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 Tr. Mat. Inst. Steklova, 2011, Volume 272, Pages 117–128 (Mi tm3253)

Affine generalizations of gravity in the light of modern cosmology

A. T. Filippov

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

Abstract: We discuss new models of an “affine” theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein's proposal to specify the space-time geometry by the use of the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric” Lagrangian that is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field (vecton), and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation. The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice of the geometric Lagrangian determines further details of the theory, for example, the nature of the vector and scalar fields that can describe massive particles, tachyons, or even “phantoms.” In “natural” geometric theories, which are discussed here, dark energy must also arise. We mainly focus on intricate relations between geometry and dynamics while only very briefly considering approximate cosmological models inspired by the geometric approach.

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Proceedings of the Steklov Institute of Mathematics, 2011, 272, 107–118

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Citation: A. T. Filippov, “Affine generalizations of gravity in the light of modern cosmology”, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Collected papers. Dedicated to Academician Andrei Alekseevich Slavnov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 272, MAIK Nauka/Interperiodica, Moscow, 2011, 117–128; Proc. Steklov Inst. Math., 272 (2011), 107–118

Citation in format AMSBIB
\Bibitem{Fil11} \by A.~T.~Filippov \paper Affine generalizations of gravity in the light of modern cosmology \inbook Problems of modern theoretical and mathematical physics: Gauge theories and superstrings \bookinfo Collected papers. Dedicated to Academician Andrei Alekseevich Slavnov on the occasion of his 70th birthday \serial Tr. Mat. Inst. Steklova \yr 2011 \vol 272 \pages 117--128 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3253} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2838843} \zmath{https://zbmath.org/?q=an:1228.83092} \elib{https://elibrary.ru/item.asp?id=15639256} \transl \jour Proc. Steklov Inst. Math. \yr 2011 \vol 272 \pages 107--118 \crossref{https://doi.org/10.1134/S008154381101010X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000290170500010} \elib{https://elibrary.ru/item.asp?id=17001599} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955741615} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. T. Filippov, “Unified description of cosmological and static solutions in affine generalized theories of gravity: Vecton–scalaron duality and its applications”, Theoret. and Math. Phys., 177:2 (2013), 1555–1577
2. A. T. Filippov, “Solving dynamical equations in general homogeneous isotropic cosmologies with a scalaron”, Theoret. and Math. Phys., 188:1 (2016), 1069–1098
3. Filippov T., “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
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