We obtain a scaling relation for spherically symmetric k-essence scalar fields $\varphi (r,t)$ for an inhomogeneous cosmology with the Lemaitre–Tolman–Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $\varphi (r,t)={\varphi }_1\left(r\right)+{\varphi }_2\left(t\right)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhomogeneous universe exhibits accelerated expansion i.e.cosmic acceleration driven by negative pressure.

我们获得了球对称k本质标量场的比例关系 $\varphi （\mathrm{[R}，Ť）$Lemaitre-Tolman-Bondi（LTB）度量的不均匀宇宙学。我们显示，在度量函数的某些标识下，当LTB度量降低为Friedmann-Lemaitre-Robertson-Walker（FLRW）度量时，这种比例关系会降低为均匀宇宙学的已知关系。建立一个k本质的拉格朗日方程，并假设以下条件解Euler-Lagrangian方程$\varphi （\mathrm{[R}，Ť）={\varphi }_{\mathrm{1个}}（\mathrm{[R}）+{\varphi }_{\mathrm{2个}}（Ť）$。该解决方案使LBT度量功能与字段相关。LTB不均匀宇宙表现出加速膨胀，即负压驱动的宇宙加速。