The Cosmic Microwave Background (CMB) is the thermal afterglow of the Big Bang — a nearly uniform bath of photons filling the entire observable universe at a temperature of 2.7255 K, first detected accidentally by Arno Penzias and Robert Wilson in 1965 (Nobel Prize 1978) and mapped in extraordinary detail by the COBE, WMAP, and Planck satellite missions. It was emitted when the universe was about 380,000 years old and cooled enough for electrons and protons to combine into neutral hydrogen (recombination), allowing photons to travel freely for the first time. The tiny temperature fluctuations in the CMB — at the level of 1 part in 100,000 — encode a wealth of information about the early universe's composition and geometry, compressed into the angular power spectrum Cℓ.
This simulator lets you explore the CMB temperature anisotropy power spectrum and how its shape changes with cosmological parameters: baryon density Ωb, cold dark matter density Ωc, and Hubble constant H₀. The characteristic acoustic peaks arise from sound waves that oscillated in the primordial plasma and were frozen at recombination — their positions and heights constrain all the major cosmological parameters simultaneously.
What do the peaks in the CMB power spectrum represent?
Before recombination, the universe was a hot plasma of baryons (protons and electrons) and photons, coupled by Thomson scattering. Gravity compressed overdense regions while photon pressure pushed back, creating acoustic oscillations — sound waves propagating at c/√3 of the speed of light. At recombination these waves were "frozen" with different regions caught at different phases. Multipole ℓ corresponds to angular scale π/ℓ degrees; the first acoustic peak at ℓ ≈ 220 marks regions compressed once, the second peak (ℓ ≈ 540) regions rarefied once, and so on.
What is the angular scale of the first acoustic peak and what does it tell us?
The first peak at ℓ ≈ 220 corresponds to an angular size of about 1 degree, which is the angle subtended by the sound horizon at recombination — the maximum distance sound could have travelled by z = 1100. The fact that this peak is at ℓ ≈ 220 (rather than higher or lower) tells us the spatial geometry of the universe is very nearly flat (Ωtotal ≈ 1.0). A curved (open or closed) universe would shift the peak position, making the CMB a sensitive probe of global geometry.
Why does increasing baryon density increase the odd-numbered peaks relative to the even-numbered ones?
Baryons add inertia to the photon-baryon fluid, enhancing compressions (odd peaks) and suppressing rarefactions (even peaks). In the simplest picture, the baryon loading shifts the zero-point of oscillation: overdense regions compress further, underdense regions decompress less. The ratio of the first to second peak height is therefore a sensitive measure of Ωbh². Planck 2018 measures Ωbh² = 0.02237 ± 0.00015 using this ratio.
Cold dark matter (CDM) does not couple to photons and does not oscillate with the baryon-photon fluid, but it contributes to the total gravitational potential. Higher CDM density deepens the gravitational wells that drive acoustic oscillations, enhancing all peaks. It also delays matter-radiation equality — the epoch when matter first dominates the energy density — which affects how quickly potentials decay after recombination (the early integrated Sachs-Wolfe effect), damping the plateau at low ℓ. The Planck measurement gives Ωch² = 0.1200 ± 0.0012.
The ordinary Sachs-Wolfe (SW) effect gives the large-angle (low ℓ) plateau of the CMB power spectrum: photons climbing out of primordial gravitational potential wells lose energy (gravitational redshift), but the denser regions were also hotter, partially compensating. The net temperature fluctuation is δT/T ≈ δΦ/3 for adiabatic perturbations. The integrated Sachs-Wolfe (ISW) effect arises from photons travelling through evolving potential wells after recombination — important at both early times (near recombination) and late times (dark energy era).
Before recombination, photon diffusion smears out density fluctuations on scales smaller than the photon mean free path — a process called Silk damping or diffusion damping. The damping scale λD ≈ 8 Mpc at recombination, corresponding to ℓ ≅ 800–1000, where the power spectrum falls exponentially. This is why the CMB power spectrum has a clear high-ℓ damping tail. The width of the damping tail constrains the baryon-to-photon ratio and the epoch of recombination.
In 1964, Arno Penzias and Robert Wilson at Bell Labs were calibrating a 6 m horn antenna in New Jersey for satellite communications when they detected a persistent microwave noise of 3.5 K from every direction in the sky. After ruling out pigeons nesting in the antenna and other terrestrial sources, they realised (with help from nearby Princeton theorists Dicke and Peebles) they had found the predicted relic radiation from the Big Bang. The discovery, published in 1965, confirmed the Big Bang model over the competing Steady State theory, and earned Penzias and Wilson the 1978 Nobel Prize.
COBE (1989–1993) confirmed the CMB is a nearly perfect blackbody at 2.735 K and made the first map of temperature anisotropies at 7° resolution (Nobel Prize 2006 to Mather and Smoot). WMAP (2001–2010) mapped the full sky at 0.2° resolution, pinning down all major cosmological parameters to percent-level precision and establishing the ΛCDM concordance model. Planck (2009–2013) achieved 5 arcminute resolution with 9 frequency bands, measuring the power spectrum out to ℓ ≈ 2500, constraining cosmological parameters to sub-percent accuracy and detecting B-mode polarisation from lensing.
CMB photons are polarised by Thomson scattering. Polarisation patterns are decomposed into curl-free E-modes (generated by both density perturbations and gravitational waves) and divergence-free B-modes (generated only by gravitational waves at linear order, or by lensing of E-modes). Primordial B-modes from inflationary gravitational waves carry the "smoking gun" signal of inflation; their amplitude is parametrised by the tensor-to-scalar ratio r, constrained to r < 0.036 (95% CL, BICEP/Keck 2021). Detecting primordial B-modes is the primary goal of next-generation CMB experiments such as CMB-S4 and LiteBIRD.
The CMB was emitted as a blackbody at T ≈ 3000 K at recombination (z ≈ 1100). As the universe expanded by a factor of 1100, photon wavelengths stretched by the same factor, reducing the temperature to T₀ = 3000/1100 ≈ 2.73 K. This is a direct consequence of the universe's expansion: T ∝ 1/a(t), where a is the cosmic scale factor. The COBE FIRAS instrument measured the CMB spectrum with exquisite precision, finding T = 2.7255 ± 0.0006 K and a spectral distortion from a perfect blackbody of less than 50 parts per million — one of the most precise measurements in cosmology.
Standard BBN predicts Li-7/H ≈ 5 × 10−10 using the baryon density from CMB measurements, but stellar observations of old halo stars find Li-7/H ≈ 1.6 × 10−10 — a factor of ~3 discrepancy. Since the CMB baryon density measurement is very robust, the discrepancy most likely lies in stellar physics (lithium depletion in stellar interiors) rather than new physics. The consistency of CMB-inferred Ωbh² with deuterium observations (within 0.2%) gives strong confidence that the CMB baryon density is correct.