Geodesic
On nonlocal cosmological equations on half-line
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 16-27

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A system of nonlocal cosmological equations where the time variable runs over a half-line is considered. These equations are more suitable for description of the Universe than the previously discussed cosmological equations on the whole line since the Friedmann metric contains a singularity at the beginning of time. Definition of the exponential operator includes a new arbitrary function which is absent in the equations on the whole line. It is shown that this function could be choosen in such a way that one of the slow roll parameters in the chaotic inflation scenario can be made arbitrary small. Solutions of the linearized nonlocal equations on the half-line are constructed.
Keywords: equations with an infinite number of derivatives, cosmological models, heat conduction equation. 
@article{VSGTU_2011_1_a2,
     author = {I. Ya. Aref'eva and I. V. Volovich},
     title = {On nonlocal cosmological equations on half-line},
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     pages = {16--27},
     publisher = {mathdoc},
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     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a2/}
}
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I. Ya. Aref'eva; I. V. Volovich. On nonlocal cosmological equations on half-line. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 16-27. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a2/