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Gravity Induced Chiral Condensate Formation and the Cosmological Constant

Stephon H. S. Alexander·Deepak Vaid
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Abstract

It is well known that the covariant coupling of fermionic matter to gravity induces a four-fermion interaction. The presence of this term in a homogenous and isotropic space-time results in a BCS-like Hamiltonian and the formation of a chiral condensate with a mass gap. We calculate the gap ($Δ$) via a mean-field approximation for minimally coupled fermionic fields in a FRW background and find that it depends on the scale factor. The calculation also yields a correction to the bare cosmological constant ($Λ_0$), and a non-zero vev for $<ψ^\dagψ>$ which then behaves as a scalar field. Hence we conjecture that the presence of fermionic matter in gravity provides a natural mechanism for relaxation of the $Λ_0$ and explains the existence of a scalar field from (almost) first principles.

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Stephon H. S. Alexander, Deepak Vaid. 2006-09-10. Gravity Induced Chiral Condensate Formation and the Cosmological Constant. https://arxiv.org/abs/hep-th/0609066

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