Evidence for a hot, dense early Universe

A smaller scale factor means a hotter radiation field

Take a freely propagating photon in a smooth expanding background. Between two epochs its wavelength changes in proportion to the scale factor a. If a doubles, the wavelength doubles and the photon energy halves. Reversing this comparison gives a shorter wavelength and a larger photon energy at the earlier, smaller scale factor.

For a radiation field with a thermal, or blackbody, spectrum that evolves without disturbance, its temperature T changes as T ∝ 1/a. The proportionality symbol means that the product Ta stays constant over this comparison. Temperature is measured in kelvin, K. The next lesson explains the spectral shape that makes this temperature meaningful.

Choose a reference epoch with scale factor a_ref and temperature T_ref. Define q = a/a_ref. At q = 1/2, T/T_ref = 2; at q = 2, T/T_ref = 1/2. These ratios do not supply years, an expansion law or a present-day temperature. They describe how the radiation changes between specified stages.

Continuing backward through the observed expanding history therefore points toward hotter conditions. A denser, hotter earlier state is the central physical idea in the hot Big Bang description. It is not an explosion from one location into an otherwise empty surrounding room.

Density and photon energy provide separate changes

A length ratio q gives a following-volume ratio q³. For a conserved population of nonrelativistic matter, the rest-energy density is proportional to q⁻³. At half the reference length scale, there are eight times as many of those particles per volume and eight times their rest energy per volume.

For conserved freely propagating photons, the number per volume also changes by q⁻³, while each photon’s energy changes by q⁻¹. Multiplying gives a radiation energy-density ratio q⁻⁴. At q = 1/2 that ratio is 16, rather than 8.

The table isolates these effects over an interval without energy transfer, photon production or changes in the particle species. Real early history includes reactions and changes in which species behave as nonrelativistic matter. One must include those processes when crossing their relevant epochs; the simple table cannot be extrapolated unchanged to arbitrarily high temperature.

Greater energy per photon affects which interactions can occur. Under sufficiently hot conditions, atoms cannot remain neutral in the way they do in a cool gas. Still earlier nuclear reactions affect the mixture of light nuclei. Those are physical mechanisms that connect a thermal history with observations, rather than a verbal claim that everything used to be hot.

Different observations test different links

Expansion measurements connect redshift, distance and the evolving geometry. They establish a changing large-scale background within a cosmological interpretation. Expansion alone does not establish a thermal spectrum, predict every nuclear abundance or reveal a time-zero event.

The cosmic microwave background supplies a different test. Its nearly thermal spectrum is a relic of an earlier radiation field. COBE/FIRAS compared the sky spectrum with calibrated thermal radiation and found close agreement after treating foreground emission and instrumental effects. That is a measured property, rather than simply a blackbody curve drawn because a model requests one.

Primordial nucleosynthesis supplies another connection. In a hot expanding early phase, nuclear reaction rates and the time available for them affect light-nucleus abundances. Observations of deuterium in carefully selected, metal-poor gas can test these predictions. The 2018 Cooke, Pettini and Steidel study is one example of such an abundance determination.

The gas is observed long after the nuclear reactions. Calling an abundance primordial requires inferring and controlling for later processing, not looking directly at the original reaction epoch. Nuclear-rate uncertainties and observational selection also matter. Success for deuterium is not a statement that every light isotope agrees perfectly; the lithium discrepancy requires its own discussion later.

Agreement across mechanisms matters

The evidential strength comes from asking one physical history to account for several kinds of measurement. The expansion history, the relic spectrum and abundance tests are connected but use different instruments and mechanisms. A proposal that accounts for only one observation must still face the others.

This is not three votes cast for a label. Each comparison can fail in a specific way: a wrong thermal history may change predicted nuclear yields; a large later injection of energy can alter a radiation spectrum; a wrong expansion history can change a distance–redshift relation. A useful model makes those links quantitative and exposes what would count against it.

The thermal spectrum was established through early interactions, including processes that could create or absorb photons. Its formation predates the recombination-era last scattering discussed later in this chapter. The background did not acquire its whole photon population at the moment neutral atoms became common.

An early phase is different from an observed origin

The hot Big Bang description gives an evolving early Universe and consequences that can be tested. It does not make the earliest mathematical extrapolation a direct observation. Extending a classical model toward a singular limit raises questions about the model’s domain, especially when quantum-gravity effects may matter.

Nothing in the ratio table allows q = 0: its inverse powers would diverge, and its assumptions were never established there. One cannot convert that divergence into a photograph of creation, a proof of emergence from nothing or a measurement of what came before.

A first reading can stop at the causal chain: expansion changes wavelengths and densities; early interactions set radiation and nuclear properties; later measurements test the resulting predictions. The advanced chronology and origin questions remain in the learning plan without being silently settled by the word Big Bang.

Worked reasoning

Try the reasoning

1. Does expansion by itself demonstrate that the radiation has a blackbody spectrum?

   Show the answer and reasoning

   No. The spectrum is a separate observable to measure and explain.

   A wavelength-scaling rule does not determine the initial distribution of photon energies.

2. Does observing deuterium absorption in remote gas mean the telescope sees nucleosynthesis taking place?

   Show the answer and reasoning

   No. It measures later gas whose inferred primordial abundance can test early-reaction predictions.

   Later processing, selection and measurement uncertainties must be considered.

3. May the ideal ratio table be used at q = 0 to establish a physical origin?

   Show the answer and reasoning

   No. q = 0 lies outside the stated comparison and its inverse powers are undefined there.

   A model extrapolation beyond its justified domain does not become an observation.

What to carry forward

• A supported hot early history connects expansion, cooling, radiation and nuclear processes.
• Relic-spectrum and light-element observations test different mechanisms within that history.
• Evidence for an early hot phase does not by itself observe time zero or settle an ultimate origin.