In this work, we studied the slow-roll approximation of cosmic inflation within the context of $f(R,T)$ gravity, where $R$ is the scalar curvature, and $T$ is the trace of the energy–momentum tensor. By choosing a minimal coupling between matter and gravity, we obtained the modified slow-roll parameters, the scalar spectral index ($n_s$), the tensor spectral index ($n_{\text{T}}$), and the tensor-to-scalar ratio ($r$). We computed these quantities for a general power-law potential, Natural & Quartic Hilltop inflation, and the Starobinsky model, plotting the trajectories on the $(n_s,r)$ plane. We found that one of the parameters of Natural/Hilltop models is non-trivially modified. Besides, if the coupling is in the interval $-0.5<\alpha <5.54$, we concluded that the Starobinsky-like model predictions are in good agreement with the last Planck measurement, but with the advantage of allowing a wide range of admissible values for $r$ and $n_{\text{T}}$.

在这项工作中，我们研究了在以下情况下宇宙膨胀的慢滚动近似 $F（\mathrm{[R}，Ť）$ 重力在哪里 $\mathrm{[R}$ 是标量曲率，并且 $Ť$是能量动量张量的迹线。通过选择物质与重力之间的最小耦合，我们获得了修改后的慢滚动参数，即标量光谱指数（${ñ}_s$），张量谱指数（${ñ}_{\text{Ť}}$）以及张量与标量之比（$\mathrm{[R}$）。我们针对一般的幂律势，自然和四方山顶通货膨胀以及Starobinsky模型计算了这些数量，并在$（{ñ}_s，\mathrm{[R}）$飞机。我们发现，Natural / Hilltop模型的参数之一是非平凡的修改。此外，如果耦合在间隔内$-0。5<\alpha <5。54$，我们得出的结论是，类似Starobinsky的模型预测与上一次的普朗克测量值非常吻合，但是其优点是可以为 $\mathrm{[R}$ 和 ${ñ}_{\text{Ť}}$。