BAO Scale Mismatch (DESI vs Planck)

The standard ruler of cosmology is two different lengths depending on who reads it. The sound horizon at the drag epoch, r_d, the distance acoustic waves traveled in the primordial plasma before baryons decoupled, calibrates every baryon acoustic oscillation distance in every galaxy survey. DESI's 2024 measurements prefer r_d near 147 +/- 1 Mpc when fit jointly with supernova distances; Planck's CMB inference within ΛCDM gives 150.0 +/- 0.4 Mpc (DESI DR1/DR2; Planck 2018): a 2.3 sigma mismatch in a quantity the model computes from supposedly settled pre-recombination physics. The ruler's length is not free: it follows from the baryon and matter densities and the plasma sound speed, all fixed by the CMB fit, so a genuine offset indicts the early-universe physics that sets the scale.

The mismatch is the quiet engine of the louder crises. The CMB-calibrated r_d is what makes BAO distances support the low Planck H0 against the distance ladder; shortening the ruler by 2 percent would realign BAO with the local measurement, which is why most early-time Hubble solutions (early dark energy, extra species) work precisely by injecting energy before recombination to shrink r_d. Each such patch buys the shorter ruler with new physics tuned for the purpose and pays for it elsewhere, in the damping tail, in structure growth, in the very DESI fits whose evolving-w preference now further destabilizes the ledger.

The standing is a precision strain at the model's foundation: the early-universe sound speed is computed, not measured, the two anchors of modern cosmology disagree about the ruler they share, and DESI's accumulating data releases are tightening the BAO side of the vise year by year.

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