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TMF, 2011, Volume 166, Number 3, Pages 452–464 (Mi tmf6622)  

This article is cited in 5 scientific papers (total in 5 papers)

Exact solutions of nonlocal nonlinear field equations in cosmology

S. Yu. Vernov

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a method for seeking exact solutions of the equation of a nonlocal scalar field in a nonflat metric. In the Friedmann–Robertson–Walker metric, the proposed method can be used in the case of an arbitrary potential except linear and quadratic potentials, and it allows obtaining solutions in quadratures depending on two arbitrary parameters. We find exact solutions for an arbitrary cubic potential, which consideration is motivated by string field theory, and also for exponential, logarithmic, and power potentials. We show that the $k$-essence field can be added to the model to obtain exact solutions satisfying all the Einstein equations.

Keywords: cosmology, nonlocal scalar field, Friedmann–Robertson–Walker metric, exact solution, elliptic function

DOI: https://doi.org/10.4213/tmf6622

Full text: PDF file (454 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 166:3, 392–402

Bibliographic databases:

Document Type: Article
Received: 18.05.2010
Revised: 04.10.2010

Citation: S. Yu. Vernov, “Exact solutions of nonlocal nonlinear field equations in cosmology”, TMF, 166:3 (2011), 452–464; Theoret. and Math. Phys., 166:3 (2011), 392–402

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vernov S.Yu., “Solutions of nonlocal cosmological equations”, XXIX Workshop on Geometric Methods in Physics, AIP Conf. Proc., 1307, eds. Kielanowski P., Buchstaber V., Odzijewicz A., Schlichenmaier M., Voronov T., Amer. Inst. Physics, Melville, NY, 2010, 185–190  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Aref'eva I.Ya., Volovich I.V., “Cosmological daemon”, Journal of High Energy Physics, 2011, no. 8, 102  crossref  zmath  isi  scopus
    3. Koshelev A.S. Vernov S.Yu., “Cosmological perturbations in SFT inspired non-local scalar field models”, Eur. Phys. J. C, 72:10 (2012), 2198  crossref  adsnasa  isi  scopus
    4. El-Nabulsi, Rami Ahmad, “Nonlinear integro-differential Einstein's field equations from nonstandard Lagrangians”, Canadian Journal of Physics, 92:10 (2014), 1149–1153  crossref  scopus
    5. Ignat'ev Yu.G., Kokh I.A., “Peculiarities of Cosmological Models Based on a Nonlinear Asymmetric Scalar Doublet With Minimal Interaction. i. Qualitative Analysis”, Gravit. Cosmol., 25:1 (2019), 24–36  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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