Big Bang Cosmology and Λ-CDM Model Limitations

Now Big Bang cosmology is a very robust theory---it would be astonishing if it were just plain wrong---a lot of fundamental observations about the observable universe would have be interpreted in some other way if it were just plain wrong.

On the other hand, the Λ-CDM model may need revision to the point of becoming a different theory. However, circa 2025, it fits nearly all observations of the observable universe from the whole on average down to the large scale structure, or more precisely, the large scale structure's statistical properties. Because it fits so much is why the Λ-CDM model is also called the concordance model (though that name is now disfavored) and sometimes standard model of cosmology (SMC).

Now limitations are things a theory does NOT explain (even if is right as far as it goes) and tensions are significant discrepancies short of falsification and which can also be called paradigm anomalies.

The Big Bang cosmology has limitations, but NO tensions at present---and as aforesaid, it would be astonishing if it was just plain wrong. The Λ-CDM model has both limitations and tensions.

1. Limitations of Big Bang Cosmology and the Λ-CDM Model:

   Limitations of Big Bang cosmology and the Λ-CDM model mostly phrased as questions:

   1. Why Λ-CDM model parameters have the values they have? Those values are fitted from observations of the observable universe (see Wikipedia: Λ-CDM: Parameters). Example free parameters are, the Hubble constant = fiducial value 70 km/s/Mpc, the density parameter = Ω = rho/rho_crit = fiducial value 1, and the baryon-to-photon ratio η=6.16*10**(-10) (Planck-2018) (see also Wikipedia: Big Bang nucleosynthesis: Baryon-to-photon ratio η; An Etymological Dictionary of Astronomy: baryon-to-photon ratio η).
   2. What happened before the Big Bang? In yours truly's view, the Big Bang is the era when the fundamental particles first existed and Big Bang nucleosynthesis occurred, and NOT the big bang singularity---which no one believes in since quantum gravity must supercede general relativity at some point as we run cosmic time back to the Planck era.
   3. What the universe is like at some point well beyond the observable universe? The observed homogeneity and isotropy of the observable universe (as an axiom called the cosmological principle) shows that the universe beyond the observable universe is probably much the same as the observable universe for a long way, but NOT far, far away. We've only verified the cosmological principle (insofar as we have verified it) for the observable universe.
   4. What will be the fate of the observable universe? Except by extreme and very speculative extrapolation, the Λ-CDM model does NOT tell us. Yes, the observable universe is well described since the Big Bang ∼ 13.8 Gyr ago (see Wikipedia: Age of the universe = 13.797(23) Gyr (Planck 2018)). But extrapolating for hundreds of gigayears and further into the future of cosmic time is, indeed, highly speculative. See Wikipedia: Graphical timeline from Big Bang to Heat Death (but note that the left-hand vertical scale is tricky: it is x=100*log[log(t_year)] and so t_year=10**[10**(x/100)]) and Wikipedia: Graphical timeline of the Stelliferous Era.
   5. What dark matter is?
   6. What dark energy is? Because we do NOT understand what dark energy is we do NOT understand the acceleration of the universe or how long it will last.
   7. Because of their limitations, Big Bang cosmology and the Λ-CDM model are actually superficial---despite the fact that they explain an awful lot about the observable universe and are huge triumphs. By superficial, one means the whole universe (the sum of all reality) may be very different on average. Maybe the whole universe is the multiverse: maybe in the version of eternal inflation; maybe in some other version.
            Recall in the eternal inflation version of the multiverse paradigm, the observable universe is embedded in a pocket universe beyond which whole universe (i.e., the multiverse) could be very different from the observable universe both in setup and even in some physical laws.

2. Tensions of the Λ-CDM Model Circa 2020s:
   1. The Hubble tension (direct value ≅ 73 (km/s)/Mpc; Λ-CDM fit value ≅ 67.5 (km/s)/Mpc) is discussed in the figure below (local link / general link: hubble_tension.html).

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   2. For other tensions with the Λ-CDM model, see, e.g., "Cosmological tensions in the birthplace of the heliocentric model", Eleonora Di Valentino, Emmanuel Saridakis, & Adam Riess, 2022.

   3. In fact, the Λ-CDM model has overcome many tensions, and so it is too soon to rule it out, but the Hubble tension (direct value ≅ 73 (km/s)/Mpc; Λ-CDM fit value ≅ 67.5 (km/s)/Mpc) is currently the toughest one.