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Abstract: In this paper we investigate to which extent noncommutativity, aintrinsically quantum property, may influence the Friedmann-Robertson-Walkercosmological dynamics at late times-large scales. To our purpose it will beenough to explore the asymptotic properties of the cosmological model in thephase space. Our recipe to build noncommutativity into our model is based inthe approach of reference Phys. Rev. Lett. {\bf 88} 2002 161301, and can besummarized in the following steps: i the Hamiltonian is derived from theEinstein-Hilbert action plus a self-interacting scalar field action for aFriedmann-Robertson-Walker spacetime with flat spatial sections, ii canonicalquantization recipe is applied, i. e., the minisuperspace variables arepromoted to operators, and the WDW equation is written in terms of thesevariables, iii noncommutativity in the minisuperspace is achieved through thereplacement of the standard product of functions by the Moyal star product inthe WDW equation, and, finally, iv semi-classical cosmological equations areobtained by means of the WKB approximation applied to the equivalent modifiedHamilton-Jacobi equation. We demonstrate, indeed, that noncommutative effectsof the kind considered here, can be those responsible for the present speed upof the cosmic expansion.



Author: Octavio Obregon, Israel Quiros

Source: https://arxiv.org/







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