动态宇宙公式

1. 动态宇宙学常数公式


\Lambda_{\text{dynamic}}(r,t) = \Lambda_0 \cdot \frac{\mathcal{T}{\text{global}}(t)}{\sqrt{\left(\frac{\Omega\Lambda}{9/13}-1\right)^2 + \left(\frac{\Omega_m}{3/13}-1\right)^2 + \left(\frac{\Omega_b}{1/13}-1\right)^2} + \epsilon}



2. 哈勃常数计算式


H_0(z) = H_{0,\text{ss}} \cdot \frac{1}{\sqrt{\left(\frac{\Omega_\Lambda(z)}{9/13}-1\right)^2 + \left(\frac{\Omega_m(z)}{3/13}-1\right)^2 + \left(\frac{\Omega_b(z)}{1/13}-1\right)^2}}


3. 中子星最大质量阈值公式


M_{\text{max, NS}} = 2.5,M_\odot \cdot \left[1 + \exp\left(-\frac{\left|\frac{\Omega_m}{\Omega_\Lambda} - \frac{1}{3}\right|}{\delta}\right)\right]



4. 黑洞最小形成质量公式


M_{\text{min, BH}} = 5.0,M_\odot \cdot \left[1 - \exp\left(-\frac{\left|\frac{\Omega_m}{\Omega_\Lambda} - \frac{1}{3}\right|}{\delta}\right)\right]



5. 暗能量状态方程演化公式



w(t) = -1 + \Delta w \cdot \frac{\Omega_\Lambda(t) - \Omega_{\Lambda,\text{ss}}}{\Omega_{\Lambda,\text{ss}}}



6. 等效引力统一公式


\frac{G_{\text{eff}}(r,z)}{G_N} = \frac{\mathcal{T}{\text{local}}(r,z)}{\mathcal{T}{\text{global}}} \cdot \frac{l_{\text{min}}}{\lambda} \propto \sqrt{\left(\frac{\Omega_m}{3/13}\right)^2 + \left(\frac{\Omega_\Lambda}{9/13}\right)^2}



7. 比例偏离能量输出公式


P_{\text{out}} = P_{\text{in}} + \eta \cdot \mathcal{T}{\text{global}} \cdot \left(1 - \frac{\sqrt{\left(\frac{\Omega\Lambda}{9/13}-1\right)^2 + \left(\frac{\Omega_m}{3/13}-1\right)^2}}{\sqrt{3}}\right) \cdot V