# 状态方程 (宇宙学)

## 方程

${\displaystyle p=\rho _{m}RT=\rho _{m}C^{2}\,}$

${\displaystyle w={\frac {p}{\rho }}={\frac {\rho _{m}C^{2}}{\rho _{m}c^{2}}}={\frac {C^{2}}{c^{2}}}\approx 0}$

### 弗里德曼-勒梅特-罗伯逊-沃尔克度规和状态方程

${\displaystyle \rho \propto a^{-3(1+w)}.}$

${\displaystyle a\propto t^{\frac {2}{3(1+w)}},}$

${\displaystyle 3{\frac {\ddot {a}}{a}}=\Lambda -4\pi G(\rho +3p)}$

${\displaystyle \rho ^{\prime }\equiv \rho +{\frac {\Lambda }{8\pi G}}}$
${\displaystyle p^{\prime }\equiv p-{\frac {\Lambda }{8\pi G}}}$

${\displaystyle p^{\prime }=w^{\prime }\rho ^{\prime }}$

${\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4}{3}}\pi G\left(\rho ^{\prime }+3p^{\prime }\right)=-{\frac {4}{3}}\pi G(1+3w^{\prime })\rho ^{\prime }}$

### 标量模型

${\displaystyle {w={\frac {{\frac {1}{2}}{\dot {\phi }}^{2}-V(\phi )}{{\frac {1}{2}}{\dot {\phi }}^{2}+V(\phi )}},}}$

## 参考资料

1. ^ A. Vikman,Can dark energy evolve to the phantom?,Phys. Rev. D 71, 023515 (2005), http://inspirehep.net/record/653821
2. ^ Hogan, Jenny. "Welcome to the Dark Side." Nature 448.7151 (2007): 240-245. http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=25801949&site=ehost-live