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Take the most successful version of the Big Bang theory

I'm aware that the Big Bang theory have unanswered questions related to the very first moments of the Big Bang.

I also know that for our current Universe state, the Big Bang theory with the Inflation theory have great success with respect to many observations like the homogeneity, CMB etc.

My question is, for our current Universe state, is there any observation(s) which could not be justified by the Big Bang theory?(except matter-antimatter amount problem)

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There is a problem with the abundance of lithium-7 relative to hydrogen, which models greatly overpredict: arxiv.org/abs/0808.2818 arxiv.org/abs/1107.1117

There is also tension between the values of the Hubble constant found from distance-ladder techniques and analysis of the CMB and BAO. The former give about $72\pm 2$, in units of km/s/Mpc, while the latter give about $67.5\pm 0.5$. This may simply be a case where people always underestimate their systematic errors, or it may be a sign of new physics causing the universe to accelerate its expansion more rapidly than predicted by $\Lambda\text{CDM}$ models. Proposed solutions involve physical ingredients such as sterile neutrinos, axions, and phantom energy.

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    $\begingroup$ Even phantom energy :( $\endgroup$
    – Alchimista
    Mar 11, 2019 at 9:24
  • $\begingroup$ We know that Li gets depleted in stars. The primordial abundance is estimated by looking at the oldest stars... $\endgroup$
    – ProfRob
    May 4, 2020 at 8:03

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