AI 中文总结
本研究推导了彩虹引力下空间平坦McVittie时空的弗里德曼动力学与表观视界热力学，构建自洽非吸积理想流体体系，结合宇宙学观测约束低能彩虹形变，验证了晚时小彩虹修正的观测可行性。
AI 中文摘要
我们推导了彩虹引力下空间平坦McVittie时空的弗里德曼动力学与表观视界热力学，构建了具有有效彩虹哈勃率的自洽非吸积理想流体体系。爱因斯坦方程、陷获视界、表面引力、Misner-Sharp能量、统一第一定律与克劳修斯关系构成了一个封闭热力学系统，可重现弗里德曼动力学。随后我们引入低能彩虹形变，利用32个宇宙钟测量数据、1580条Pantheon+光变曲线及完整协方差矩阵对其进行约束。结合普朗克卫星的物质密度先验，拟合得到$H_0=68.75\pm2.63~\mathrm{km\,s^{-1}\,Mpc^{-1}}$、$Ω_m=0.3157\pm0.0070$和$ε=0.0106^{+0.0234}_{-0.0231}$。所得约束证实了晚时小彩虹修正的观测可行性，且广义相对论极限处于优选参数区间内。
英文摘要
We derive the Friedmann dynamics and apparent-horizon thermodynamics of a spatially flat McVittie spacetime in Gravity's Rainbow and construct a consistent non-accreting perfect-fluid sector with an effective rainbow Hubble rate. The Einstein equations, trapping horizon, surface gravity, Misner--Sharp energy, unified first law, and Clausius relation form a closed thermodynamic system reproducing the Friedmann dynamics. We then introduce a low-energy rainbow deformation and constrain it using 32 cosmic-chronometer measurements and 1580 Pantheon+ light curves with the full covariance matrix. Combined with the Planck matter-density prior, the fit gives $H_0=68.75\pm2.63~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $Ω_m=0.3157\pm0.0070$, and $ε=0.0106^{+0.0234}_{-0.0231}$. The resulting constraints establish the observational viability of small late-time rainbow corrections and place the general-relativistic limit within the preferred parameter region.
Comments23 pages, 10 figures
