宇宙学常数的简单（SISYPHUS）动力学模型
Simple (SISYPHUS) dynamical model of the cosmological constant
摘要：
在这项工作中，我们建议（在正式类比林德混沌暴胀的情况下）简单的动力学模型的暗能量或宇宙学常数。具体地说，我们提出了一种依赖于宇宙标度因子和标量场的拉格朗日量（总能量密度为常数和正的宇宙学常数）。然后，宇宙尺度因子的Euler-Lagrange方程等价于具有宇宙学常数的平坦真空的第二Friedman方程（在这个意义上，我们的模型与最近的天文观测完全一致）。标量场的Euler-Lagrange方程中还包括附加的“摩擦”项和未知势能能量密度的负一阶偏导数（该方程在某种程度上类似于Linde混沌暴胀方案中为宇宙膨胀而修改的Klein-Gordon方程）。最后，（常数）标量场总能量密度的总时间导数必须为零。它包含了第三动力学方程，该方程等价于通常的Euler-Lagrange方程，该方程具有未知势能能量密度的正偏导数（该方程在形式上与静态宇宙中的相应方程完全等价）。后两个方程允许标量场和能量密度的简单精确确定，而宇宙学常数代表“自由参数”。势能量密度表示标量场的平方函数，具有唯一的最大值（动态非稳定点）。任何初始标量场在时间上趋向于（共指数地）相同的最终标量场，即势能能量密度最大值的幅角。它承认一种可能性，即当一切重新开始时，最终的动态非稳定的标量场值自发地出现在任何其他标量场值中（如西西弗斯巨石运动）。
英文摘要：
In this work we suggest (in a formal analogy with Linde chaotic inflation scenario) simple dynamical model of the dark energy or cosmological constant. Concretely, we suggest a Lagrangian dependent of Universe scale factor and scalar field (with constant and positive total energy density as cosmological constant). Then, Euler-Lagrange equation for Universe scale factor is equivalent to the second Friedman equation for the flat empty space with cosmological constant (in this sense our model is full agreement with recent astronomical observations). Also there is Euler-Lagrange equation for scalar field that includes additional "friction" term and negative first partial derivative of unknown potential energy density (this equation is, in some way, similar to Klein-Gordon equation modified for cosmic expansion in Linde chaotic inflation scenario). Finally, total time derivative of the (constant) scalar field total energy density must be zero. It implies third dynamical equation which is equivalent to usual Euler-Lagrange equation with positive partial derivative of unknown potential energy density (this equation is formally exactly equivalent to corresponding equation in static Universe). Last two equations admit simple exact determination of scalar field and potential energy density, while cosmological constant stands a "free parameter". Potential energy density represents a square function of scalar field with unique maximum (dynamically non-stable point). Any initial scalar field tends (co-exponentially) during time toward the same final scalar field, argument of the maximum of the potential energy density. It admits a possibility that final dynamically non-stable scalar field value turns out spontaneously in any other scalar field value when all begins again (like Sisyphus boulder motion).
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