Nonsmooth mechanics for cosmology: Biaxial Bianchi IX

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Title: Nonsmooth mechanics for cosmology: Biaxial Bianchi IX

Author: Ding Jia

Abstract: This paper investigates cosmological singularity resolution by applying nonsmooth mechanics to the Biaxial Bianchi IX (BB9) minisuperspace model. We demonstrate how unilateral (inequality) constraints on cosmological scale factors yield novel bouncing solutions, overcoming the traditional Big Bang breakdown. These solutions feature a “singular bounce” where one biaxial scale factor momentarily vanishes with zero velocity, while the other scale factor is fixed by the cosmological constant at a positive constant. These classical real-valued bouncing solutions form dominant saddle points in the Lorentzian gravitational path integral, offering a physically preferred alternative to complex saddles and suggesting that initial boundary conditions need not be fixed at small scale factors. Our analysis provides new insights into the dynamics of the early anisotropic universe and offers a concrete mechanism for evolving cosmological solutions beyond singularities.

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• Original versions: Article v1.0