arXiv 2603.293372026-03gr-qc

在包含标量场的$f(R,L_{m})$引力中进行相空间分析

Accelerating Cosmological Model with Scalar Field in $f(R,\mathcal{L}_{m})$ Gravity

Birla Institute of Technology and Science, Pilani（比拉理工学院）

Y. Kalpana Devi, Rahul Bhagat, B. Mishra

发表信息：: Annals of Physics, 493, 170597, 2026
DOI：: 10.1016/j.aop.2026.170597

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AI总结：

本文研究了包含标量场的$f(R,L_{m})$引力框架的宇宙动力学，通过引入无量纲变量并构建自主系统，分析了临界点及稳定性，揭示了物质主导和加速膨胀相，以及从减速到加速的转变。

摘要：

在本文中，我们研究了$f(R, \mathcal{L}_m)$引力框架中的宇宙动力学，特别关注标量场的贡献。考虑一个包含物质拉格朗日量线性和指数依赖的功能形式，我们通过引入适当的无量纲变量并构建相应的自主系统，进行了详细的动态系统分析。通过获得并分析临界点，由于其非超双曲性质，采用中心流形理论确定其稳定性。分析揭示了宇宙的物质主导相和加速相，以及从减速到加速膨胀的转变。我们进一步扩展模型，引入一个与标量场最小耦合的广义标量场，包含动能项和指数自相互作用势，这丰富了动态行为并导致稳定的晚期吸引子解。宇宙学参数的演变，包括减速参数和有效物态方程，表明模型在晚期时间接近de Sitter相。这些结果表明，包含标量场扩展的$f(R, \mathcal{L}_m)$引力框架提供了一种无需引入宇宙学常数的解释晚期宇宙加速的可行机制。

英文摘要：

In this work, we investigate the cosmological dynamics of $f(R,\mathcal{L}_m)$ gravity using two complementary scenarios: without a scalar field and with a minimally coupled generalized scalar field. For the case without a scalar field, we consider a functional form with linear and exponential dependence on the matter Lagrangian and perform a dynamical system analysis. The resulting autonomous system admits a matter-dominated saddle configuration and a de Sitter attractor . Due to the non-hyperbolic nature of the critical curves, Center Manifold Theory (CMT) is employed to establish the local asymptotic stability of the de Sitter solution. We then extend the framework by including a minimally coupled generalized scalar field with an exponential self-interacting potential. The extended autonomous system also contains a matter-dominated saddle point and a stable dark-energy-dominated attractor corresponding to a late-time de Sitter phase. The stability of the attractor is confirmed through CMT, and the evolution of the cosmological parameters demonstrates a smooth transition from a matter-dominated decelerating era to accelerated. Also, in the absence of the scalar field, the matter-dominated configuration associated with a vanishing nonlinear contribution remains stable, whereas the inclusion of the scalar field transforms the matter era into a saddle configuration, thereby enabling the Universe to naturally evolve toward the late-time accelerated attractor. In both scenarios, the exponential power term equal to $-1$ corresponds to a late-time de Sitter phase. These results show that both scenarios lead to late-time cosmic acceleration, while the inclusion of the scalar field provides an additional dynamical mechanism for realizing a stable dark-energy-dominated Universe without invoking a cosmological constant.

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