The Hubble Tension

Two fundamentally different methods of measuring the expansion rate of the universe give answers that disagree at the level of 5 standard deviations or more. Early-universe measurements (from the cosmic microwave background, assuming $\Lambda$CDM) give $H_0 \approx 67.4$ km/s/Mpc. Late-universe measurements (from the cosmic distance ladder) give $H_0 \approx 73.0$ km/s/Mpc. This is either the most important anomaly in modern cosmology or the most persistent systematic error in the history of precision measurement.

How the Measurements Work

The Early-Universe Method: Planck CMB in Detail

The CMB provides a snapshot of the universe at $z \approx 1100$. The angular size of the sound horizon (the maximum distance sound could travel in the early universe) serves as a standard ruler. Given a cosmological model ($\Lambda$CDM), this constrains $H_0$ very precisely. The measurement depends on the assumption that $\Lambda$CDM is the correct model.

The physical sound horizon $r_s$ at recombination depends on the baryon-to-photon ratio and the radiation content of the early universe. Its value is approximately 147 Mpc. The angular scale at which it appears on the sky depends on the angular diameter distance to the last scattering surface, which itself depends on $H_0$ and all the other cosmological parameters. The Planck satellite measured the CMB temperature and polarization power spectra with exquisite precision across multipoles $\ell = 2$ to $\ell \approx 2500$. The resulting six-parameter $\Lambda$CDM fit yields:

This measurement is highly precise (0.8% uncertainty) but it is model-dependent: if $\Lambda$CDM is wrong (for instance, if there is early dark energy or extra relativistic species), the inferred $H_0$ changes. The CMB does not measure $H_0$ directly; it measures $\theta_s = r_s/d_A$, and $H_0$ is derived from the model.

The Distance Ladder: SH0ES in Detail

The local measurement builds a chain of distance indicators:

• Rung 1 (Anchors): Geometric distances to nearby calibrators. The SH0ES team uses three independent anchors: NGC 4258 (distance from water maser measurements, $d = 7.58 \pm 0.11$ Mpc), the Large Magellanic Cloud (distance from detached eclipsing binaries, $d = 49.59 \pm 0.54$ kpc), and Milky Way Cepheids with Gaia EDR3 parallaxes
• Rung 2 (Cepheids): Cepheid variable stars in 37 galaxies that also host Type Ia supernovae. The Leavitt law (period-luminosity relation) ties the Cepheid period to absolute magnitude, allowing calibration across galaxies
• Rung 3 (Supernovae): Type Ia supernovae in the Hubble flow ($0.023 < z < 0.15$), where the recession velocity is dominated by the Hubble expansion rather than local peculiar velocities

Each rung calibrates the next. The result is a direct, model-independent measurement of $H_0$, but one that depends on understanding the systematic properties of each distance indicator. The SH0ES 2022 result combines all three anchors:

TRGB: An Independent Distance Indicator

The Tip of the Red Giant Branch (TRGB) is an alternative distance indicator. Red giant stars in old, metal-poor populations undergo a helium flash at a nearly universal luminosity, creating a sharp cutoff in the luminosity function at $M_I \approx -4.05$ mag. Because TRGB stars are found in the uncrowded halos of galaxies (rather than in the dusty disks), they are less susceptible to crowding and extinction systematics than Cepheids.

Statistical Significance of the Tension

The tension between Planck and SH0ES stands at approximately $5\sigma$ when comparing Gaussian posteriors. This corresponds to a probability of less than 1 in 3.5 million of occurring by chance. However, the significance depends on assumptions:

• If the TRGB-based value ($H_0 \approx 69.8$) is used instead of SH0ES, the tension reduces to $\sim 2\sigma$
• If one allows for non-Gaussian systematic uncertainties (e.g., population-dependent Cepheid properties), the effective significance may be lower
• The frequentist significance ($5\sigma$) and Bayesian model comparison (Bayes factor) can give different assessments, as the Bayesian analysis penalizes additional parameters in proposed solutions

JWST Deepened the Mystery

The James Webb Space Telescope was expected to resolve the tension by checking whether crowding, dust, or other systematic effects were biasing Cepheid measurements. Instead, JWST confirmed that the SH0ES Cepheids are reliable, ruling out the leading systematic error candidates at high significance. The tension became more robust, not less.

JWST's NIRCam instrument observes in the near-infrared (1-5 $\mu$m), where dust extinction is reduced by a factor of $\sim 7$ compared to optical wavelengths and where stellar crowding is far less severe (the point spread function is sharper and the background of unresolved stars is fainter). The SH0ES team reobserved Cepheids in several calibrator galaxies with JWST and found that the HST and JWST photometry agreed to within 0.01 mag, confirming that crowding was not biasing the HST measurements. Riess et al. (2024) reported $H_0 = 72.6 \pm 2.0$ km/s/Mpc from JWST Cepheids alone.

Other Independent Methods

Beyond Cepheids and TRGB, several independent methods provide $H_0$ measurements with varying precision:

• Strong lensing time delays (H0LiCOW/TDCOSMO): Measuring the time delay between multiple images of a lensed quasar gives $H_0 = 73.3^{+1.7}_{-1.8}$ km/s/Mpc, consistent with the distance ladder. However, this result depends on the assumed mass profile of the lens galaxy
• Megamaser distances: Water masers in accretion disks of active galaxies provide geometric distances independent of any calibration chain. The Megamaser Cosmology Project gives $H_0 = 73.9 \pm 3.0$ km/s/Mpc
• Gravitational wave standard sirens: The binary neutron star merger GW170817 provided $H_0 = 70.0^{+12}_{-8}$ km/s/Mpc. Current precision is too low to discriminate, but future detections with LIGO/Virgo/KAGRA and the Einstein Telescope will reach percent-level precision
• Surface brightness fluctuations (SBF): Jensen et al. built a Cepheid-free, supernova-free distance ladder using SBF and obtained $H_0 = 73.8 \pm 2.1$ km/s/Mpc

The Intermediate Value

Freedman's Carnegie-Chicago Hubble Program (CCHP) uses the Tip of the Red Giant Branch (TRGB) method calibrated with JWST data and obtains $H_0 = 70.4 \pm 1.8$ km/s/Mpc. This sits between the Planck and SH0ES values, with error bars overlapping both. Whether this represents the true value (making both extremes slightly wrong) or is itself subject to calibration issues remains actively debated.

The CCHP also measured $H_0$ using the J-region Asymptotic Giant Branch (JAGB) method, a carbon-star standard candle, obtaining a consistent intermediate value. However, the Riess/SH0ES team has disputed the CCHP TRGB calibration, arguing that the choice of color cut and zero-point calibration explains the discrepancy. This debate remains unresolved and highlights how subtle systematic choices propagate through the distance ladder.

Leading Theoretical Explanations

If the tension is real (not a systematic error), it implies that $\Lambda$CDM is incomplete. The most promising proposed solutions include:

Early Dark Energy

A brief episode of dark energy near the time of recombination ($z \approx 1100$) could reduce the sound horizon, shifting the CMB-inferred $H_0$ upward. The canonical model (Poulin et al., 2019) posits an ultra-light axion-like field that contributes $\sim 10\%$ of the energy density near $z \approx 3500$ and then dilutes rapidly. The sound horizon shrinks by approximately 5%, and the inferred $H_0$ increases to $\sim 71$ km/s/Mpc, reducing the tension to approximately $2\sigma$.

However, early dark energy introduces new problems. It worsens the $S_8$ tension (the disagreement in the amplitude of matter fluctuations measured locally versus from the CMB) because the extra energy density changes the growth of structure. It is also constrained by Lyman-$\alpha$ forest measurements and by the detailed shape of the CMB damping tail at high multipoles. The model requires fine-tuning of the field mass ($m \sim 10^{-27}$ eV) and the initial field displacement.

Extra Relativistic Species

Adding extra radiation (parametrized by $\Delta N_{\text{eff}}$) speeds up the early expansion, reduces the sound horizon, and increases the inferred $H_0$. An increase of $\Delta N_{\text{eff}} \approx 0.4$ can bring $H_0$ up to $\sim 69$ km/s/Mpc. However, this is constrained by Big Bang nucleosynthesis (BBN), which limits $N_{\text{eff}} < 3.4$ at 95% confidence, and by the CMB damping tail. Extra radiation alone cannot fully resolve the tension.

Varying Electron Mass

If the electron mass were about 1% larger at recombination ($\Delta m_e / m_e \approx 0.01$), it would modify the recombination history by changing the binding energy of hydrogen and the Thomson scattering cross-section. This shifts the epoch of recombination and changes the inferred $H_0$. Combined with DESI data, this brings $H_0$ to approximately 69.6 km/s/Mpc. The proposal is preferred at $2\text{-}3.6\sigma$ by CMB data but cannot fully close the gap alone.

Interacting Dark Sector

Models combining early dark energy with interactions between dark matter and dark energy (iDEDM) can potentially address both the $H_0$ and $S_8$ tensions simultaneously. In these models, dark matter decays or interacts with dark energy, changing the late-time expansion history and the growth rate of structure. The interacting dark energy-dark matter model (iDEDM) of Allali et al. achieves $H_0 \approx 72$ km/s/Mpc while keeping $S_8$ consistent with weak lensing measurements. These remain speculative but represent the most complete theoretical framework.

Late-Universe Solutions

An alternative approach modifies the expansion history at low redshifts ($z < 2$) rather than at recombination. These include evolving dark energy (as hinted by DESI), a local void (the KBC void hypothesis, where we live in a $\sim 300$ Mpc underdensity), or a transition in the dark energy equation of state. Late-universe solutions face a generic difficulty: the BAO measurements at $0.1 < z < 2.5$ tightly constrain $H(z)$ at intermediate redshifts, leaving little room for modifications that do not also conflict with these constraints.

The Bigger Picture

The Hubble tension does not exist in isolation. Together with the DESI dark energy hints and the swampland conjectures, it may point toward a single conclusion: $\Lambda$CDM is not the final word on cosmology. The universe's expansion history is more complex than a simple cosmological constant can accommodate.

What Will Resolve It

• Euclid primary results (2026): Independent constraints on the expansion history
• CMB-S4 and Simons Observatory: Next-generation CMB measurements with reduced systematic uncertainties
• Complete JWST recalibration: All 37 SH0ES calibrator galaxies reobserved with JWST
• Additional DESI data: More precise BAO measurements to constrain the dark energy equation of state