Lesson 2 of 6 · Hot plasma, cooling & evidence
Run the thermal history backward
10 minute lesson · 3 checks along the way
Your goal for this lessonUse explicit expansion assumptions to compare radiation temperature and density, while distinguishing tested early history from uncertain beginnings.
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A hot beginning is a physical model
The describes an early, dense state that expanded and cooled. It is supported by several linked observations, including cosmic expansion, light-element abundances, and relic radiation with a nearly thermal spectrum. These are different tests of a connected history. The model is not merely the assertion that everything exploded from one location, and its success does not by itself settle what an absolute beginning means.
At high temperatures, matter was a with freely moving charged particles. Collisions and radiation maintained conditions unlike a modern cold interstellar cloud. As the temperature fell, different reactions ceased to keep up with expansion. Some particles survived, light nuclei formed, and much later electrons could remain bound in neutral atoms. Cooling therefore changed which physical processes could operate, rather than simply dimming an unchanged collection of stars.
Follow an expanding volume carefully
Consider a region following the average expansion after significant photon production and energy injection have become negligible. Its physical linear dimensions grow with a, so its volume grows with a³. Conserved particles spread over that growing volume. For freely propagating photons, wavelength also grows with a; energy per photon, E=hc/λ, decreases in inverse proportion. Both effects enter radiation energy density.
For an initially thermal photon bath under these assumptions, radiation temperature follows T∝1/a. follows 1/a³, and follows 1/a⁴. The fourth power includes the extra loss of energy per photon, beyond dilution alone. These relations do not say that every gas or star cools at the same rate, or that an expanding universe has a simple fixed total energy in a universal container.
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Work through a decision
Separate dilution from photon energy
Imagine the scale factor doubles between two chosen epochs. Start with an illustrative radiation temperature of 6 kelvin, photon number density of 80 units, and radiation energy density of 160 units. The later temperature is 3 kelvin. The volume factor is 2³=8, giving a photon number density of 10 units. Each photon’s energy also halves, so radiation energy density becomes 160/(8×2)=10 units.
If conserved nonrelativistic matter in that region initially has rest-mass density 80 units, its later rest-mass density is 10 units: dilution supplies the factor of eight without a of each particle’s rest mass. These invented numbers compare scaling laws, not measured cosmic inventories. Extending the exercise across substantial particle annihilation or another heat-injection episode requires accounting for transferred energy instead of blindly applying the same temperature rule.
Track two reasons radiation density falls
Original ratio diagram for negligible photon creation or energy injection and conserved nonrelativistic rest mass. Every bar is normalized to its own initial value of one; the bars do not compare absolute densities of different components.
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Test the thermal record, then mark the frontier
COBE helped turn the relic radiation into a precise observational test. Its instruments measured the sky’s microwave properties, including the thermal spectrum and tiny directional variations. The preparation photograph shows a spacecraft being cleaned, not the primordial plasma. Establishing a cosmic signal required calibrated detectors and control of contamination from the instrument, Earth, and other sky emission. Hardware made the measurement possible; the photograph alone does not supply its numerical result.
proposes an earlier phase of accelerated expansion and offers explanations for several large-scale features, but its detailed mechanism remains unsettled. Extrapolating equations toward arbitrarily high temperature is not equivalent to observing that era. Keep the well-tested hot phases distinct from candidate explanations for what preceded them. A useful timeline labels both the evidence supporting each stage and the physical assumptions that become uncertain farther back.
COBE undergoing cleaning at NASA Goddard before shipment for final integration in 1989. The photograph records spacecraft preparation; its later microwave measurements tested the relic radiation spectrum and directional variations.
Look closely
Identify the spacecraft and the surrounding preparation work. Can this photograph by itself establish that the sky has a thermal microwave spectrum?
See what to notice
No. It documents the apparatus and its preparation. Establishing a thermal spectrum requires calibrated sky measurements across wavelengths, with instrument emission and other signals controlled.
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Put it together
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