标题： 芬斯勒-兰德斯宇宙学：动力学分析与物质扰动的增长 显示英文标题

标题： Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations

摘要： 我们首次研究了芬斯勒-兰德斯（FR）宇宙学模型的动态性质及其线性物质扰动的增长指数，假设宇宙流体包含物质、辐射和一个标量场。首先，对于各种FR场景，我们实施了临界点分析，并找到了提供宇宙加速的解，在某些情况下我们可以有de-Sitter点作为稳定晚期吸引子。然后我们推导了各种芬斯勒-兰德斯宇宙学中物质涨落的增长指数。考虑冷暗物质并忽略扰动分析中的标量场分量，我们发现增长指数的渐近值为$\gamma_{\infty}^{(FR)}\approx\frac {9}{16}$，这与协调的$\Lambda$宇宙学，$\gamma^{(\Lambda)} \approx\frac{6}{11}$相近。在此背景下，我们表明当前的FR模型提供了与Dvali、Gabadadze和Porrati（DGP）引力模型相同的哈勃膨胀率。然而，由于FR模型的增长指数比DPG引力的$\gamma^{(DGP)} \approx \frac{11}{16}$低$\sim18.2\%$，这两种模型可以在扰动水平上区分开来。如果允许物质流体中有压力，则得到$\gamma_{\infty}^{(FR)}\approx\frac{9(1+w_{m})(1+2w_{m})}{2[8+3w_{m}% (5+3w_{m})]}$，其中$w_{m}$是物质的状态方程参数。最后，通过使用标量场扩展了增长指数分析，我们发现FR宇宙学中增长指数的演化受标量场的存在影响。 显示英文摘要

摘要： We study for the first time the dynamical properties and the growth index of linear matter perturbations of the Finsler-Randers (FR) cosmological model, for which we consider that the cosmic fluid contains matter, radiation and a scalar field. Initially, for various FR scenarios we implement a critical point analysis and we find solutions which provide cosmic acceleration and under certain circumstances we can have de-Sitter points as stable late-time attractors. Then we derive the growth index of matter fluctuations in various Finsler-Randers cosmologies. Considering cold dark matter and neglecting the scalar field component from the perturbation analysis we find that the asymptotic value of the growth index is $\gamma_{\infty}^{(FR)}\approx\frac {9}{16}$, which is close to that of the concordance $\Lambda$ cosmology, $\gamma^{(\Lambda)} \approx\frac{6}{11}$. In this context, we show that the current FR model provides the same Hubble expansion with that of Dvali, Gabadadze and Porrati (DGP) gravity model. However, the two models can be distinguished at the perturbation level since the growth index of FR model is $\sim18.2\%$ lower than that of the DPG gravity $\gamma^{(DGP)} \approx \frac{11}{16}$. If we allow pressure in the matter fluid then we obtain $\gamma_{\infty}^{(FR)}\approx\frac{9(1+w_{m})(1+2w_{m})}{2[8+3w_{m}% (5+3w_{m})]}$, where $w_{m}$ is the matter equation of state parameter. Finally, we extend the growth index analysis by using the scalar field and we find that the evolution of the growth index in FR cosmologies is affected by the presence of scalar field.