Conformal inflation in the metric-affine geometry

Abstract

Systematic understanding for classes of inflationary models is investigated from the viewpoint of the local conformal symmetry and the slightly broken global symmetry in the framework of the metric-affine geometry. In the metric-affine geometry, which is a generalisation of the Riemannian one adopted in the ordinary General Relativity, the affine connection is an independent variable of the metric rather than given e.g. by the Levi-Civita connection as its function. Thanks to this independency, the metric-affine geometry can preserve the local conformal symmetry in each term of the Lagrangian contrary to the Riemannian geometry, and then the local conformal invariance can be compatible with much more kinds of global symmetries. As simple examples, we consider the two-scalar models with the broken $\mathrm{SO}(1,1)$ or $\mathrm{O}(2)$, leading to the well-known $\alpha$-attractor or natural inflation, respectively. The inflaton can be understood as their pseudo Nambu-Goldstone boson.

6 pages, v2: published version, EPL Editor's Choice, v3: references added

References in corpus (8)

• The Standard Model Higgs boson as the inflaton
• The Unity of Cosmological Attractors
• Metric-affine f(R) theories of gravity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Superconformal Symmetry, NMSSM, and Inflation
• Large Field Inflation and Double $\alpha$-Attractors
• Metric-affine Gravity and Inflation
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar

Cited by in corpus (25)

• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Primordial black holes and induced gravitational waves from double-pole inflation
• The Full Quadratic Metric-Affine Gravity (Including Parity Odd Terms): Exact solutions for the Affine-Connection
• Cosmology of Quadratic Metric-Affine Gravity
• Describing metric-affine theories anew: alternative frameworks, examples and solutions
• FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity
• Einstein-Proca theory from the Einstein-Cartan formulation
• Quadratic Metric-Affine Gravity: Solving for the Affine-Connection
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology
• General Einstein-Cartan quadratic gravity with derivative couplings
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity II: The Hypermomentum Equation
• Cosmic inflation from broken conformal symmetry
• Isocurvature modes and non-Gaussianity in affine inflation
• Friedmann cosmology with hyperfluids
• Subcritical hybrid inflation in a generalized superconformal model
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
• Lost in translation: the Abelian affine connection (in the coincident gauge)