We explore cosmological perturbations in a modified Gauss–Bonnet f(G) gravity, using a 1 + 3 covariant formalism. In such a formalism, we define gradient variables to get perturbed linear evolution equations. We transform these linear evolution equations into ordinary differential equations using a spherical harmonic decomposition method. The obtained ordinary differential equations are time-dependent and then transformed into redshift-dependent. After these transformations, we analyze energy-density perturbations for two fluid systems, namely, for a Gauss–Bonnet field-dust system and for a Gauss–Bonnet field-radiation system for three different pedagogical f(G) models: trigonometric, exponential and logarithmic. For the Gauss–Bonnet field-dust system, energy-density perturbations decay with increase in redshift for all the three models. For the Gauss–Bonnet field-radiation system, the energy-density perturbations decay with increase in redshift for all of the three f(G) models for long wavelength modes whereas for short wavelength modes, the energy-density perturbations decay with increasing redshift for the logarithmic and exponential f(G) models and oscillate with decreasing amplitude for the trigonometric f(G) model.

中文翻译：

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f(G) 引力中的宇宙学扰动

我们探索修改后的 Gauss-Bonnet 中的宇宙学扰动F(G)重力，使用1 + 3协变形式主义。在这样的形式中，我们定义梯度变量来得到扰动的线性演化方程。我们使用球谐分解方法将这些线性演化方程转换为常微分方程。得到的常微分方程是时间相关的，然后转化为红移相关的。在这些转换之后，我们分析了两个流体系统的能量密度扰动，即高斯-博内场尘埃系统和高斯-博内场辐射系统，用于三种不同的教学F(G)模型：三角函数、指数函数和对数函数。对于 Gauss-Bonnet 场尘系统，所有三个模型的能量密度扰动都随着红移的增加而衰减。对于 Gauss-Bonnet 场辐射系统，能量密度扰动随着红移的增加而衰减，对于所有这三个F(G)长波长模式的模型，而对于短波长模式，能量密度扰动随着对数和指数的红移增加而衰减F(G)模型并随着三角函数的幅度减小而振荡F(G)模型。