![]() ![]() We demonstrate, indeed, that noncommutative effects of the kind considered here, can be those responsible for the present speed up of the cosmic expansion. e., the minisuperspace variables are promoted to operators, and the WDW equation is written in terms of these variables, iii) noncommutativity in the minisuperspace is achieved through the replacement of the standard product of functions by the Moyal star product in the WDW equation, and, finally, iv) semi-classical cosmological equations are obtained by means of the WKB approximation applied to the (equivalent) modified Hamilton-Jacobi equation. Indeed, her latest book, Noncommutative Cosmology, is based on discussions and collaborations she had with Perimeter researchers during her DVRC visits. She already had ties with Perimeter, as a Distinguished Visiting Research Chair (DVRC). Our recipe to build noncommutativity into our model is based in the approach of reference, and can be summarized in the following steps: i) the Hamiltonian is derived from the Einstein-Hilbert action (plus a self-interacting scalar field action) for a Friedmann-Robertson-Walker spacetime with flat spatial sections, ii) canonical quantization recipe is applied, i. Marcolli’s eclectic research interests span mathematics, physics, and computational linguistics. We make some brief remarks on the relation of the mixmaster universe model of chaotic cosmology to the geometry of modular curves and to noncom-mutative geometry. To our purpose it will be enough to explore the asymptotic properties of the cosmological model in the phase space. and Chaotic Cosmology Matilde Marcolli MaxPlanck Institut fur¨ Mathematik, Bonn, Germany Summary. Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology. and Florida State U.) hep-th math-ph Author Identifier: M.Marcolli.1. Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Matilde Marcolli (Bonn, Max Planck Inst., Math. 320–399, Lecture Notes in Math., vol.In this paper we investigate to which extent noncommutativity, a intrinsically quantum property, may influence the Friedmann-Robertson-Walker cosmological dynamics at late times/large scales. Motives and periods in Bianchi IX gravity models 15. In: K-theory, Arithmetic and Geometry (Moscow, 1984–1986), pp. Wodzicki M.: Local invariants of spectral asymmetry. Princeton University Press, Princeton (2000) Voevodsly V., Suslin A., Friedlander E.M.: Cyles, Transfers, and Motivic Homology Theories. In: Geometric methods in the algebraic theory of quadratic forms, pp. ![]() Vishik, A.: Motives of quadrics with applications to the theory of quadratic forms. Max-Planck-Institut für Mathematik Bonn, Preprint MPI-1998-13, pp. Vishik, A.: Integral motives of quadrics. Suijlekom W.: Noncommutative Geometry and Particle Physics. (eds.) Mathematics Unlimited: 2001 and Beyond, pp. Gracia-Bondia J.M., Varilly J.C., Figueroa H.: Elements of Noncommutative Geometry. Goncharov, A.B., Spradlin, M., Vergu, C., Volovich, A.: Classical polylogarithms for amplitudes and Wilson loops. Golden J., Goncharov A.B., Spradlin M., Vergu C., Volovich A.: Motivic amplitudes and cluster coordinates. arXiv:1511.05321įathizadeh, F., Ghorbanpour, A., Khalkhali, M.: Rationality of spectral action for Robertson–Walker metrics. Noncommutative cosmology is a new and rapidly developing area of re- search, which aims at building cosmological models based on a \modi ed gravity' action functional which arises naturally in the context of noncom- mutative geometry, the spectral action functional of 4. 11, 115018 2J.W.Barrett,Lorentzian version of the noncommutative geometry of the Standard Model of particle physics,J.Math.Phys.48 (2007), no. 10, 085 (2015)įan, W., Fathizadeh, F., Marcolli M.: Modular forms in the spectral action of Bianchi IX gravitational instantons. Marcolli, Spectral action models of gravity on packed swiss cheese cosmology, Classical and Quantum Gravity, 33 (2016) no. 76, 4073–4091 (2004)įan W., Fathizadeh F., Marcolli M.: Spectral action for Bianchi type-IX cosmological models. 34(3), 203–238 (1995)Ĭonnes, A., Marcolli, M.: Renormalization and motivic Galois theory. 10, 101 (2012)Ĭhamseddine A.H., Connes A.: The spectral action principle. Marcolli, Noncommutative Geometry, Quantum Fields and Motives. 267(1), 181–225 (2006)īrown F., Schnetz O.: A K3 in \(\). 8 The Modern Cosmology Cosmology is the part of physics that has the whole. Bloch S., Esnault H., Kreimer D.: On motives associated to graph polynomials.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |