<p>This paper is dedicated to examining the dynamical stability behavior of the Einstein universe using the theoretical context of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ f(Q) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> gravity. We consider linear, homogeneous, and isotropic perturbations applied to both the scale factor and matter variables. The field equations are formulated using a closed FLRW metric and parameterized via a linear equation of state. To analyze the dynamics of perturbations, we adopt the Starobinsky-type model <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ f(Q) = Q + \alpha Q^2 $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>α</mi> <msup> <mi>Q</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, and derive the corresponding static and perturbed field equations. The stability conditions are examined by studying the behavior of perturbations around the static solution, and the resulting stability regions are graphically presented in the relevant parameter space. Our analysis shows that, in contrast to general relativity, stable Einstein static universe solutions can exist under isotropic perturbations for appropriate choices of model parameters in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ f(Q) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> gravity.</p>

Stability of the closed Einstein universe in symmetric teleparallel f(Q) gravity

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发表日期：

2026年4月3日

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Sana Saleem,
M. Z. Bhatti

摘要

This paper is dedicated to examining the dynamical stability behavior of the Einstein universe using the theoretical context of $ f(Q) $ $f (Q)$ gravity. We consider linear, homogeneous, and isotropic perturbations applied to both the scale factor and matter variables. The field equations are formulated using a closed FLRW metric and parameterized via a linear equation of state. To analyze the dynamics of perturbations, we adopt the Starobinsky-type model $ f(Q) = Q + \alpha Q^2 $ $f (Q) = Q + α Q^{2}$ , and derive the corresponding static and perturbed field equations. The stability conditions are examined by studying the behavior of perturbations around the static solution, and the resulting stability regions are graphically presented in the relevant parameter space. Our analysis shows that, in contrast to general relativity, stable Einstein static universe solutions can exist under isotropic perturbations for appropriate choices of model parameters in $ f(Q) $ $f (Q)$ gravity.