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

MAKE IMPACT

R. R. Cuzinatto , Rajendra P. Gupta , P. J. Pompeia · YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2204.00119

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 $ϕ$. 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 $Λ$ is accommodated within a possible behaviour of $ϕ$. We analyze the dynamics of $ϕ$ in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential $V(ϕ)$ 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 $\dot{G}/G=σ\left(\dot{c}/c\right)$ where $σ=3$ must hold for the rest of cosmic evolution after the system gets to the globally asymptotically stable fixed point and the dynamics of $ϕ$ 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.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2204.00119

PDF

https://arxiv.org/pdf/2204.00119

OA Status

green

Related Works

10

OpenAlex ID

https://openalex.org/W4224903440

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W4224903440

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.48550/arxiv.2204.00119

Digital Object Identifier

Title

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

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2022

Year of publication

Publication date

2022-03-31

Full publication date if available

Authors

R. R. Cuzinatto, Rajendra P. Gupta, P. J. Pompeia

List of authors in order

Landing page

https://arxiv.org/abs/2204.00119

Publisher landing page

PDF URL

https://arxiv.org/pdf/2204.00119

Direct link to full text PDF

Open access

Yes

Whether a free full text is available

OA status

green

Open access status per OpenAlex

OA URL

https://arxiv.org/pdf/2204.00119

Direct OA link when available

Concepts

Physics, Scalar (mathematics), Phase space, Scalar field, Attractor, Gravitation, Mathematical physics, Tensor (intrinsic definition), Dark energy, Hubble's law, Classical mechanics, Theoretical physics, Cosmology, Quantum mechanics, Mathematical analysis, Mathematics, Geometry

Top concepts (fields/topics) attached by OpenAlex

Cited by

0

Total citation count in OpenAlex

Related works (count)

10

Other works algorithmically related by OpenAlex

Full payload