也未 (哪怕在平均意义上) 考虑量子场对经典时空的影响。
黑洞的蒸发难道不算是考虑了量子场对经典时空的反作用吗？尽管严格这样的方程解是困难的。此外，当我们在考虑宇宙的演化的时候，把物质场的密度作为影响宇宙演化的源是否也可以看作是量子场的反作用呢。因为在这里，那些物质场是各种光子场 电子场 中微子场。。。。

黑洞蒸发的计算是在固定背景时空，而不是引力与（平均意义上的）量子场耦合体系中进行计算的。至于宇宙演化，不知你指的是哪一种理论，普通宇宙学中的宇宙演化连弯曲时空量子场论也不是，实质上只是满足一定物态条件的经典物质与引力的相互作用。

hawking radiation is performed on the fixed background, but if we consider its backreaction to background such that we know black hole is shrinking with a certain velocity, the semiclassical einstein is employed naively.

我们计算得到的比如说光子的密度\rho~T^4, 我觉得这是把电磁场量子化的观点的所得到的结果。

:: if we consider its backreaction to background such that we know
:: black hole is shrinking with a certain velocity, the semiclassical
:: einstein is employed naively.

The definition of QFT in curved spacetime - which is what I was talking about in my preface - only says what kind of calculations belong to that research area. It does NOT mean that's the only type of calculation one can do. You can certainly extend the calculation along whatever direction you want - even into the full quantum gravity if you can. To make the logic plain: you can define what a chair is, the fact you can construct a table has nothing to do with whether your definition of chair is valid or not.

:: 我觉得这是把电磁场量子化的观点的所得到的结果。

That has nothing specific to do with QFT in curved spacetime.