The oldest light is a surface, not a moment
The cosmic microwave background is routinely described as a photograph of the infant universe. The phrase is useful for a first pass and misleading on a second. What a millimetre-wave telescope records is not an instant but a surface: the locus of points from which photons last scattered off a free electron and then travelled to us unimpeded. That surface has a thickness, its position depends on a calculated ionisation history rather than a measured one, and everything downstream of it — every parameter quoted with four significant figures — inherits whatever is uncertain in that calculation.
The physical origin is straightforward to state. In the early universe, photons, electrons and baryons were tightly coupled: Thomson scattering off free electrons made the plasma opaque. As the universe expanded and the photon temperature fell to a few thousand kelvin, electrons and protons combined into neutral hydrogen. The scattering rate collapsed, the mean free path grew to cosmological scale, and the radiation decoupled. What we see is the last scattering event of each photon, which is why the surface is a shell around the observer rather than a place in the sky.
The word “recombination” hides a substantial computation. The transition is not in thermal equilibrium; it is governed by the escape of Lyman-alpha photons and by two-photon decay from the excited states of hydrogen, and it happens after a separate and slower recombination of helium. Seager, Sasselov and Scott recomputed this history with a multilevel atom and found that the ionisation fraction was about ten per cent smaller than earlier treatments gave for redshifts below roughly 800, and that neutral helium recombination is much slower than had been assumed, delayed until just before hydrogen recombines [6]. That correction is not cosmetic. The width and position of the visibility function set the damping scale and shift the acoustic peaks, so a systematic error in the atomic physics propagates directly into the inferred densities. This is the first place in the chain where a theoretical input is doing work that is easy to mistake for an observation.
The spectrum was the decisive measurement, before the map
Penzias and Wilson reported an excess zenith antenna temperature at 4080 megacycles per second that they could not attribute to the atmosphere, to ohmic losses in the horn, or to back-lobe pickup from the ground. Their number, after subtracting a measured atmospheric contribution of 2.3 plus or minus 0.3 kelvin and a computed ohmic contribution, was 3.5 plus or minus 1.0 kelvin, and they noted that within their observational limits it was isotropic, unpolarised and free from seasonal variation across ten months of observing [1]. The isotropy mattered as much as the amplitude: a Galactic or local source would have shown structure or an annual term.
What made the interpretation decisive, though, was not the single-frequency temperature but the shape of the spectrum across many frequencies. A radio source population, or thermalised starlight, or dust reprocessing, can produce a diffuse microwave glow; none of them naturally produces a blackbody. The COBE FIRAS instrument measured the spectrum against an internal reference and found deviations from a Planck function smaller than fifty parts per million of the peak brightness, with a temperature of 2.728 plus or minus 0.004 kelvin at 95 per cent confidence, a limit on Compton distortion of |y| below 15 times ten to the minus six, and a limit on chemical potential distortion of |mu| below 9 times ten to the minus five [4]. A later reanalysis combining the available absolute measurements gave 2.72548 plus or minus 0.00057 kelvin [5].
The reason this counts as a decisive measurement rather than a confirmation is that it closes off an entire class of alternatives at once. Any mechanism that injects energy into the photon field after thermalisation becomes inefficient leaves a spectral signature; the FIRAS limits therefore constrain energy release across a wide span of cosmic history without needing a specific model of what might have released it. The same FIRAS data set the dipole at 3.372 plus or minus 0.007 millikelvin toward Galactic coordinates approximately 264 degrees longitude and 48 degrees latitude [4]. That dipole is kinematic — our motion with respect to the rest frame of the radiation — and it is removed before anything cosmological is extracted from the map.
One part in a hundred thousand
Once the dipole is subtracted, what remains is very nearly nothing. COBE’s Differential Microwave Radiometers detected structure at greater than seven sigma and reported an rms sky variation, smoothed to a ten-degree beam and cutting Galactic latitudes below twenty degrees, of 30 plus or minus 5 microkelvin, corresponding to a fractional temperature fluctuation of 11 parts per million; the cosmic quadrupole component was 13 plus or minus 4 microkelvin, roughly a hundred times smaller than the dipole [2]. The familiar summary “one part in a hundred thousand” is a rounding of that ten-degree number. The four-year DMR analysis refined the normalisation to a quadrupole amplitude of 15.3 microkelvin, with 18 plus or minus 1.6 microkelvin when the spectral index is fixed to the scale-invariant value [3].
Two distinct physical effects produce these fluctuations, and they dominate on different scales. On angular scales larger than the horizon at last scattering, the temperature variation is essentially gravitational: photons climbing out of potential wells are redshifted, and the local time dilation shifts the effective emission epoch. On smaller scales, the fluctuations are the imprint of oscillations that had time to run before decoupling. The transition between the two regimes is what makes the CMB such an unusually clean cosmological probe: the large-scale part is nearly a direct image of the primordial potential, and the small-scale part is a piece of well-understood fluid dynamics running on top of it [7].
Sound in a plasma, stopped at one instant
Before recombination, photons and baryons behave as a single fluid. Radiation pressure resists compression; gravity, mostly supplied by the dark matter that does not participate in the pressure, drives it. The result is a set of standing acoustic oscillations. Each Fourier mode oscillates at its own frequency, set by the sound speed and the wavenumber, and at recombination the oscillation stops abruptly because the pressure support disappears with the free electrons.
The consequence is a harmonic series in the sky. Modes that happened to be at maximum compression or maximum rarefaction at last scattering show the largest temperature contrast; modes caught at their zero crossing show the least. Because the phase depends on wavenumber times the sound horizon, the peaks fall at multiples of a fundamental scale. The physical length of that scale is the comoving sound horizon at last scattering, and the angle it subtends is a ratio of two lengths:
The numerator is set by pre-recombination physics — the expansion rate and sound speed before decoupling, which depend on the baryon and radiation densities. The denominator is set by everything that happened afterwards along the line of sight, including spatial curvature and the late-time expansion history. This single ratio is why an angular measurement can constrain geometry, and it is also the origin of the degeneracies that make CMB-only constraints on some parameters much weaker than the headline error bars suggest.
The first clear resolution of the fundamental peak came from balloon-borne observations: BOOMERanG located it at multipole 197 plus or minus 6 with an amplitude of 69 plus or minus 8 microkelvin, and read that position as consistent with cold dark matter models in a spatially flat universe [8]. That is the cleanest example in modern cosmology of a geometric argument made from a single angle.
What the peak heights carry that the positions do not
Positions encode geometry; heights encode content, and they do so through two distinguishable mechanisms.
Baryons add inertia to the photon-baryon fluid without adding pressure. Loading the oscillator this way deepens the compressions relative to the rarefactions, so odd-numbered peaks — the compression peaks — are enhanced relative to even-numbered ones. The ratio of the first peak to the second is therefore a baryon-density measurement that is largely independent of the geometry read off the peak spacing. Planck’s final analysis reports a baryon density of 0.0224 plus or minus 0.0001 in the usual dimensionless units [14].
Dark matter enters differently. It fixes the epoch of matter-radiation equality, and modes that entered the horizon while radiation still dominated experience a decay of the gravitational potential that drives their oscillation amplitude up. The overall height of the first few peaks relative to the large-scale plateau therefore measures how much non-baryonic matter was present when those modes were oscillating. The ACT DR6 analysis, combining its own spectra with Planck, CMB lensing and DESI baryon acoustic oscillation data, reports a cold dark matter density of 0.118 plus or minus 0.001 and a scalar spectral index of 0.974 plus or minus 0.003 [18].
At small angular scales a third effect takes over. The last-scattering surface is not infinitely thin, and photons random-walk a finite distance during recombination, so fluctuations below that diffusion length are washed out. The peaks decline in amplitude toward high multipole rather than continuing indefinitely, and the rate of that decline is itself an observable that depends on the recombination history — which is where the atomic physics of the first section re-enters as a systematic.
The statistic that is actually fitted
No one fits a map. The quantity carried into a likelihood is the angular power spectrum, the variance of the spherical-harmonic coefficients at each multipole:
This choice embeds an assumption that deserves to be stated rather than assumed: that the fluctuation field is statistically isotropic and Gaussian, so that the power spectrum is a sufficient statistic. If the primordial field had significant non-Gaussianity, the power spectrum would discard real information; the assumption is tested separately, not granted.
It also imposes a hard floor on precision. At each multipole there are only two-l-plus-one independent modes on the sky, so even a perfect noiseless experiment has an irreducible sampling variance at low multipole. Cosmic variance is not a limitation of instruments; it is a limitation of having one sky.
The practical construction is more elaborate than the formula suggests. Planck’s likelihood is a hybrid: a pixel-based or cross-spectrum treatment at low multipole, where the distribution is non-Gaussian and the reionisation optical depth is constrained by large-scale polarisation, and a Gaussian cross-spectrum treatment at high multipole with explicit modelling of temperature-to-polarisation leakage and calibration. The collaboration reports that including polarisation improves constraints on the base model by 20 to 30 per cent over temperature alone, and estimates internal consistency between alternative implementations at better than half a sigma [15]. Optical depth is the parameter most exposed to this machinery, and Planck’s value of 0.054 plus or minus 0.007 rests on the large-scale polarisation data whose systematics are hardest to control [14].
Polarisation, and the seam the light comes through
Thomson scattering produces linear polarisation when the radiation field incident on an electron has a quadrupole anisotropy. At last scattering that condition is met, so the CMB is polarised at the per-cent level of its own anisotropy.
The useful decomposition is not into Stokes parameters but into two components of opposite parity. Zaldarriaga and Seljak showed that the spin-weighted harmonic expansion of the polarisation field admits two rotationally invariant combinations, one of electric and one of magnetic parity, and that the magnetic-parity component receives no contribution from scalar density perturbations and does not correlate with either temperature or the electric-parity component [9]. That last clause is the entire strategic value of B modes: scalar perturbations, which produce everything else we see, cannot make them at linear order.
The E-mode signal was detected by DASI at 4.9 sigma, with an amplitude of 0.80 in units where the prediction from prior temperature measurements was 0.9 to 1.1, and a 95 per cent upper limit of 0.59 on B modes in the same units [10]. The consistency of the E-mode amplitude with a prediction made from temperature data alone is a strong internal check on the acoustic picture: the polarisation is sourced by the velocity of the same fluid whose density we read in temperature, so it peaks out of phase with the temperature spectrum, and it did.
B modes are where the field has repeatedly been embarrassed, and the reason is not subtle. Our own Galaxy produces polarised emission from magnetically aligned dust grains and from synchrotron radiation, and both have B-mode components. Planck measured the angular power spectrum of polarised dust at 353 gigahertz and extrapolated it to 150 gigahertz over the multipole range 40 to 120, finding a dust B-mode power of 1.32 times ten to the minus two square microkelvin, with a statistical uncertainty of 0.29 and an extrapolation uncertainty of roughly 0.28 in the same units. The collaboration stated plainly that this was the same magnitude as the signal reported by BICEP2 over that multipole range, and that even the cleanest windows on the sky require assessment of the polarised dust contribution [11].
The joint reanalysis by the two collaborations reached the same conclusion from the combined data: marginalising over dust and over the tensor amplitude, the excess over the lensing expectation was not significant as a primordial signal, and the resulting limit was a tensor-to-scalar ratio below 0.12 at 95 per cent confidence, with lensing B modes themselves detected at 7.0 sigma [12]. The episode is worth remembering precisely because nothing went wrong procedurally. A real signal was measured; its attribution was wrong; the correction came from adding a frequency channel that could separate a Galactic spectrum from a cosmological one.
The current limit reflects that lesson being institutionalised. The BICEP/Keck analysis through the 2018 season reports a tensor-to-scalar ratio below 0.036 at 95 per cent confidence with a per-experiment uncertainty of 0.009, using a seven-parameter foreground model that no longer imports a prior on the dust spectral index from other sky regions, and notes that its 220 gigahertz maps now exceed Planck’s 353 gigahertz signal-to-noise on polarised dust in that field [13]. The constraint improved because the foreground measurement improved, not because the primordial measurement got cleaner in isolation.
Lensing is a second, later measurement inside the same data
Photons travelling from last scattering pass through the growing web of structure, and the intervening potentials deflect them by of order an arcminute. This remaps the observed field. The remapping is small, but it is coherent, and it correlates the fluctuation field with its own gradient in a way that a statistically isotropic unlensed field would not. That correlation is estimated quadratically from the maps and yields a reconstruction of the projected mass along the line of sight.
The value of this probe is that it is sensitive to structure at intermediate redshift, not to conditions at recombination, while living inside exactly the same data set. Planck detected lensing in polarisation alone at 9 sigma, up from 5 sigma in the previous release, and at 40 sigma in combination with temperature; the lensing likelihood alone constrains a particular combination of the fluctuation amplitude and matter density to 0.589 plus or minus 0.020, and in combination with the power spectra gives an amplitude of 0.811 plus or minus 0.006 [16]. ACT’s DR6 lensing measurement, over 9400 square degrees, reaches 2.3 per cent precision at 43 sigma and reports a structure-growth amplitude of 0.818 plus or minus 0.022 from ACT alone and 0.813 plus or minus 0.018 combined with the Planck NPIPE maps, with no evidence for a suppression of structure at low redshift [17].
That last clause is a live claim, because several galaxy-survey analyses have reported lower amplitudes. It is also in some tension with the primary Planck spectra themselves, which the collaboration described as continuing to prefer higher lensing amplitudes than the base model predicts [14]. Two independent handles on lensing inside one experiment disagreeing mildly is a reminder that the smoothing of the acoustic peaks and the reconstructed lensing power are not the same measurement.
The disagreement that has not gone away
The expansion rate inferred from the CMB assumes the base six-parameter model. Under that assumption Planck gives 67.4 plus or minus 0.5 kilometres per second per megaparsec, with a matter density of 0.315 plus or minus 0.007 and a spectral index of 0.965 plus or minus 0.004 [14]. Ground-based experiments now reach comparable precision independently: ACT DR6, combined with Planck, lensing and DESI, gives 68.43 plus or minus 0.27 [18], and SPT-3G reports 66.66 plus or minus 0.60 from its own data and 67.19 plus or minus 0.38 in combination with ACT and Planck [20].
The distance ladder does not agree. The SH0ES analysis reports 73.04 plus or minus 1.04 and characterises the gap as a five-sigma difference from the Planck value under the standard model, adding that the source of the discrepancy remains unknown [21]. The SPT-3G collaboration quotes its own single-experiment result as 6.2 sigma from the SH0ES value [20].
It would be convenient to stop there and call it a crisis. The honest picture is more awkward, because the local measurements do not agree among themselves either. The Chicago-Carnegie Hubble Program, using JWST, reports 70.39 from a combined tip-of-the-red-giant-branch calibration with statistical and systematic uncertainties of 1.22 and 1.33, 68.81 from JWST-only tip-of-the-red-giant-branch data, and 67.80 from the JWST-only J-region asymptotic giant branch method, and states that its results are consistent with the standard model without requiring new physics [22]. Two experienced groups using overlapping data and different distance indicators reach conclusions that differ by roughly the size of the effect in dispute. That is a disagreement about the local ladder, not only between the ladder and the CMB, and it is not currently resolved by any argument that a neutral reader can check without adjudicating supernova host calibrations.
On the other side, the CMB experiments have looked directly for the modifications that would close the gap and have not found support for them. The ACT DR6 extended-model analysis finds no statistically significant preference for departures from the baseline model, no evidence for additional light relativistic species, and states that models introduced to raise the Hubble constant or to lower the inferred fluctuation amplitude are not favoured by its data [19]. SPT-3G likewise finds no evidence for physics beyond the base model from CMB data alone, while noting a 2.8 sigma difference between its CMB result and baryon acoustic oscillation constraints [20]. Planck’s own combination with BAO gives an effective number of relativistic species of 2.99 plus or minus 0.17, close to the standard expectation [14].
Characterising the state of play rather than picking a side: the CMB inference is internally consistent across three independent instruments with different systematics, and it is consistent with an early-universe sound horizon that leaves little room for the pre-recombination modifications most often proposed. The distance-ladder inference is not internally consistent at the precision required to settle the question. Either a systematic remains in one of the local calibrations, or the resolution lies in physics that CMB data alone are poorly placed to detect, or both.
What would move this, and what would refute it
Analysis, with an explicit horizon. Over roughly the next five years, the parameter that most plausibly changes the picture is not the Hubble constant itself but the sound horizon, constrained jointly by higher-precision small-scale polarisation and by lensing cross-correlations with galaxy surveys. The assumptions behind that expectation are that ground-based polarisation sensitivity continues to improve at roughly its recent rate, that foreground separation in polarisation does not hit an unmodelled wall of the kind dust presented in 2014, and that recombination physics remains adequately described by current multilevel calculations.
Observable indicators that the picture is shifting: a CMB-only determination of the fluctuation amplitude that moves outside the current combined range; a lensing amplitude from the reconstructed spectrum that disagrees with the smoothing of the acoustic peaks by more than the current mild preference; convergence or further divergence between the tip-of-the-red-giant-branch and Cepheid calibrations as JWST samples grow.
Disconfirmation condition, stated so it can fail. If, by 2031, an independent local calibration with systematics uncorrelated with both SH0ES and CCHP lands at or below 69 kilometres per second per megaparsec with an uncertainty under 1, the reading offered here — that the local ladder is the less settled half of the disagreement — would be wrong, and the burden would shift decisively back to the early-universe model. If instead such a calibration lands at or above 72 with comparable precision, the case for new pre-recombination physics becomes much harder to avoid, and the CMB collaborations’ current statements that their data do not favour such models would need to be revisited against a stronger prior.
The general lesson holds regardless of which way that goes. A temperature map becomes a cosmology through a chain: an atomic-physics calculation, an absolute spectral measurement, a statistic that assumes Gaussianity, a foreground model, and a six-parameter fit. Each link is testable. The disagreements that matter are the ones that survive a change of instrument, and this one has.
