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TMF, 2013, Volume 177, Number 2, Pages 323–352 (Mi tmf8539)  

This article is cited in 3 scientific papers (total in 3 papers)

Unified description of cosmological and static solutions in affine generalized theories of gravity: Vecton–scalaron duality and its applications

A. T. Filippov

Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: We briefly describe the simplest class of affine theories of gravity in multidimensional space–times with symmetric connections and their reductions to two-dimensional dilaton–vecton gravity field theories. The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with an essentially nonlinear coupling to the dilaton gravity. We emphasize that the vecton field in dilaton–vecton gravity can be consistently replaced by a new effectively massive scalar field (scalaron) with an unusual coupling to the dilaton gravity. With this vecton–scalaron duality, we can use the methods and results of the standard dilaton gravity coupled to usual scalars in more complex dilaton–scalaron gravity theories equivalent to dilaton–vecton gravity. We present the dilaton–vecton gravity models derived by reductions of multidimensional affine theories and obtain one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully applicable to studying static and cosmological solutions in multidimensional theories and also in general one-dimensional dilaton–scalaron gravity models. We focus on general and global properties of the models, seeking integrals and analyzing the structure of the solution space. In integrable cases, it can be usefully visualized by drawing a "topological portrait" resembling the phase portraits of dynamical systems and simply exposing the global properties of static and cosmological solutions, including horizons, singularities, etc. For analytic approximations, we also propose an integral equation well suited for iterations.

Keywords: modified gravity, dilaton gravity, cosmology, integrable system

DOI: https://doi.org/10.4213/tmf8539

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English version:
Theoretical and Mathematical Physics, 2013, 177:2, 1555–1577

Bibliographic databases:

Received: 12.04.2013

Citation: A. T. Filippov, “Unified description of cosmological and static solutions in affine generalized theories of gravity: Vecton–scalaron duality and its applications”, TMF, 177:2 (2013), 323–352; Theoret. and Math. Phys., 177:2 (2013), 1555–1577

Citation in format AMSBIB
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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. E. A. Davydov, “Polynomial integrals of motion in dilaton gravity theories”, Theoret. and Math. Phys., 183:1 (2015), 567–577  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. T. Filippov, “Solving dynamical equations in general homogeneous isotropic cosmologies with a scalaron”, Theoret. and Math. Phys., 188:1 (2016), 1069–1098  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. T. Filippov, “A fresh view of cosmological models describing very early universe: general solution of the dynamical equations”, Phys. Part. Nuclei Lett., 14:2 (2017), 298–303  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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