A model for the very early universe

Abstract

A model with N species of massless fermions interacting via (microscopic) gravitational torsion in de Sitter spacetime is investigated in the limit N → ∞. The U V (N ) × U A (N ) flavor symmetry is broken dynamically irrespective of the (positive) value of the induced four-fermion coupling. This model is equivalent to a theory with free but massive fermions fluctuating about the chiral condensate. When the fermions are integrated out in a way demonstrated long ago by Candelas and Raine, the associated gap equation together with the Friedmann equation predict that the Hubble parameter vanishes. Introducing a matter sector (subject to a finite gauge symmetry) as a source for subsequent cosmology, the neutral Goldstone field acquires mass by the chiral anomaly, resulting in a Planck-scale axion.

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

“…A possibility we leave for future study is to allow for a time-varying N (t) or coupling M (t). For instance, previous literature [11,12,44] have considered different choices for a physical cutoff, λ = µ or λ = H, which would correspond to having a time-varying N . 7 This may lead to interesting situations, including the possibility of not having to tune M to the very tiny meV scale.…”

“…We have introduced a physical cutoff by hand as in Minkowski nonrenormalizable theories, but in [12] it was argued that this type of BCS models in curved space may be renormalizable. In the same work, the running of the mass coupling M and a cosmological constant term was considered for a de Sitter background.…”

“…As a consistency check, we obtain gap equations similar 3 to those in [6] and reproduce the same bouncing cosmology. A mechanism of fermion condensation was argued to be relevant to dark energy also in [7,8] (see also [9,10]); for another approach describing fermions and condensates on FLRW spacetimes, see [11][12][13].…”

D-foam-induced flavor condensates and breaking of supersymmetry in free Wess-Zumino fluids

“…[18], which enters the expression for the respective condensates. When the analysis of chiral symmetry breaking is performed in curved, and in particular de Sitter space time [17], as appropriate for our D-foam framework, any potential Ultra Violet (UV) infinities may be absorbed in the cosmological constant and Planck scale of the de Sitter space-time, as demonstrated explicitly in the related analysis of refs. [16,17].…”

“…When the analysis of chiral symmetry breaking is performed in curved, and in particular de Sitter space time [17], as appropriate for our D-foam framework, any potential Ultra Violet (UV) infinities may be absorbed in the cosmological constant and Planck scale of the de Sitter space-time, as demonstrated explicitly in the related analysis of refs. [16,17]. In our context one should expect a similar behaviour, since the flavour-vacuum condensates are also induced in our D-foam model from appropriate (non-renormalizable) four-fermion interactions in the effective low-energy theory (17), which become better behaved in the UV in our (anti) de Sitter backgrounds.…”