Metric-affine gravity and inflation

2018/12/21 by Keigo Shimada, Katsuki Aoki, Kei-ichi Maeda · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Affine transformation #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #General relativity #Linearized gravity #Mathematical physics #Mathematics #Metric (unit) #Physics #Pure mathematics #Theoretical physics #astro-ph.CO #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.99.104020

published as Phys. Rev. D 99, 104020 (2019) · 18 pages, 6 figures, comments welcome. v2: references added

arxiv created 2018/12/21 · openalex publication_date 2019/05/13 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

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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Cited by

• General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach
• Minimal Higgs inflation with an R2 term in Palatini gravity