Qualitative behaviour of higher-curvature gravity with boundary terms i.e the f(Q) gravity models by dynamical system analysis

Pooja Vishwakarma; Parth Shah

doi:10.1140/epjc/s10052-024-12523-0

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 159
https://doi.org/10.1140/epjc/s10052-024-12523-0

Regular Article - Theoretical Physics

Qualitative behaviour of higher-curvature gravity with boundary terms i.e the f(Q) gravity models by dynamical system analysis

Pooja Vishwakarma and Parth Shah^b

Department of Mathematics, School of Advanced Sciences, VIT-AP University, 522237, Amaravati, India

^b parthshah2908@gmail.com

Received: 9 January 2024
Accepted: 4 February 2024
Published online: 15 February 2024

Abstract

The higher-curvature gravity with boundary terms i.e the f(Q) theories, grounded on non-metricity as a fundamental geometric quantity, exhibit remarkable efficacy in portraying late-time universe phenomena. The aim is to delineate constraints on two prevalent models within this framework, namely the Log-square-root model and the Hyperbolic tangent-power model, by employing the framework of Big Bang Nucleosynthesis (BBN). The approach involves elucidating deviations induced by higher-curvature gravity with boundary terms in the freeze-out temperature ( $T_{f}$ $T_{f}$ ) concerning its departure from the standard $Λ$ $\Lambda$ CDM evolution. Subsequently, constraints on pertinent model parameters are established by imposing limitations on $| \frac{δ T_{f}}{T_{f}} |$ $\vert \frac{\delta T_{f}}{T_{f}}\vert$ derived from observational bounds. This investigation employs dynamical system analysis, scrutinizing both background and perturbed equations. The study systematically explores the phase space of the models, identifying equilibrium points, evaluating their stability, and comprehending the system’s trajectory around each critical point. Moreover, the application of “Center Manifold Theory” facilitates the examination of stability properties at non-hyperbolic points. The principal findings of this analysis reveal the presence of a matter-dominated saddle point characterized by the appropriate matter perturbation growth rate. Subsequently, this phase transitions into a stable phase of a dark-energy-dominated, accelerating universe, marked by consistent matter perturbations. Overall, the study substantiates observational confrontations, affirming the potential of higher-curvature gravity with boundary terms as a promising alternative to the $Λ$ $\Lambda$ CDM concordance model. The methodological approach underscores the significance of dynamical systems as an independent means to validate and comprehend the cosmological implications of these theories.

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.