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 TMF, 2010, Volume 163, Number 3, Pages 430–448 (Mi tmf6512)

Weyl–Eddington–Einstein affine gravity in the context of modern cosmology

A. T. Filippov

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

Abstract: We propose new models of the “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 proposed method for obtaining the geometry using 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, other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard Einstein theory with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) meson, 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 Lagrangian determines further details of the theory, for example, the nature of the fields that can describe massive particles, tachyons, or even “phantoms”. In “natural" geometric theories, dark energy must also arise. The basic parameters of the theory (cosmological constant, mass, possible dimensionless constants) are theoretically indeterminate, but in the framework of modern "multiverse” ideas, this is more a virtue than a defect. We consider further extensions of the affine models and in more detail discuss approximate effective (“physical”) Lagrangians that can be applied to the cosmology of the early Universe.

Keywords: gravitation, cosmology, affine connection, dark energy, inflation

DOI: https://doi.org/10.4213/tmf6512

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English version:
Theoretical and Mathematical Physics, 2010, 163:3, 753–767

Bibliographic databases:

Citation: A. T. Filippov, “Weyl–Eddington–Einstein affine gravity in the context of modern cosmology”, TMF, 163:3 (2010), 430–448; Theoret. and Math. Phys., 163:3 (2010), 753–767

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf6512
• https://doi.org/10.4213/tmf6512
• http://mi.mathnet.ru/eng/tmf/v163/i3/p430

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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. Proc. Steklov Inst. Math., 272 (2011), 107–118
2. Davydov E.A., “Vector fields in cosmology”, 8th International Conference on Progress in Theoretical Physics (ICPTP 2011), AIP Conf. Proc., 1444, eds. Mebarki N., Mimouni J., Belaloui N., Moussa K., Amer. Inst. Physics, 2012, 125–132
3. 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
4. Davydov E., Filippov A.T., “Dilaton-Scalar Models in the Context of Generalized Affine Gravity Theories: their Properties and Integrability”, Gravit. Cosmol., 19:4 (2013), 209–218
5. E. A. Davydov, “Polynomial integrals of motion in dilaton gravity theories”, Theoret. and Math. Phys., 183:1 (2015), 567–577
6. A. T. Filippov, “Solving dynamical equations in general homogeneous isotropic cosmologies with a scalaron”, Theoret. and Math. Phys., 188:1 (2016), 1069–1098
7. 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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