We reconstruct the viable f(G) gravity models from the observations and provide the analytic solutions that well describe our numerical results. In order to avoid unphysical challenges that occur during the numerical reconstruction, we generalize f(G) models into f(GA), which is the simple extension of f(G) models with the introduction of a constant A parameter. We employ several observational data together with the stability condition, which reads d2f/dG2 > 0 and must be satisfied in the late-time evolution of the universe, to give proper initial conditions for solving the perturbation equation. As a result, we obtain the analytic functions that match the numerical solutions. Furthermore, it might be interesting if one can find the physical origin of those analytic solutions and its cosmological implications.

中文翻译：

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通过观测重建可行的 f(G) 重力模型

我们从观测中重建可行的 f(G) 重力模型，并提供很好地描述我们的数值结果的解析解。为了避免数值重建过程中出现的非物理挑战，我们将 f(G) 模型推广到 f(GA)，这是 f(G) 模型的简单扩展，引入了常数 A 参数。我们使用多个观测数据和稳定性条件，即 d2f/dG2 > 0，并且必须在宇宙后期演化中得到满足，以给出求解微扰方程的适当初始条件。结果，我们获得了与数值解匹配的解析函数。此外，如果人们能够找到这些解析解的物理起源及其宇宙学意义，可能会很有趣。