Abstract:
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.
Original article submitted 22/III/2011 revision submitted – 27/III/2011
Citation:
I. Ya. Aref'eva, I. V. Volovich, “On nonlocal cosmological equations on half-line”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 16–27
\Bibitem{AreVol11}
\by I.~Ya.~Aref'eva, I.~V.~Volovich
\paper On nonlocal cosmological equations on half-line
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 16--27
\mathnet{http://mi.mathnet.ru/vsgtu938}
\crossref{https://doi.org/10.14498/vsgtu938}
\elib{https://elibrary.ru/item.asp?id=16387154}
Linking options:
https://www.mathnet.ru/eng/vsgtu938
https://www.mathnet.ru/eng/vsgtu/v122/p16
This publication is cited in the following 5 articles:
Kh. A. Khachatryan, A. Kh. Khachatryan, A. Zh. Narimanyan, “Numerical Solutions of some Nonlinear Integral Equations Arising in the Theory of pp-Adic Strings and Physical Kinetics”, P-Adic Num Ultrametr Anal Appl, 16:1 (2024), 43
Kh. A. Khachatryan, H. S. Petrosyan, “Constructive study of the solvability of one class of nonlinear integral equations with a symmetric kernel”, Siberian Adv. Math., 34:4 (2024), 320–336
Khachatryan Kh.A., Andriyan S.M., “on Solvability of One Class of Nonlinear Integral Equations on Whole Line With Two Monotone Nonlinearities”, P-Adic Numbers Ultrametric Anal. Appl., 12:4 (2020), 259–275
Z. M. Gandaloeva, O. A. Krichevskaya, S. I. Glukhova, T. V. Dubinina, A. M. Lila, “Pregnancy in ankylosing spondylitis: the view of a female patient and a physician”, Sovremennaâ revmatologiâ, 13:1 (2019), 71
Kh. A. Khachatryan, “Positive solubility of some classes of non-linear integral equations
of Hammerstein type on the semi-axis and on the whole line”, Izv. Math., 79:2 (2015), 411–430
Citation in format AMSBIB
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