The theory of cosmic inflation has received a great amount of deserved attention in recent years due to it’s stunning predictions about the early universe. Alongside the usual cold inflation paradigm, warm inflation has garnered a huge amount of interest in modern inflationary studies. It’s peculiar features and specifically different predictions from cold inflation have led to a substantial amount of literature about it. Various modified cosmological scenarios have also been studied in the warm inflationary regime. In this work, we introduce the exact solution approach for warm inflation. This approach allows one to directly study warm inflationary regime in a variety of modified cosmological scenarios. We begin by outlining our method and show that it generalizes the modified Friedmann approach of Del Campo, and reduces to the well known Hamilton–Jacobi formalism for inflation in particular limits. We also find the perturbation spectra for cosmological and tensor perturbations in the early universe, and then apply our method to study warm inflation in a Tsallis entropy modified Friedmann universe. We end our paper with some concluding remarks on the domain of applicability of our work.

中文翻译：

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暖通胀的精确解决方法

近年来，宇宙膨胀理论因其对早期宇宙的惊人预测而受到了广泛的关注。除了通常的冷通胀范式之外，暖通胀在现代通胀研究中也引起了极大的兴趣。它的奇特特征以及与冷膨胀的特别不同的预测导致了大量关于它的文献。在温暖的暴胀状态下，各种修改后的宇宙学情景也得到了研究。在这项工作中，我们介绍了热通胀的精确求解方法。这种方法允许人们直接研究各种修改后的宇宙学情景中的暖通货膨胀制度。我们首先概述我们的方法，并表明它概括了 Del Campo 的修正弗里德曼方法，并在特定限制下简化为众所周知的暴胀的汉密尔顿-雅可比形式主义。我们还找到了早期宇宙中宇宙学和张量扰动的扰动谱，然后应用我们的方法来研究 Tsallis 熵修正弗里德曼宇宙中的热膨胀。我们以关于我们工作的适用性领域的一些总结性评论结束我们的论文。