The non-minimal coupling constant and the primordial de Sitter state

Abstract

Dynamical systems methods are used to investigate dynamics of a flat Friedmann-Robertson-Walker cosmological model with the non-minimally coupled scalar field and a potential function. Performed analysis distinguishes the value of non-minimal coupling constant parameter $\xi =\frac{3}{16}$, which is the conformal coupling in five dimensional theory of gravity. It is shown that for a monomial potential functions at infinite values of the scalar field there exist generic de Sitter and Einstein-de Sitter states. The de Sitter state is unstable with respect to expansion of the Universe for potential functions which do not change faster than linearly. This leads to a generic cosmological evolution without the initial singularity.

arXiv comment22 pages; 6 multiple figures; (v2) published version

References in corpus (53)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Dynamics of dark energy
• Cosmology and the Fate of Dilatation Symmetry
• The Standard Model Higgs boson as the inflaton
• General relativity as an effective field theory: The leading quantum corrections
• Generalized G-inflation: Inflation with the most general second-order field equations
• Planck 2013 results. XXII. Constraints on inflation
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Scaling solutions in general non-minimal coupling theories
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Cosmological scaling solutions of non-minimally coupled scalar fields
• Running Inflation in the Standard Model
• Inflation scenario via the Standard Model Higgs boson and LHC
• Standard Model Higgs boson mass from inflation
• Quintessence, the Gravitational Constant, and Gravity
• The Best Inflationary Models After Planck
• Scalar-Tensor Gravity and Quintessence
• Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field
• Cosmology With Negative Potentials
• Scalar-Tensor Models of Normal and Phantom Dark Energy
• A Cosmological Theory without Singularities
• Question of quantum equivalence between Jordan frame and Einstein frame
• Non-minimal coupling of the scalar field and inflation
• Non-minimally coupled canonical, phantom and quintom models of holographic dark energy
• Self-similar cosmological solutions with a non-minimally coupled scalar field
• Fast-Roll Inflation
• Quantum scale of inflation and particle physics of the early universe
• Cosmological dynamics of Scalar--Tensor Gravity
• The Standard Model Higgs Boson-Inflaton and Dark Matter
• Extended Slow-Roll Conditions and Rapid-Roll Conditions
• Braneworld models with a non-minimally coupled phantom bulk field: a simple way to obtain the -1-crossing at late times
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• Bounds on the Nonminimal Coupling of the Higgs Boson to Gravity
• Effective equations of motion and initial conditions for inflation in quantum cosmology
• Extended Quintessence with non-minimally coupled phantom scalar field
• Non-Minimal Inflation after WMAP3
• Bouncing Universes in Scalar-Tensor Gravity Models admitting Negative Potentials
• Non-minimally coupled scalar field cosmology on the phase plane
• Rapid roll Inflation with Conformal Coupling
• Coupling constant constraints in a nonminimally coupled phantom cosmology
• On the unitarity of linearized General Relativity coupled to matter
• Fitting Non-Minimally Coupled Scalar Models to Gold SnIa Dataset
• Unitarity bounds on low scale quantum gravity
• Non-minimally coupled complex scalar field in classical and quantum cosmology
• What $\xi$? Cosmological constraints on the non-minimal coupling constant
• What is modified gravity and how to differentiate it from particle dark matter?
• Cosmological dynamics with non-minimally coupled scalar field and a constant potential function
• Uniting cosmological epochs through the twister solution in cosmology with non-minimal coupling
• Twister quintessence scenario
• Bifurcations in Ratra-Peebles quintessence models and their extensions
• From inflation to dark energy in scalar-tensor cosmology
• Towards generic cosmological evolution without singularity and fundamental symmetry of space-time

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