14.1 The standard ΛCDM model

Key Components and Observations

The ΛCDM model (Lambda–Cold Dark Matter) is the standard framework of modern cosmology. It describes the universe's composition, its evolution from the Big Bang to today, and the physics driving its accelerating expansion. Three ingredients make up the model: dark energy, cold dark matter, and ordinary (baryonic) matter. Together, they account for observations of the CMB, large-scale structure, and distant supernovae.

Components of the ΛCDM Model

Dark energy, represented by the cosmological constant $\Lambda$, drives the accelerating expansion of the universe. It accounts for roughly 68% of the universe's total energy density. In the ΛCDM framework, $\Lambda$ acts as a constant energy density filling space uniformly.

Cold dark matter (CDM) is non-baryonic matter that does not interact electromagnetically, meaning it neither emits nor absorbs light. It makes up about 27% of the energy density. CDM is called "cold" because its particles move slowly compared to the speed of light, which matters because slow-moving particles clump together gravitationally and seed the formation of galaxies and large-scale structures.

Baryonic matter is ordinary matter made of protons, neutrons, and electrons. It accounts for only about 5% of the total energy density. This is everything you can directly observe: stars, gas, planets, and dust.

The model is characterized by several key parameters:

• Hubble constant $H_0$: the current expansion rate of the universe, measured in km/s/Mpc. Current best estimates place it around 67–73 km/s/Mpc, depending on the measurement method.
• Density parameters describe how much each component contributes relative to the critical density:
  • $\Omega_\Lambda$: density parameter for dark energy (~0.68)
  • $\Omega_m$: density parameter for total matter, both dark and baryonic (~0.32)
  • $\Omega_k$: density parameter for spatial curvature, which is nearly zero in ΛCDM, meaning the universe is very close to spatially flat

ΛCDM and Cosmic Observations

Cosmic Microwave Background (CMB). The CMB is relic radiation released about 380,000 years after the Big Bang, when the universe cooled enough for photons to travel freely. ΛCDM predicts the tiny temperature fluctuations (on the order of 1 part in 100,000) observed in the CMB, as well as the detailed shape of the angular power spectrum. The relative heights and positions of the peaks in that power spectrum are directly sensitive to the baryonic matter density and dark matter density, making the CMB one of the most precise tests of the model.

Large-scale structure. On scales of hundreds of millions of light-years, galaxies are not randomly distributed. They form a "cosmic web" of filaments, walls, and voids. ΛCDM explains this pattern through gravitational instability: small density fluctuations in the early universe (visible in the CMB) grew over billions of years as dark matter gravitationally attracted surrounding matter, eventually forming the scaffolding on which galaxies and clusters assembled.

Accelerating expansion. Observations of distant Type Ia supernovae in the late 1990s revealed that the universe's expansion is speeding up, not slowing down. In ΛCDM, the cosmological constant $\Lambda$ provides the repulsive dark energy responsible for this acceleration. The model accurately predicts the observed relationship between redshift and luminosity distance for these supernovae.

Successes, Limitations, and Evidence

Successes vs. Limitations of ΛCDM

Successes:

• Accurately predicts the observed CMB temperature fluctuations and the detailed shape of the angular power spectrum
• Explains the formation and evolution of large-scale structure from initial density perturbations
• Accounts for the observed accelerating expansion of the universe
• Provides a self-consistent framework that ties together the universe's composition, geometry, and expansion history using just six free parameters

Limitations:

• Does not explain what dark matter and dark energy actually are. $\Lambda$ is a placeholder, not a physical explanation.
• The observed value of the cosmological constant is roughly $10^{120}$ times smaller than naive quantum field theory predictions, a discrepancy known as the cosmological constant problem (or fine-tuning problem).
• Struggles with several small-scale discrepancies:
  • Cuspy halo problem: simulations predict dark matter halos with steep central density profiles, but many observed galaxies have flatter cores.
  • Missing satellites problem: simulations predict far more small satellite galaxies around hosts like the Milky Way than are actually observed.
• Does not incorporate a quantum theory of gravity, which would be needed to describe the universe's earliest moments (the Planck epoch).

Evidence for the ΛCDM Model

Multiple independent lines of evidence converge on ΛCDM, which is a major reason cosmologists treat it as the standard model.

• CMB observations from COBE, WMAP, and Planck satellites match ΛCDM predictions for temperature fluctuations and the angular power spectrum with remarkable precision. Planck data alone constrain the model's six parameters to percent-level accuracy.
• Large-scale structure surveys such as SDSS and DES map the distribution of galaxies and clusters across billions of light-years. The observed cosmic web is consistent with ΛCDM simulations of structure growth driven by cold dark matter.
• Type Ia supernovae serve as standardizable candles. Their observed redshift-luminosity distance relation confirms accelerating expansion, as predicted by a universe dominated by dark energy.
• Baryon acoustic oscillations (BAO) are periodic fluctuations in visible matter density imprinted by sound waves in the early universe. The characteristic BAO scale (~490 million light-years in today's universe) acts as a "standard ruler" and provides an independent measurement of the expansion history that agrees with ΛCDM.
• Gravitational lensing, both strong lensing (multiple images of background objects) and weak lensing (subtle statistical distortions of galaxy shapes), maps the distribution of mass including dark matter. The observed lensing signals are consistent with the dark matter distribution predicted by ΛCDM.