<p>This paper explores the impact of extra spatial dimensions on scalar field dynamics and cosmic evolution within the framework of the Sáez–Ballester scalar-tensor theory. Using higher-dimensional FLRW metric, a time-dependent deceleration parameter linked to the Hubble parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$H$</EquationSource> <EquationSource Format="MATHML"><math> <mi>H</mi> </math></EquationSource> </InlineEquation> is introduced to describe the universe’s smooth transition from deceleration to acceleration. The inclusion of extra dimensions through a conformal transformation simplifies the field equations and clarifies the behavior of key cosmological quantities such as energy density, pressure, and the scalar field. The model’s stability is examined via perturbation analysis, where small fluctuations in the energy density are studied and their temporal evolution is numerically analyzed using the fourth-order Runge–Kutta method. The EoS parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\xi (z)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> approaches <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$-1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, indicating a shift toward a dark energy dominated era, while all energy conditions vanish as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$z \rightarrow -1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo stretchy="false">→</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Model parameters are further constrained using Hubble, Pantheon+SH0ES, and DESI DR2 BAO datasets through Maximum Likelihood Estimation and Markov Chain Monte Carlo techniques, confirming the stability and observational consistency of the proposed higher-dimensional model.</p>

Stability and statistical validation of the Sáez-Ballester theory in multidimensional spacetime

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发表日期：

2026年7月10日

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Navya Jain,
R. K. Mishra

摘要

This paper explores the impact of extra spatial dimensions on scalar field dynamics and cosmic evolution within the framework of the Sáez–Ballester scalar-tensor theory. Using higher-dimensional FLRW metric, a time-dependent deceleration parameter linked to the Hubble parameter $H$ $H$ is introduced to describe the universe’s smooth transition from deceleration to acceleration. The inclusion of extra dimensions through a conformal transformation simplifies the field equations and clarifies the behavior of key cosmological quantities such as energy density, pressure, and the scalar field. The model’s stability is examined via perturbation analysis, where small fluctuations in the energy density are studied and their temporal evolution is numerically analyzed using the fourth-order Runge–Kutta method. The EoS parameter $\xi (z)$ $ξ (z)$ approaches $-1$ $- 1$ , indicating a shift toward a dark energy dominated era, while all energy conditions vanish as $z \rightarrow -1$ $z \to - 1$ . Model parameters are further constrained using Hubble, Pantheon+SH0ES, and DESI DR2 BAO datasets through Maximum Likelihood Estimation and Markov Chain Monte Carlo techniques, confirming the stability and observational consistency of the proposed higher-dimensional model.