声速与标量谱指数：在非正则理论中重构暴胀与再加热
Speed of sound and scalar spectral index: Reconstructing inflation and reheating in a non-canonical theory
AI总结：
本研究在含非线性动能项的非正则理论框架下，结合慢滚近似与标量谱指数、声速的参数化，重构暴胀的有效势与耦合函数，分析再加热时期特征，并利用天文观测数据约束模型参数空间。
摘要：
本文在非正则理论框架下分析了暴胀的重构问题。就此而言，我们研究了在假设非线性动能项为$K(X,\phi)=X+g(\phi)X^2$的情况下重构背景变量的可行性，其中$X$是与标量场$\phi$相关的标准动能项，$g(\phi)$是任意耦合函数。为了在暴胀背景下实现这一重构，我们采用慢滚近似，同时将标量谱指数$n_s$和声速$c_s$参数化为$e-$折叠数$N$的函数。通过假设最简单的参数化形式$n_s-1=-2/N$和$c_s\propto N^{-\beta}$（其中$\beta$为常数），我们得到了用标量场表示的有效势$V(\phi)$和耦合函数$g(\phi)$的重构结果。此外，我们通过考虑常数状态方程参数研究了再加热时期，确定了用重构变量和观测参数表示的再加热时期温度与$e-$折叠数。通过这种方式，我们利用来自Planck和BICEP/Keck结果的当前天文数据，在暴胀和再加热时期对与重构暴胀模型相关的参数空间进行了约束。
英文摘要：
In this article we analyze the reconstruction of inflation in the framework of a non-canonical theory. In this sense, we study the viability of reconstructing the background variables assuming a non-lineal kinetic term given by $K(X,ϕ)=X+g(ϕ)X^2$, with $X$ the standard kinetic term associated to the scalar field $ϕ$ and $g(ϕ)$ an arbitrary coupling function. In order to achieve this reconstruction in the context of inflation, we assume the slow-roll approximation together with the parametrization of the scalar spectral index $n_s$ and the speed of sound $c_s$ as a function of the number of $e-$folds $N$. By assuming the simplest parametrizations for $n_s-1=-2/N$ and $c_s\propto N^{-β}$ with $β$ a constant, we find the reconstruction of the effective potential $V(ϕ)$ and the coupling function $g(ϕ)$ in terms of the scalar field. Besides, we study the reheating epoch by considering a constant equation of state parameter, where we determine the temperature and number of $e-$folds during the reheating epoch in terms of the reconstructed variables and the observational parameters. In this way, the parameter-space related to the reconstructed inflationary model are constrained during the epochs of inflation and reheating by assuming the current astronomical data from Planck and BICEP/Keck results.
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