标题： 在$f(\mathcal{G})$引力背景下粒子产生与暗组分相互作用之间的对应关系 显示英文标题

标题： Correspondence between particle creation and dark components interaction in the context of $f(\mathcal{G})$ gravity

摘要： 本文中，我们探讨了在平坦的FLRW度规下$f(\mathcal{G})$引力中的粒子产生场景。 为此，从热力学的角度出发，并考虑一个绝热宇宙，我们得到了以动态粒子数$N$表达的修正连续性方程。 另一方面，在$f(\mathcal{G})$引力中我们得到 Friedmann 方程，然后写出物质和暗能量组分的连续性方程，同时考虑它们之间的相互作用。 接下来，通过建立粒子产生场景与$f(\mathcal{G})$引力之间的对应关系，我们用$N$表达宇宙学参数。 之后，我们利用幂律宇宙学找到宇宙学解，并将其与哈勃参数数据进行比较。 最后，我们将当前模型拟合哈勃数据，并用红移参数表示最佳拟合曲线。 显示英文摘要

摘要： In this paper, we explore the particle creation scenario in the context of $f(\mathcal{G})$ gravity in flat-FLRW metric. For this purpose, from the perspective of thermodynamics and considering an adiabatic universe, we obtain the modified continuity equation in terms of the dynamic number of particles $N$. On the other hand, we obtain Friedmann's equations in $f(\mathcal{G})$ gravity and then write down the continuity equations of the components of matter and dark energy, taking into account the interaction between them. In what follows, by establishing a correspondence between the particle production scenario and $f(\mathcal{G})$ gravity, we obtain the cosmological parameters in terms of $N$. After that, we find cosmological solutions using power-law cosmology and compare them with Hubble parameter data. Finally, we fit the current model with Hubble data and plot the best fit in terms of the redshift parameter.