Metric-affine gravity and inflation

We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity...

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Bibliographic Details
Published in:Physical review. D Vol. 99; no. 10; p. 104020
Main Authors: Shimada, Keigo, Aoki, Katsuki, Maeda, Kei-ichi
Format: Journal Article
Language:English
Published: College Park American Physical Society 15.05.2019
Subjects:
Distortion
Einstein equations
Gravitation
Independent variables
Tensors
ISSN:2470-0010, 2470-0029
Online Access:Get full text
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Summary:We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metric-affine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.
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ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.99.104020