Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism

Abstract

In the framework of classical scale invariance, we consider quadratic gravity in the Palatini formalism and investigate the inflationary predictions of the theory. Our model corresponds to a two-field scalar-tensor theory, that involves the Higgs field and an extra scalar field stemming from a gauge $U(1{)}_X$ extension of the Standard Model, which contains an extra gauge boson and three right-handed neutrinos. Both scalar fields couple nonminimally to gravity and induce the Planck scale dynamically, once they develop vacuum expectation values. By means of the Gildener-Weinberg approach, we describe the inflationary dynamics in terms of a single scalar degree of freedom along the flat direction of the tree-level potential. The one-loop effective potential in the Einstein frame exhibits plateaus on both sides of the minimum and thus the model can accommodate both small and large field inflation. The inflationary predictions of the model are found to comply with the latest bounds set by the Planck collaboration for a wide range of parameters and the effect of the quadratic in curvature terms is to reduce the value of the tensor-to-scalar ratio.

matches version to be published in PRD

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• Constraining Palatini-Horndeski theory with gravitational waves after GW170817
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Gravitational Coleman-Weinberg Mechanism
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• Inflationary Dynamics of Mutated Hilltop Inflation in Einstein-Gauss-Bonnet Gravity Under New Slow-Roll Approximations with Generalised Reheating
• Inflation and dark matter after spontaneous Planck scale generation by hidden chiral symmetry breaking
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• Inflationary Dynamics in Einstein-Gauss-Bonnet Gravity Using New Slow-Roll Approximations considering Generalised Reheating
• $\tilde{\xi }$-attractors in metric-affine gravity
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• Isocurvature modes and non-Gaussianity in affine inflation
• Observational Constraints on Extended Starobinsky and Weyl Gravity Model of Inflation
• Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
• Natural inflation in Palatini $F(R,X)$
• Ephemeral Oscillons in Scalar-Tensor Theories: The Higgs-like case
• Dynamically induced spin-2 mass in a Weyl-invariant framework
• On the KG-constrained general disformal transformation of the Einstein-Hilbert action
• On Conformal Transformation with Multiple Scalar Fields and Geometric Property of Field Space with Einstein-like Solutions
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