Minimal $k$-inflation in light of the conformal metric-affine geometry

Abstract

We motivate a minimal realization of slow-roll $k$-inflation by incorporating the local conformal symmetry and the broken global $\mathrm{SO}(1,1)$ symmetry in the metric-affine geometry. With use of the metric-affine geometry where both the metric and the affine connection are treated as independent variables, the local conformal symmetry can be preserved in each term of the Lagrangian and thus higher derivatives of scalar fields can be easily added in a conformally invariant way. Predictions of this minimal slow-roll $k$-inflation, $n_{\mathrm{s}}\sim 0.96$, $r\sim 0.005$, and $c_{\mathrm{s}}\sim 0.03$, are not only consistent with current observational data but also have a prospect to be tested by forthcoming observations.

8 pages, 1 figure, v2:published version, references added, v3:reference added

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Cited by in corpus (23)

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• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
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• Cosmology of Quadratic Metric-Affine Gravity
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• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
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• Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology
• General Einstein-Cartan quadratic gravity with derivative couplings
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• Cosmic inflation from broken conformal symmetry
• Isocurvature modes and non-Gaussianity in affine inflation
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• Friedmann cosmology with hyperfluids
• Subcritical hybrid inflation in a generalized superconformal model
• Metric-Affine Version of Myrzakulov $F(R,T,Q,\mathcal{T})$ Gravity and Cosmological Applications
• Reconstructing square-law k-inflation from Planck data
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity