Metric-affine Gravity and Inflation

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.

18 pages, 6 figures, comments welcome. v2: references added

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• Cosmology in $f(Q)$ geometry
• A New Class of Ghost and Tachyon Free Metric Affine Gravities
• Reheating in $R^2$ Palatini inflationary models
• Cosmological Hyperfluids, Torsion and Non-metricity
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
• Dynamically induced Planck scale and inflation in the Palatini formulation
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• Palatini-Higgs inflation with non-minimal derivative coupling
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• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Primordial backgrounds of relic gravitons
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• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• Dimensional Transmutation in Gravity and Cosmology
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• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
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• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Constant-roll in the Palatini-$R^2$ models
• Initial conditions for plateau inflation: a case study
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• The Full Quadratic Metric-Affine Gravity (Including Parity Odd Terms): Exact solutions for the Affine-Connection
• Post-inflationary phases stiffer than radiation and Palatini formulation
• Polarization Modes of Gravitational Waves in Palatini Horndeski theory
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• Cosmic Acceleration with Torsion and Non-metricity in Friedmann-like Universes
• A metric-affine version of the Horndeski theory
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• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity
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