![]() ![]() The advantages of the new method are discussed, which combined with symmetries of the Bianchi type-IX metric, yield an elegant proof of the rationality result. An efficient method is devised for computing the Seeley-de Witt coefficients of a geometry by making use of Wodzicki’s noncommutative residue, and it is confirmed that the method checks out for the cosmological model studied in this article. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients a 0 ,a 2 ,a 4 of the spectral action by using heat kernel methods and parametric pseudodifferential calculus. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors w 1( t), w 2( t), w 3( t), and their higher derivates with respect to time. MAA Reviews, Mathematical Association of America ( December 4, 2015).A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace.
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