<p>This work revisits the agegraphic dark energy (ADE) model by associating fractional entropy with the apparent horizon. This reveals the extent to which quantum-gravitational effects deform the horizon. The thermodynamic-gravity conjecture modifies the entropy expression, leading to changes in the energy density of ADE and the Friedmann equations. Based on this relationship, we have utilized modified fractional cosmology to investigate the cosmological implications of ADE and demonstrate how the exponent <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3401_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> affects the evolution of cosmic parameters. Depending on the value of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3401_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>, the equation of state (EoS) parameter <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3401_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega _{\text {DE}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ω</mi> <mtext>DE</mtext> </msub> </math></EquationSource> </InlineEquation> make transition from the quintessence range (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3401_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="135" /> </InlineMediaObject> <EquationSource Format="TEX">$-1< \omega _{\text {DE}} < -1/3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1</mn> <mo><</mo> <msub> <mi>ω</mi> <mtext>DE</mtext> </msub> <mo><</mo> <mo>-</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>) to the phantom regime <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3401_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">$(\omega _{\text {DE}} < -1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mtext>DE</mtext> </msub> <mo><</mo> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, resulting in a shift from early deceleration to late time acceleration. Furthermore, the stability, theoretical and observational analyses of both the old and the new ADE models are discussed. All ADE results are reproduced in standard cosmology when <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3401_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta = 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

Agegraphic dark energy with fractional entropy: Implications for cosmological evolution

期刊论文
发表日期：

2025年4月11日

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Muhammad Naeem,
Aysha Bibi

摘要

This work revisits the agegraphic dark energy (ADE) model by associating fractional entropy with the apparent horizon. This reveals the extent to which quantum-gravitational effects deform the horizon. The thermodynamic-gravity conjecture modifies the entropy expression, leading to changes in the energy density of ADE and the Friedmann equations. Based on this relationship, we have utilized modified fractional cosmology to investigate the cosmological implications of ADE and demonstrate how the exponent $\delta $ $δ$ affects the evolution of cosmic parameters. Depending on the value of $\delta $ $δ$ , the equation of state (EoS) parameter $\omega _{\text {DE}}$ $ω_{DE}$ make transition from the quintessence range ( $-1< \omega _{\text {DE}} < -1/3$ $- 1 < ω_{DE} < - 1 / 3$ ) to the phantom regime $(\omega _{\text {DE}} < -1)$ $(ω_{DE} < - 1)$ , resulting in a shift from early deceleration to late time acceleration. Furthermore, the stability, theoretical and observational analyses of both the old and the new ADE models are discussed. All ADE results are reproduced in standard cosmology when $\delta = 2$ $δ = 2$ .