用$ω\approx-1$研究宇宙加速膨胀的k-本质经典哈密顿方法
k-essence classical Hamiltonian approach for an accelerated expansion of the Universe with $ω\approx-1$
摘要：
我们得到了具有Friedmann-Lemaitre-Robertson-Walker（FLRW）度规的标量曲率$k$的$k$ -本质标量场$ϕ(r,t)$的拉格朗日量.得到的拉格朗日量有两个广义坐标$ϕ$和标度因子对数（$q=\ln a$）。利用两个相应的共轭动量$p_{q}$和$p_ϕ$得到了经典哈密顿量$({\mathcal H})$.求解Hamilton运动方程，得到了标度因子$a(t)$、能量密度$ρ$、状态方程参数$ω$和减速参数$q_{0}$的经典解。在$t\rightarrow\infty$的晚期，标度因子随时间呈指数增长，能量密度$ρ$变为常数，可以认为是暗能量密度，状态方程参数变为$ω\approx -1$，减速参数变为$ q_{0}\approx -1$。所有这些结果都表明，在被称为暗能量的负压驱动下，宇宙加速膨胀。
英文摘要：
We obtain lagrangian for $k$-essence scalar field $ϕ(r,t)$ with scalar curvature $k$ of Friedmann-Lemaitre-Robertson-Walker (FLRW) metric . Obtained lagrangian has two generalised co-ordinates $ϕ$ and logarithm of scale factor ($q=\ln a$). Classical Hamiltonian $({\mathcal H})$ is obtained in terms of two corresponding conjugate momentum $p_{q}$ and $p_ϕ$. Solving Hamilton's equation of motion , we obtain classical solution for scale factor $a(t)$, energy density $ρ$, equation of state parameter $ω$ and deceleration parameter $q_{0}$ . At late time as $t\rightarrow\infty$, we have an exponential growth of scale factor with time, energy density $ρ$ becomes constant, which we can identify as dark energy density, equation of state parameter becomes $ω\approx -1$ and deceleration parameter becomes $ q_{0}\approx -1$. All this results indicates an accelerated expansion of universe driven by negative pressure known as dark energy.
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