The Observable Universe as Seen Through the Cosmic Microwave Background

Map of anisotropies in the cosmic microwave background — Image description: The first glows of the observable universe as seen by the Planck mission (March 2013). This image shows traces of the earliest moments of creation, about 380,000 years after the Big Bang. Image source: ESA and Planck collaboration (new window)

What is the Observable Universe?

The observable universe corresponds to the region of spacetime from which light has had time to reach us since the Big Bang, given the age of the universe (\(13.8 \, Ga\)) and the speed of light. This defines a radius of about \(46 \, Gly\) (billion light-years). Beyond this, information cannot yet reach us, as light from these regions has not had time to travel to us.

The Transparent Universe: When Light Could Travel Freely

The cosmic microwave background (CMB) was emitted about 380,000 years after the Big Bang, when electrons and protons combined to form the first hydrogen atoms. Before this time, the universe was opaque to photons, trapped in a dense plasma. When recombination occurred, the universe became transparent, and light could travel freely. This radiation, now cooled to \(T \approx 2.725 \, K\), reaches us as microwaves.

CMB Anisotropies: The Cosmic Seeds of Galaxies

The temperature of the CMB is remarkably uniform, but tiny fluctuations (\(\Delta T/T \sim 10^{-5}\)) are present. These anisotropies reveal primordial density differences, which later led to the formation of galaxies, clusters, and large-scale structures. The acoustic peaks in the anisotropy power spectrum trace the physics of the early universe: interactions between photons, baryons, and gravity.

Observable Horizon and the Geometry of the Universe

The study of the CMB has shown that the geometry of space is almost flat (\(\Omega_k \approx 0\)). This means that Euclidean laws apply on large scales. The characteristic angular size of the first acoustic peak sets the sound horizon at the time of recombination. Thus, the CMB serves as a cosmological ruler: it measures the scale of the observable universe and its dynamic parameters.

N.B.:
The term recombination refers to the era, about 380,000 years after the Big Bang (redshift \(z \approx 1100\)), when the temperature of the universe dropped below \(3000 \, K\). Electrons bound to protons to form the first hydrogen atoms, making the universe transparent to photons. These photons now constitute the cosmic microwave background. Some older publications mention ≈300,000 years, but Planck 2018 (new window) measurements specify the value at about 380,000 years.

Table of Fundamental Parameters Derived from CMB Analysis

Cosmological Parameters Constrained by the CMB
Parameter	Measured Value	Physical Meaning	Comment
Age of the Universe	\(13.80 \pm 0.02\) Ga	Time elapsed since the Big Bang	Sets the total time available for cosmic evolution
Average Temperature of the CMB	\(2.725 \, K\)	Fossil microwave radiation	Confirms that the spectrum corresponds to an almost perfect blackbody
Baryonic Density	\(\Omega_b h^2 = 0.0224 \pm 0.0001\)	Fraction of ordinary matter	Essential for explaining nucleosynthesis and star formation
Dark Matter Density	\(\Omega_c h^2 = 0.120 \pm 0.001\)	Invisible matter governing gravity	Explains the rapid formation of galactic structures
Hubble Constant	\(H_0 = 67.4 \pm 0.5 \, km/s/Mpc\)	Current expansion rate	Value from the CMB is lower than that measured locally (Hubble tension)
Spectral Index of Perturbations	\(n_s = 0.965 \pm 0.004\)	Signature of cosmic inflation	Shows that fluctuations are not exactly scale-invariant
Spatial Curvature	\(\Omega_k \approx 0\)	Flat universe on large scales	Confirms the prediction of inflationary models

Sources: ESA Planck (2013-2018), NASA COBE/WMAP, ACT, SPT, NASA LAMBDA Archive (new window).

Limitations and Uncertainties

Despite its precision, the study of the CMB is not without constraints and areas of uncertainty. These arise from both the fundamental properties of the universe and the limitations of our instruments.

Cosmic Variance: Since we only have access to one universe and one sky, some statistical quantities (e.g., the spectrum at large angular scales) suffer from irreducible uncertainty. This sets a fundamental limit on possible precision.
Astrophysical Foregrounds: Our galaxy emits microwaves (interstellar dust, ionized gas, synchrotron). These signals must be separated using complex models, but the subtraction is never perfect, leaving an uncertain residue.
Instrumental Noise: Even the best detectors (COBE, WMAP, Planck, ACT, SPT) introduce noise, related to the sensitivity of bolometers and thermal stability. This noise limits the detection of the finest anisotropies.
Resolution and Coverage: Some experiments measure large scales well (COBE, WMAP), others measure small scales (ACT, SPT), but no mission perfectly covers the entire angular spectrum. Surveys must be combined, which introduces correlations and margins of error.
Secondary Effects: The fossil radiation undergoes modifications after recombination, such as gravitational lensing by large structures, or the Sunyaev-Zel’dovich effect produced by galaxy clusters. These signatures slightly blur the primordial signal.
Parametric Degeneracies: Some cosmological parameters (e.g., dark matter density and Hubble constant) produce similar effects in the CMB spectrum, making their determination interdependent. Measured values must therefore be cross-checked with other observations (supernovae, gravitational lenses, baryon acoustic oscillations).

These limitations explain why CMB results are always associated with uncertainty intervals and why new missions (such as LiteBIRD or CMB-S4) are expected. They aim to refine the measurement of CMB polarization, particularly the B-mode, which could directly reveal the primordial gravitational waves of inflation.