Non-minimally coupled scalar field and scaling symmetry in a cosmological background

Abstract

We study scaling symmetry in a class of non-minimally coupled scalar field in a background of Friedmann-Robertson-Walker (FRW) spacetime. We use a non-minimally coupling $R{L}^{(\phi )}$. We find the corresponding conserved charge of that symmetry and see its role in cosmology, and search for its possible breaking down and its outcomes. A suitable potential $V(\phi )={\phi }^2/2$ of scalar field is adopted which is necessary to get a scaling symmetric Lagrangian of the system including scalar field, non-minimally coupling to Ricci scalar $R{L}^{(\phi )}$ and dark matter dust. We study evolution of the scalar field in the phase space of the model and explore the stability of the obtained critical point. In this manner we derive a relation that relates the cosmological constant and gravitational constant via a unique identity which reflects the scaling symmetry breaking in the space $(a,\phi )$. And relate the cosmological constant to the vacuum expectation value of the potential energy of $\phi$. Finally we study the stability of that vacuum expectation value.

Accepted manuscript in Physica Scripta

References in corpus (19)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Power-counting and the Validity of the Classical Approximation During Inflation
• On Inflation with Non-minimal Coupling
• Black holes with non-minimal derivative coupling
• New observational constraints on $f(R)$ gravity from cosmic chronometers
• Noether symmetry in $f(R)$ cosmology
• TASI Lectures on Inflation
• Reconstructing the inflationary $f(R)$ from observations
• On the unitarity of linearized General Relativity coupled to matter
• Self-unitarization of New Higgs Inflation and compatibility with Planck and BICEP2 data
• Genuine Dilatons in Gauge Theories
• Vacuum decay constraints on the Higgs curvature coupling from inflation
• The Noether Symmetry Approach: Foundation and applications. The case of scalar-tensor Gauss-Bonnet gravity
• Interacting quintessence cosmology from Noether symmetries: comparing theoretical predictions with observational data
• Noether symmetry approach in non-minimal derivative coupling gravity
• A cosmographic outlook on dark energy and modified gravity