Global Portraits of Nonminimal Inflation: Metric and Palatini
arXiv:2401.12314 · doi:10.1103/PhysRevD.109.084073
Abstract
In this paper, we study the global phase space dynamics of single nonminimally coupled scalar field inflation models in the metric and Palatini formalisms. Working in the Jordan frame, we derive the scalar-tensor general field equations and flat FLRW cosmological equations, and present the Palatini and metric equations in a common framework. We show that inflation is characterized by a "master" trajectory from a saddle-type de Sitter fixed point to a stable node fixed point, approximated by slow roll conditions (presented for the first time in the Palatini formalism). We show that, despite different underlying equations, the fixed point structure and properties of many models are congruent in metric and Palatini, which explains their qualitative similarities and their suitability for driving inflation. On the other hand, the global phase portraits reveal how even models which predict the same values for observable perturbations differ, both to the extent of the phase space physically available to their trajectories, as well as their past asymptotic states. We also note how the slow roll conditions tend to underestimate the end of inflationary accelerated expansion experienced by the true nonlinear "master" solution. The explicit examples we consider range from the metric and Palatini induced gravity quintic potential with a Coleman-Weinberg correction factor to Starobinsky, metric and Palatini nonminimal Higgs, second order pole, and several nontrivial Palatini models.
32 pages, 4 figures; improved wordings, added references and corrected typos
References in corpus (40)
- The Standard Model Higgs boson as the inflaton
- Palatini Approach to Modified Gravity: f(R) Theories and Beyond
- The Unity of Cosmological Attractors
- Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
- Equivalence of the Einstein and Jordan frames
- Planck, LHC, and -attractors
- Higgs inflation with loop corrections in the Palatini formulation
- Invariant quantities in the scalar-tensor theories of gravitation
- Frame-dependence of higher-order inflationary observables in scalar-tensor theories
- Cosmological dynamics of Scalar--Tensor Gravity
- Coleman-Weinberg linear inflation: metric vs. Palatini formulation
- An analytic approach to non-slow-roll inflation
- Universality classes for models of inflation
- Tracing the high energy theory of gravity: an introduction to Palatini inflation
- Palatini-Higgs inflation with non-minimal derivative coupling
- Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
- Cosmological dynamics of exponential gravity
- Frame Covariant Nonminimal Multifield Inflation
- Stringy-Running-Vacuum-Model Inflation: from primordial Gravitational Waves and stiff Axion Matter to Dynamical Dark Energy
- On the dynamics of a quadratic scalar field potential
- Higgs inflation in Einstein-Cartan gravity
- Non-minimally coupled scalar field cosmology on the phase plane
- Global dynamics and inflationary center manifold and slow-roll approximants
- Global stability analysis for cosmological models with non-minimally coupled scalar fields
- Rapid roll Inflation with Conformal Coupling
- Implications of Palatini gravity for inflation and beyond
- Scalar-tensor cosmologies: fixed points of the Jordan frame scalar field
- Potential dominated scalar-tensor cosmologies in the general relativity limit: phase space view
- Post-Newtonian parameter for multiscalar-tensor gravity with a general potential
- Testing Predictions of the Quantum Landscape Multiverse 1: The Starobinsky Inflationary Potential
- On the number of -folds in the Jordan and Einstein frames
- Multiple point criticality principle and Coleman-Weinberg inflation
- Slow-Roll Inflation in the Jordan Frame
- T-Model Inflation and Bouncing Cosmology
- Formalizing Slow-roll Inflation in Scalar-Tensor Theories of Gravitation
- Cosmological constraints of Palatini gravity
- The non-minimal coupling constant and the primordial de Sitter state
- Parametrizations in scalar-tensor theories of gravity and the limit of general relativity
- Inflationary equilibrium configurations of scalar-tensor theories of gravity
- A new generic and structurally stable cosmological model without singularity