Dynamical analysis of the covarying coupling constants in scalar-tensor gravity

Abstract

A scalar-tensor theory of gravity is considered wherein the gravitational coupling $G$ and the speed of light $c$ are admitted as space-time functions and combine to form the definition of the scalar field $\varphi$. The varying $c$ participates in the definition of the variation of the matter part of the action; it is related to the effective stress-energy tensor which is a result of the requirement of symmetry under general coordinate transformations. The effect of the cosmological coupling $\Lambda$ is accommodated within a possible behaviour of $\varphi$. We analyze the dynamics of $\varphi$ in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential $V(\varphi )$ and no particular assumption on the Hubble function. The phase space analysis is performed both with the linear stability theory and via the more general Lyapunov's method. Either method lead to the conclusion that the condition $\dot{G}/G=\sigma \left(\dot{c}/c\right)$ where $\sigma =3$ must hold for the rest of cosmic evolution after the system gets to the globally asymptotically stable fixed point and the dynamics of $\varphi$ ceases. This result provides a physical foundation for the phenomenological model admitting $\left(G/G_0\right)={\left(c/c_0\right)}^3$ used recently to interpret cosmological and astrophysical data. The thus co-varying couplings $G$ and $c$ impact the cosmic evolution after the dynamical system settles to equilibrium. This impact is investigated by constructing the generalized continuity equation in our scalar-tensor model and considering two possible regimes for the varying speed of light -- decreasing $c(a)$ and increasing $c(a)$ -- while solving our modified Friedmann equations. The solutions to the latter equations make room for radiation- and matter-dominated eras that progress to a dark-energy-type of accelerated expansion.

15 pages, 4 figures. v2: 19 pages, 6 figures; stability analysis expanded and generalized; discussion improved. v3: 27 pages, 6 figures; appendix added; abstract edited due to arXiv's policy; content matches the published version

References in corpus (16)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Early modified gravity in light of the $H_0$ tension and LSS data
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Phase Space Analysis of the Accelerating Multi-fluid Universe
• How fundamental are fundamental constants?
• Effects of Spatial Curvature on the $f(R)$ Gravity Phase Space: no Inflationary Attractor?
• Cosmological constraints on the gravitational constant
• Cosmology with relativistically varying physical constants
• Effect of evolutionary physical constants on type-1a supernova luminosity
• Higher-order extension of Starobinsky inflation: initial conditions, slow-roll regime, and reheating phase
• The Classical and Loop Quantum Cosmology Phase Space of Interacting Dark Energy and Superfluid Dark Matter
• Varying Coupling Constants and Their Interdependence
• Quasi Static Evolution of Compact Objects in Modified Gravity
• LyST: a Scalar-Tensor Theory of Gravity on Lyra Manifold
• On Generalized Theories of Varying Fine Structure Constant
• Stealth metastable state of scalar-tensor thermodynamics

Cited by in corpus (9)

• Review on the minimally extended varying speed of light model
• Shadows of black holes at cosmological distances in the co-varying physical couplings framework
• Constraining Coupling Constants' Variation with Supernovae, Quasars, and GRBs
• Testing CCC+TL Cosmology with Galaxy Rotation Curves
• Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric
• Constraining Co-Varying Coupling Constants from Globular Cluster Age
• Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn
• Brans-Dicke-like field for co-varying $G$ and $c$: observational constraints
• Perturbation Theory in the Minimally Extended Varying Speed of Light (meVSL) Model