In previous work we argued that the correct procedure to predict the gravitational wave signal from preheating after inflation rests on the in-in formalism. We extend here our previous analysis to include the backreaction of the produced matter on the motion of the inflaton and the expansion of the universe, and study how the latter affect the spectrum of the resulting gravitational waves. The addition of backreaction demands the appropriate renormalization of divergent expectation values, which we regularize by preserving diffeomorphism invariance in a manner that is amenable to numerical integration. The very same calculation also allows us to determine for which strength of the inflaton to matter couplings reheating is successful. We illustrate our results with the scalar version of the Starobinsky model of inflation, and observe that it is hard to reheat the universe while keeping radiative corrections under control.

中文翻译：

---

关于预热过程中预期的逆反应

在之前的工作中，我们认为预测暴胀后预热产生的引力波信号的正确程序取决于 in-in 形式主义。我们在这里扩展我们之前的分析，包括产生的物质对暴胀子运动和宇宙膨胀的反向反应，并研究后者如何影响产生的引力波的光谱。反向反应的添加要求对不同的期望值进行适当的重整化，我们通过以适合数值积分的方式保持微分同胚不变性来对其进行正则化。同样的计算也使我们能够确定暴胀子的强度与物质耦合再加热是成功的。我们用 Starobinsky 通货膨胀模型的标量版本来说明我们的结果，