Early-universe cosmology on The Broken-Born program

The radiation era: thermal history and N_eff

Mon, 01 Jan 0001 00:00:00 +0000

The radiation era is the early period in which the universe’s energy was dominated by radiation and by particles moving at nearly the speed of light, so that the temperature alone set how fast the universe expanded. Three standard quantities describe it. The first is the expansion rate as a function of temperature, H = 1.66√g* T²/M_Pl. The second is the entropy density: it falls as the volume grows, so the ratio of a relic’s number density to it, the yield, stays fixed once the relic is no longer made or destroyed. The third is N_eff, the effective number of light neutrino-like species, which nucleosynthesis and the cosmic microwave background both measure. The program uses these quantities twice: in its optional prediction of fewer effective species from the conjugate universe, and in the review that retired its soliton dark-matter candidate, whose central error was a dropped factor of the radiation-era expansion rate.

A hidden sector at its own temperature

Mon, 01 Jan 0001 00:00:00 +0000

A hidden sector at its own temperature is a collection of particles and forces that takes no part in the strong, weak or electromagnetic interactions of ordinary matter and, because nothing lets it exchange energy with our plasma, keeps a temperature T_h of its own, which can differ from ours. The ratio of the two temperatures, written ξ, is set when the universe is reheated after inflation, or when the two sectors last exchanged energy; afterwards it changes only when the heavy particles of one sector annihilate and their entropy heats the light particles of that sector alone. The ratio fixes how much extra radiation the hidden sector adds in the radiation era, an excess that grows as ξ⁴ and that nucleosynthesis and the cosmic microwave background measure. It also fixes when, by our clock, the hidden particles freeze out, and it lasts only while no coupling between the sectors, such as a Higgs portal or kinetic mixing, brings the two plasmas into contact. The program met this physics in the review of its soliton dark-matter candidate, whose hidden sector contained a massless hidden photon: the withdrawn manuscript #14 required ξ < 0.77, and round 3 corrected the bound to ξ < 0.760. The candidate is dead, and these numbers are kept as its record.

Big Bang nucleosynthesis

Mon, 01 Jan 0001 00:00:00 +0000

Big Bang nucleosynthesis (BBN) is the formation of the lightest atomic nuclei, mostly helium-4 with small amounts of deuterium, helium-3 and lithium-7, in the first minutes of the hot early universe. Its outcome depends on the expansion rate at the time. Neutrons and protons stop converting into each other once the weak interactions that convert them become slower than the expansion, and nearly every neutron left when nuclei can survive ends up in helium, so the primordial helium abundance measures how fast the universe was expanding in its first minutes. That makes nucleosynthesis a test of two things at that time, the radiation content, counted as the effective number of light species N_eff, and the strength of gravity; it also limits particles that decay or release energy during or after it. The program uses this timing in two places. The lab notebook dates an optional step in the effective strength of gravity, G_eff, “before BBN” (row 10), and the round-3 review found that the light hidden fermion ψ of the retired soliton candidate would, at MeV masses, still have been freezing out during nucleosynthesis, so the lower edge of its relic window was wrong.

The cosmic microwave background

Mon, 01 Jan 0001 00:00:00 +0000

The cosmic microwave background (CMB) is the thermal radiation left over from the hot early universe, released when the universe became transparent. Until then electrons and nuclei formed a plasma in which light scattered constantly; once the plasma had cooled enough for them to combine into neutral atoms, an event called recombination, the light travelled freely, and the expansion has since stretched it to microwave wavelengths. Small differences in its temperature across the sky preserve the sound waves that ran through the plasma until that moment. Their pattern measures the densities of ordinary and dark matter, the length of the ruler that galaxy surveys use, and the amount of radiation in the early universe, counted as the effective number of light species N_eff. The program has used the CMB in the round-3 review of its retired soliton dark-matter candidate: the Planck satellite’s 2018 measurement of N_eff bounded the candidate’s extra radiation, and Planck’s dark-matter density is the target of the review’s abundance calculations. Row 10, the program’s optional early-universe prediction, names a proposed CMB experiment, CMB-S4, as its probe.

The relic yield Y = n/s and entropy dilution

Mon, 01 Jan 0001 00:00:00 +0000

The yield of a relic is its number of particles per unit of entropy, Y = n/s: the number density n divided by the entropy density s of the hot plasma that filled the early universe. While nothing creates or destroys the particles, both quantities fall in inverse proportion to the volume as the universe expands, so the yield stays fixed, and multiplying it by today’s entropy density gives the relic’s density now. Entropy dilution is the standard way a yield can still fall after it has been fixed: a large release of entropy into the plasma, such as the decay of heavy particles that dominated the universe for a time (a period called early matter domination), divides every yield fixed before the release by the factor by which the entropy grew. Both entered the review that retired the program’s soliton dark-matter candidate. Its count of monopoles per unit entropy had dropped a factor of about 4.6×10³ that comes from the expansion rate (Obituary: the Kibble normalization). Counted correctly, monopoles at the candidate’s benchmark mass could make up the dark matter only with a dilution factor of at least 10³–10⁴ left free, and the program rejected that route because a free factor removes the mass prediction.

Inflation, reheating and entropy dilution

Mon, 01 Jan 0001 00:00:00 +0000

Inflation is a proposed early period of extremely rapid, accelerating expansion, which thins any relics produced before it until essentially none remain in the observable universe; reheating is its end, when the energy that drove inflation turns into hot particles and sets the starting temperature of the radiation era. Relics made after reheating can still be thinned later if something releases a large amount of entropy into the plasma, for example the decay of heavy particles that dominated the universe for a time, a period called early matter domination. The program uses this physics in two places. Inflation is the standard reason no magnetic monopoles of our own sector are seen, which is one of the two reasons the early claim that the conjugate sector explains their absence is dead. And late dilution was the only way the retired soliton dark-matter candidate could have kept its heavy mass, a route the program rejected because it removes the mass prediction.

Gravitational waves from phase transitions

Mon, 01 Jan 0001 00:00:00 +0000

A first-order phase transition in the early universe proceeds by bubbles of the new phase forming, growing and colliding, much as water boils, and the collisions and the sound waves they leave in the plasma produce gravitational waves that arrive today from every direction as a random background. The waves’ characteristic frequency is set at the transition by its temperature and duration and has been stretched by the expansion ever since, so a transition at a higher temperature leaves a higher frequency today. A related background, the primordial one, comes from inflation, and its spectrum records how fast the universe expanded at each early epoch. The program met this physics in two places: the hidden-sector transition of its retired soliton dark-matter candidate, whose signal would have lain far above the frequencies of current detectors, and an early idea, since dropped, that its conjugate gravity sector would leave a step in the primordial gravitational-wave background.