problem

hubble tension

Discrepancy in measurements of the universe's expansion rate from different methods.
72 related articles · 6 formulas

Description

The Hubble tension is a major unsolved problem in cosmology: two independent methods of measuring the universe's expansion rate (the Hubble constant, H₀) yield significantly different values. One method uses the cosmic microwave background (CMB) — the leftover radiation from the Big Bang — and assumes the standard cosmological model, giving a value of about 67.4 km/s/Mpc. The other method uses local distance measurements, such as Cepheid variable stars and Type Ia supernovae, giving a higher value of about 73.0 km/s/Mpc. The discrepancy is far beyond measurement uncertainties, suggesting either unknown physics or a flaw in our cosmological model.

History

The tension emerged in the 2010s as measurements improved. The Planck satellite's 2013 CMB data gave a low value, while the Hubble Space Telescope's SH0ES project, led by Adam Riess, consistently measured a higher value, sharpening the discrepancy over subsequent years.

How it works

The CMB method measures the expansion rate indirectly by fitting the angular scale of acoustic oscillations in the early universe, which depend on the sound horizon at recombination. This requires assuming a specific cosmological model (ΛCDM). The local method builds a cosmic distance ladder: parallax calibrates Cepheids, Cepheids calibrate supernovae, and supernovae reveal the expansion rate. The tension arises because the two approaches disagree at the 5-6 sigma level, meaning the chance of it being a statistical fluke is extremely low. Possible resolutions include new physics like early dark energy, varying fundamental constants, or systematic errors in distance measurements.

In practice

Resolving the Hubble tension is crucial for accurate cosmological parameter estimation, which affects our understanding of dark energy, dark matter, and the fate of the universe. It also impacts precision tests of general relativity on cosmic scales.

Fun fact

The Hubble tension has been called the 'crack in the standard model of cosmology' because it hints that our understanding of the universe's composition and evolution may be incomplete, potentially requiring a revision of the ΛCDM model.

Concept graph →

Formulas

$$D_{KL}(P\|Q) = \int P(x) \log \frac{P(x)}{Q(x)} dx$$
Measures difference between two probability distributions.
What is in the formula
D_{KL}variableKullback-Leibler divergence — information divergence
P(x)variableprobability density of distribution P — probability density
Q(x)variableprobability density of distribution Q — probability density
xvariablerandom variable — random variable
\intoperatorsums the integrand over all values of x — integral operator
\logoperatorcomputes the logarithm of the ratio — logarithm
d_{kl}(p\|q)=\intp(x)\log\frac{p(x)}{q(x)}d^2x · 2606.04462v1
$$\hat{P}_1 - \hat{P}_2$$
Difference of projection operators measures state occupation.
What is in the formula
\hat{P}_1variableProjection operator onto state 1 — projection operator
\hat{P}_2variableProjection operator onto state 2 — projection operator
\hat{a}=|1\rangle\langle1|-|2\rangle\langle2| · 2505.00336v2
$$m = H + 5\log_{10}\left(\frac{d}{10\,\text{pc}}\right) + \text{phase correction}$$
Apparent magnitude depends on absolute magnitude, distance, and phase angle.
What is in the formula
mvariableapparent magnitude — apparent magnitude
Hvariableabsolute magnitude — absolute magnitude
dvariabledistance to the object — distance parsec
\text{phase correctivariablecorrection for phase angle (e.g., for planets or asteroids) — phase correction
\log_{10}operatorlogarithm to base 10 — logarithm base 10
m=h+2.5\log_{10}(\frac{d_{os}^2d_{oe}^2}{q(α)d_{es}^4}) · 2606.05344v1
$$\mathcal{L} = -\sum_i y_i \log(p_i)$$
Measures difference between predicted and true probability distributions.
What is in the formula
\mathcal{L}variableCross-entropy loss value — loss
y_ivariableTrue probability (or one-hot label) for class i — probability
p_ivariablePredicted probability for class i — probability
\sum_ioperatorAdds the terms for each class — summation
\logoperatorComputes the logarithm to base e — natural logarithm
\mathcal{l}=-\frac{1}{n}\sum_{i=1}^n[y_i\log(p_i)+(1-y_i)\log(1-p_i)]w_i · 2606.28603
$$B = S_E[\phi_b] - S_E[\phi_{\text{vacuum}}]$$
Tunneling rate depends on action difference.
What is in the formula
BvariableEuclidean action difference — action difference
S_EvariableEuclidean action of a field configuration — action
\phi_bvariableField configuration of the bounce (instanton) — field configuration
\phi_{\text{vacuum}}variableField configuration of the vacuum state — field configuration
b=s_e[φ_b(x)]-s_e[φ_{{fv}}] · 2607.06680
$$t_H \approx \frac{1}{H}$$
The characteristic expansion time of the universe.
What is in the formula
t_HvariableHubble time — time second
HvariableHubble parameter — hubble parameter per second
τ_{cosm}\approx0.5(\frac{1{мэв}}{t})^2{сек} · 2606.03316v2

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