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I understand that the $\Lambda$CDM cosmological model is mainly built over general relativity, however many of it's features invoke quantum field theory (such as inflation). I find this confusing because they are distinct theoretical frameworks with, apparently, no clear connections.

Is there a deeper way to look at this conundrum rather than saying that we just don't know enough yet?

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    $\begingroup$ Since you mention inflation, you might be interested to know that there is a torsion-based version of it that's even more purely relativistic than the one based on a scalar field of hypothetical "inflaton" particles: It's Nikodem J. Poplawski's model, described in numerous papers written by him between 2010 & 2020, that are available free on the Arxiv site. You may also want to look into Rovelli's "relational" version of quantum mechanics, described by Vidotto in one chapter of the 2017 book titled "The Philosophy of Cosmology". $\endgroup$ – Edouard Sep 16 '20 at 15:40
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    $\begingroup$ You can build QFT in curved backgrounds. In the context of cosmology this is useful during inflation where the background in approximately de Sitter, and dark energy epoch (exactly de Sitter, if we model dark energy as the cosmological constant). $\endgroup$ – Kosm Sep 16 '20 at 18:11
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It is helpful to distinguish between the $\Lambda$CDM model itself and the underlying physical mechanisms that may drive the values of its parameters (such as the cosmological constant $\Lambda$) at different epochs in the universe's history. Even though some of the underlying physical mechanisms may depend on quantum theory (and may not be completely understood), the $\Lambda$CDM model itself is purely relativistic and does not use quantum theory.

To use an analogy from classical mechanics, we know that the macroscopic behaviour of two surfaces in contact is affected by the coefficient of friction between them. So we represent this by a parameter $\mu$ in our equations of motion. The equations of motion are purely classical, even though the underlying mechanism that determines the value of $\mu$ depends on the microscopic nature of the surfaces and the forces between them, and so depends ultimately on quantum mechanics.

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