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<p>We investigate the cosmological dynamics of a nonminimally coupled scalar field model focusing on Hilltop potential with quadratic and quartic forms. We perform a comprehensive phase space analysis to identify the critical points and examine their stability properties. Our analysis shows that for both Hilltop quadratic and quartic potentials, there exist stable de Sitter attractors characterized by an equation of state parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(w_{\phi }=-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>w</mi> <mi>ϕ</mi> </msub> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and positive effective Newtonian gravitational constant <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(G_{eff}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mrow> <mi mathvariant="italic">eff</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. In addition, we perform a perturbation analysis around the de-Sitter background to examine the stability of the solutions. The perturbation equations reveal that the de-Sitter solutions correspond to stable spiral attractors. These results demonstrate that Hilltop potentials within nonminimally coupled scalar field theories can naturally lead to a physically consistent late-time accelerated universe, overcoming limitations observed in earlier studies with monomial potentials.</p>

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Cosmological evolution of a nonminimally coupled scalar field with hilltop potential

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Yerlan Myrzakulov

摘要

We investigate the cosmological dynamics of a nonminimally coupled scalar field model focusing on Hilltop potential with quadratic and quartic forms. We perform a comprehensive phase space analysis to identify the critical points and examine their stability properties. Our analysis shows that for both Hilltop quadratic and quartic potentials, there exist stable de Sitter attractors characterized by an equation of state parameter \(w_{\phi }=-1\) w ϕ = - 1 and positive effective Newtonian gravitational constant \(G_{eff}\) G eff . In addition, we perform a perturbation analysis around the de-Sitter background to examine the stability of the solutions. The perturbation equations reveal that the de-Sitter solutions correspond to stable spiral attractors. These results demonstrate that Hilltop potentials within nonminimally coupled scalar field theories can naturally lead to a physically consistent late-time accelerated universe, overcoming limitations observed in earlier studies with monomial potentials.