In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3-tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommutative torus moduli, and how the resulting dynamics differs from the classical one, for example, in the appearance of exotic smooth structures. We discuss properties of the spectral action, focussing on how the slow-roll inflation potential determined by the spectral action affects the mixmaster dynamics. We relate the model to other recent results on spectral action computation and we identify other physical contexts in which this model may be relevant.

We study the renormalization group flow for the Higgs self coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.Ella está en el horizonte. Me acerco dos pasos, ella se aleja dos pasos. Camino diez pasos y el horizonte se corre diez pasos más allá. Por mucho que yo camine, nunca la alcanzaré. ¿Para que sirve la utopía? Para eso sirve: para caminar.(Eduardo Galeano) arXiv:1208.5023v1 [hep-th]