Abstract
We use pseudodifferential calculus and heat kernel techniques to prove a conjecture by Chamseddine and Connes on rationality of the coefficients of the polynomials in the cosmic scale factor a(t) and its higher derivatives, which describe the general terms a 2n in the expansion of the spectral action for general Robertson-Walker metrics. We also compute the terms up to a 12 in the expansion of the spectral action by our method. As a byproduct, we verify that our computations agree with the terms up to a 10 that were previously computed by Chamseddine and Connes by a different method.
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Fathizadeh, F., Ghorbanpour, A. & Khalkhali, M. Rationality of spectral action for Robertson-Walker metrics. J. High Energ. Phys. 2014, 64 (2014). https://doi.org/10.1007/JHEP12(2014)064
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DOI: https://doi.org/10.1007/JHEP12(2014)064