What can tiny departures from a perfect blackbody record?

Light set by a single number

Heat a stove ring and it glows dull red, then orange. A hotter object gives off more light, and its brightest colour moves towards shorter wavelengths. When light and matter have traded energy for long enough, the brightness at every colour follows one curve fixed by temperature alone. That curve is called a blackbody spectrum.

The early universe was such a place. Light, electrons and atomic nuclei were packed tightly and collided constantly. As space expanded, the light cooled but kept the shape of its spectrum. Today it peaks at microwave frequencies with a temperature a little under 2.73 kelvin.

In the early 1990s the FIRAS instrument on the COBE satellite measured this spectrum. It agreed with a blackbody to within a few parts in a hundred thousand of the brightness, at wavelengths from a tenth of a millimetre to a centimetre. Chluba, 2013, section 1

Why very early energy leaves no trace

Suppose something released extra energy into this hot gas, for example particles decaying. The electrons heat up first and pass the energy to the light by scattering.

In the first couple of months the gas was dense and hot enough to do two jobs. Scattering shuffled the photons between frequencies, and other collisions created and destroyed photons. Together they rebuilt a blackbody, just a slightly hotter one. A hotter blackbody looks like any other blackbody, so the extra energy left no visible mark. In the teaching model used on this site, this limit sits near a redshift of two million, about 70 days after the start.

Two fingerprints in the spectrum

Later, photons could still be shuffled between frequencies but were no longer created fast enough. The light settled into a shape with the right energy but the wrong number of photons, so it had too few photons at low frequencies. Physicists describe this shape with a chemical potential, written $\mu$, which here simply measures the photon shortage. This applied for energy released between about two months and a few hundred years.

After a few hundred years even the shuffling slowed down. Hot electrons gave some photons a kick up in frequency but could not spread the energy evenly. The spectrum then lost brightness at low frequencies and gained it at high frequencies, crossing over near 218 gigahertz. This is called a Compton $y$ distortion, named after the scattering process.

The boundary between the two shapes is gradual: energy released at intermediate times leaves a mixture. Chluba, 2013, section 2

FIRAS found neither shape. Its published 95 per cent limits are below nine parts in a hundred thousand for $\mu$ and below 15 parts in a million for $y$. Fixsen and colleagues, 1996, abstract Both shapes carry a known share of the added energy, so either limit means that no process released more than about six parts in a hundred thousand of the light's energy between a few months and a few hundred thousand years after the start.

When the fog cleared

For the first 370,000 years, light could not travel far. Free electrons scattered it constantly, the way water droplets scatter car headlights in fog. As the universe cooled to about 3,000 kelvin, electrons and protons combined into hydrogen atoms and the fog cleared.

That temperature is surprisingly low. Freeing an electron from hydrogen takes far more energy than a typical photon at 3,000 kelvin carries. The reason is the sheer number of photons: there are about two billion for every hydrogen nucleus. Only a tiny fraction of them carry enough energy to break up an atom, but in such thin gas an electron and a proton take a long time to find each other, and those rare photons break atoms apart just as fast. A second hold-up is that each atom forming in its lowest state emits a photon that can break up a neighbour.

The last scatterings of most of the light happened within a range of a few hundred in redshift around 1,090. The Planck satellite measured the related redshift from the pattern of hot and cold spots: $z_\ast=1089.92\pm0.25$. Planck Collaboration, 2018, Table 2

Energy released during or after this time barely changes the spectrum, because little energy is needed to disturb so few atoms. It knocks some electrons free and keeps the fog from clearing fully. That shift in transparency shows up in the pattern of hot and cold spots on the sky.

What is still being looked for

The standard picture of the universe predicts distortions far below the FIRAS limits. Proposed spectrometers aim to reach them. One published forecast for a PIXIE-like mission, assuming foregrounds can be removed almost perfectly, finds that the sensitivity to $\mu$ could improve by a factor of several thousand. The same study points to a smaller guaranteed signal: faint emission lines released as hydrogen and helium atoms formed. Lucca and colleagues, 2020, sections 2.4 and 3.3

Each kind of departure points to a different time. A perfect blackbody says nothing happened after the first couple of months, or that it happened too early to leave a mark. A photon shortage would point to energy released before a few hundred years. A $y$ shape would point to later energy, and a shift in the time of transparency would point to energy released while the atoms were forming.