Hamiltonian analysis of mimetic scalar gravity revisited
Hamiltonian analysis of mimetic scalar gravity revisited
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DOI：
10.1103/physrevd.99.064009
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发表时间：
2018-12
影响因子：
5
通讯作者：
A. Ganz;P. Karmakar;S. Matarrese;D. Sorokin
中科院分区：
文献类型：
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作者：
A. Ganz;P. Karmakar;S. Matarrese;D. Sorokin
我们对几个模拟重力模型进行了哈密顿分析，并将我们的结果与不同作者之前获得的结果进行了比较。我们验证了对于健康的拟态标量张量理论，哈密顿量的相应部分从下方有界的条件是拟态场能量密度 $\lambda$ 的正值。我们表明，对于具有平移对称性的拟态暗物质，只要对其初始值施加适当的边界条件，拟态能量密度在时间上保持正值，而在不具有平移对称性的模型中，只需将 $\lambda\ 替换为 e^{\lambda}$ 即可保持正能量密度。同样的结果也适用于模拟 $f(R)$ 重力，如果假设标准 $f(R)$ 重力的通常稳定性条件并且 $\lambda>0$，那么这是健康的。相反，如果我们将拟态物质添加到不健康的种子行为中，所得到的拟态引力理论总体上仍然不稳定。作为一个例子，我们考虑具有高阶导数项 $(\Box \varphi)^2$ 的标量张量理论，其中包含 Ostrogradski 幽灵。我们还重新审视了普通标量物质存在下模拟暗物质 FLRW 背景周围线性扰动稳定性问题的结果。我们发现常规物质的存在不会恢复动态幻影模式（至少在紫外线极限内）。这些模式的哈密顿量不是正定的，是非传播的（声速为零）并且与拟态物质本身相关。在不存在普通标量流体的情况下，它们已经存在，导致灰尘超密度增长。
We perform the Hamiltonian analysis of several mimetic gravity models and compare our results with those obtained previously by different authors. We verify that for healthy mimetic scalar-tensor theories the condition for the corresponding part of the Hamiltonian to be bounded from below is the positive value of the mimetic field energy density $\lambda$. We show that for mimetic dark matter possessing a shift symmetry the mimetic energy density remains positive in time, provided appropriate boundary conditions are imposed on its initial value, while in models without shift symmetry the positive energy density can be maintained by simply replacing $\lambda\to e^{\lambda}$. The same result also applies to mimetic $f(R)$ gravity, which is healthy if the usual stability conditions of the standard $f(R)$ gravity are assumed and $\lambda>0$. In contrast, if we add mimetic matter to an unhealthy seed action, the resulting mimetic gravity theory remains, in general, unstable. As an example, we consider a scalar-tensor theory with the higher-derivative term $(\Box \varphi)^2$, which contains an Ostrogradski ghost. We also revisit results regarding stability issues of linear perturbations around the FLRW background of the mimetic dark matter in the presence of ordinary scalar matter. We find that the presence of conventional matter does not revive dynamical ghost modes (at least in the UV limit). The modes, whose Hamiltonian is not positive definite, are non-propagating (have zero sound speed) and are associated with the mimetic matter itself. They are already present in the case in which the ordinary scalar fluid is absent, causing a growth of dust overdensity.