Bardeen-Cooper-Schrieffer condensate of fermions in the presence of torsion, which forms in the early Universe [13], or from dark spinors [14].In this paper, we present a simple and natural way to derive the small, positive cosmological constant from fermionic condensates and the Einstein-Cartan-Sciama-Kibble theory of gravity with torsion. Such a constant arises from a vacuum expectation value of the Dirac-Heisenberg-Ivanenko-Hehl-Datta fourfermion interaction term in the Lagrangian for quark (and lepton) fields.…”

On dark energy and accelerated reference frames

“…A cosmological BCS mechanism is used to derive the effective equations of motion which leads to an acceleration [20]. Another approach, in the same context, is given in [21], where an effective lagrangian density is used to derive an effective cosmological constant.…”