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The LCDM is the standard model of cosmology and is well validated by experiments. If we go back to the Big Bang, the energy density diverges. Therefore, my question is "How far back can experiments confirm the LCDM model and what is the experiment which can look furthest back into the past?"

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I think the right word should be observations rather than experiments. You cannot make experiments on the universe. $\Lambda CDM$ model can work pretty well in some cases but it has also some problems. I mean you can explain the BBN with $\Lambda CDM$ model but there's Lithium problem. One of the fundamental parameter in the cosmological model $H_0$ gives different results for different measurements.

There's also $\sigma_8$ discrepancy. However it also explains lots of things. It really depends on your perspective of "success"

what is the experiment which can look furthest back into the past?

If we forget about inflation, I would say the BBN and the abundance of the light elements.

camarman
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