Cosmology

Cosmology became a quantitative science within about thirty years. The standard model now fits a wide range of independent observations with six parameters, and its two largest components are things nobody has identified.

The expanding universe

Hubble established in 1929 that galaxies recede with velocity proportional to distance:

The correct interpretation is not that galaxies move through space but that space itself expands, carrying galaxies with it. Redshift is not a Doppler shift but a stretching of wavelength along with the expansion of space during the light’s travel.

The dynamics follow from general relativity applied to a homogeneous, isotropic universe. The Friedmann equations govern the scale factor $a(t)$:

The three terms are matter and radiation density, spatial curvature, and the cosmological constant. Their relative importance changes with time because each scales differently with $a$: radiation as $a^{-4}$, matter as $a^{-3}$, and the cosmological constant not at all. The universe therefore passes through radiation-dominated, matter-dominated and dark-energy-dominated eras, and it is currently in the third.

The contents

Everything ever observed directly is in the 5%. See Dark matter and dark energy.

The cosmic microwave background

For the first 380 000 years the universe was hot enough that hydrogen remained ionised, making it opaque to photons. As it expanded and cooled below about 3000 K, electrons combined with protons and the universe became transparent. The photons released at that moment have travelled freely ever since, redshifted by expansion to a temperature of 2.7255 K.

The CMB is the strongest evidence in cosmology, for three reasons.

Its spectrum is a near-perfect blackbody, measured by COBE to a precision that remains among the best-fit blackbodies ever observed. Only a hot, dense, thermal early phase produces that.

Its temperature is uniform to about one part in 100 000, establishing large-scale homogeneity and posing the horizon problem that inflation was proposed to solve.

Its tiny anisotropies encode the parameters. The angular power spectrum of the temperature fluctuations shows a series of acoustic peaks, produced by sound waves in the pre-recombination plasma. Their positions and relative heights constrain the geometry, the baryon density and the dark matter density simultaneously and independently, which is why the CMB has been the single most constraining dataset in cosmology.

Big Bang nucleosynthesis

Between roughly one second and twenty minutes, the universe was hot enough for nuclear fusion. The light elements formed then, and their abundances are predicted by a single parameter, the baryon-to-photon ratio.

The agreement for deuterium and helium is a strong and independent check on the model, and importantly the baryon density it gives matches the value derived from the CMB acoustic peaks by a completely different method. The persistent lithium discrepancy is a real anomaly rather than a rounding error.

Structure

Tiny density fluctuations imprinted in the early universe grew under gravity into the cosmic web of filaments, clusters and voids observed today.

Dark matter is essential to this account. Baryons could not begin collapsing until after recombination, because radiation pressure resisted it. Dark matter, which does not couple to photons, began collapsing much earlier and built the gravitational wells that baryons later fell into. Without it, structure would not have had time to form.

Baryon acoustic oscillations are the surviving imprint of the same sound waves that produce the CMB peaks. They appear as a preferred separation of about 150 megaparsecs in the galaxy distribution, and because that scale is calculable from first principles, it serves as a standard ruler for measuring expansion history.

The Hubble tension

The most significant open problem in observational cosmology is that two good measurements of the expansion rate disagree.

The discrepancy is about 8% and, on the quoted uncertainties, statistically significant at roughly five standard deviations. Both are careful measurements with extensively examined systematics.

The distinction that matters is that the CMB value is not a direct measurement. It is the value of $H_0$ that the standard cosmological model requires in order to fit the CMB, so a discrepancy could indicate either an error in one of the measurements or that the model is incomplete between recombination and today.

Proposed resolutions include early dark energy, additional relativistic species, evolving dark energy and unrecognised systematics in the distance ladder. None is established, and several proposals that fix $H_0$ worsen the fit to other data. It remains genuinely open, and it is the clearest current indication that the standard model is not the final account.

References

• Dodelson, S. and Schmidt, F. Modern Cosmology, 2nd ed., Academic Press, 2020.
• Peebles, P. J. E. Principles of Physical Cosmology, Princeton University Press, 1993.
• Planck Collaboration, “Planck 2018 results VI: Cosmological parameters”, Astronomy and Astrophysics, 641:A6, 2020.
• Riess, A. G. et al. “A Comprehensive Measurement of the Local Value of the Hubble Constant”, The Astrophysical Journal Letters, 934:L7, 2022.
• Fixsen, D. J. “The Temperature of the Cosmic Microwave Background”, The Astrophysical Journal, 707:916, 2009.
• Cyburt, R. H. et al. “Big Bang Nucleosynthesis: Present Status”, Reviews of Modern Physics, 88:015004, 2016.