= Solution
The <cosmic microwave background> has an almost perfect <blackbody spectrum> at about $2.725\ \mathrm{K}$. This is strong evidence for an earlier hot, dense phase in which <radiation> thermalized, followed by expansion that redshifted the <photon> spectrum while preserving its Planck form. <COBE> <FIRAS> compared the sky with a precision reference <blackbody>; instrument <temperature>, gain, foregrounds and calibrator emissivity were crucial controls. Agreement with a <blackbody> constrains substantial late <energy> injection or photon-production distortions.<Nobel Lecture: From the Big Bang to the Nobel Prize and beyond by John C. Mather>[FIRAS measurement and external-blackbody calibration account]{ref}
After subtracting the dominant dipole associated mainly with observer motion, anisotropies at the level of roughly $10^{-5}$ reveal primordial structure. <COBE> DMR established large-angular-scale anisotropy; multifrequency measurements and independent maps were needed to distinguish it from Galactic emission and instrumental artifacts.<Structure in the COBE Differential Microwave Radiometer First-Year Maps by George F. Smoot and others>[L1–L5, statistical and systematic checks]{ref} Approximate isotropy supports a homogeneous background model under the usual cosmological assumptions, but isotropy at one observing position is not alone a proof of spatial homogeneity everywhere.
The <temperature> <CMB angular power spectrum> has multiple acoustic peaks. Their coherent pattern follows oscillations in the pre-recombination <photon-baryon fluid>. Peak positions compare the <sound horizon> with <angular diameter distance> and hence constrain geometry together with expansion parameters. Relative peak heights test <baryon> inertia, matter–<radiation> equality and gravitational-potential evolution, motivating both baryonic and nonbaryonic matter. <Cosmic microwave background diffusion damping> suppresses small-scale power. <Cosmic microwave background polarization> and <temperature>–polarization correlations provide further tests of scattering, acoustic phase and <reionization>; <gravitational lensing> remaps the observed pattern and probes intervening structure.
By the time of this examination, the Planck 2013 <temperature> and lensing analysis supported a spatially flat six-parameter model with <cold dark matter> and a <cosmological constant>. This is a joint fit within an explicit model, not an inference that each peak uniquely measures one parameter.<Planck 2013 results. XVI. Cosmological parameters by Planck Collaboration>[Abstract and cosmological parameter/extension analysis]{ref} Foreground separation requires frequency coverage, sky masks, beam and noise characterization, and consistency across instruments. The primary microwave background has geometric and other parameter degeneracies, so acoustic-ruler, supernova and structure observations are valuable complements. \b[The spectrum establishes a thermal hot-universe history; anisotropy and polarization constrain its geometry, contents and <primordial perturbations>.] None of these observations by itself demonstrates a unique <cosmic inflation> mechanism.
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