<p>We study the Bianchi I model to explore the evolution of the universe with cosmic fluid, dynamical <i>G</i> and cosmological constant <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3587_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Lambda$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>. By making a closed system of equations, we utilize the statistical Markov Chain Monte Carlo (MCMC) method to examine the compatibility of the model with observations. We apply the late-time cosmic observations to obtain the present-day expansion rate <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3587_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="224" /> </InlineMediaObject> <EquationSource Format="TEX">$H_0=68.9\pm 1.9 \ Km/sec/Mpc$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>68.9</mn> <mo>±</mo> <mn>1.9</mn> <mspace width="4pt" /> <mi>K</mi> <mi>m</mi> <mo stretchy="false">/</mo> <mi>s</mi> <mi>e</mi> <mi>c</mi> <mo stretchy="false">/</mo> <mi>M</mi> <mi>p</mi> <mi>c</mi> </mrow> </math></EquationSource> </InlineEquation>. We further analyze the evolution of the directional scale factor with the cosmographic parameters. The anisotropy vanishes in the asymptotic limits. Using the median values of the model parameters from the MCMC analysis, the behavior of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3587_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega _{s_0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Ω</mi> <msub> <mi>s</mi> <mn>0</mn> </msub> </msub> </math></EquationSource> </InlineEquation> suggests that it is approximately of order <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3587_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$10^{-4}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> and thus compatible with the late-time observations. The model does not possess any finite-time future singularity.</p>

Anisotropic model with variable $\Lambda$ and G: observational aspects and singularity analysis

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发表日期：

2025年3月24日

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S. Kotambkar,
Prerna Parkhi,
Ashutosh Singh

摘要

We study the Bianchi I model to explore the evolution of the universe with cosmic fluid, dynamical G and cosmological constant $\Lambda$ $Λ$ . By making a closed system of equations, we utilize the statistical Markov Chain Monte Carlo (MCMC) method to examine the compatibility of the model with observations. We apply the late-time cosmic observations to obtain the present-day expansion rate $H_0=68.9\pm 1.9 \ Km/sec/Mpc$ $H_{0} = 68.9 \pm 1.9 K m / s e c / M p c$ . We further analyze the evolution of the directional scale factor with the cosmographic parameters. The anisotropy vanishes in the asymptotic limits. Using the median values of the model parameters from the MCMC analysis, the behavior of $\Omega _{s_0}$ $Ω_{s_{0}}$ suggests that it is approximately of order $10^{-4}$ $10^{- 4}$ and thus compatible with the late-time observations. The model does not possess any finite-time future singularity.

Anisotropic model with variable \(\Lambda\) and G: observational aspects and singularity analysis

摘要