Early-universe cosmology

Early-universe cosmology is the physics of the hot, dense first stages of cosmic history, when the universe was filled with radiation whose temperature fell as it expanded. This section holds established physics only: the thermal history of that radiation era and the count of light particle species it fixes, including the species of a hidden sector at its own temperature; the two observations that measure them, Big Bang nucleosynthesis and the cosmic microwave background; the yield that carries a relic’s abundance to the present, and inflation and the later processes that thin out relics; and the gravitational waves that a phase transition or inflation would leave. The program uses this physics in two places: its optional prediction of an early change in the strength of gravity and in the effective number of light species (row 10), and the review that retired its soliton dark-matter candidate, which turned on how many relics the early universe makes, how far later processes could dilute them, and how cold the candidate’s hidden sector had to be.

Literature only: all seven pages are established physics, so the section ranks no claims of the program’s own; those are tracked in the registers of claims that stand, the graveyard, open problems and the queue, conjectures and superseded statements. Each page says where the program used its physics, with the program’s tags and machine checks: the Friedmann coefficient 1.66, the one-species normalization of ΔN_eff, the dark-radiation bound and the corrected upper end of the retired candidate’s gravitational-wave band are checked by the soliton-obituary script. Most of the numbers on these pages come from the retired soliton episode and are kept as its record.

Map#

The pages run from the thermal history that the others assume and a sector that keeps a temperature of its own, through the two observations that measure them, the yield that carries a relic’s abundance forward and the processes that thin relics, to the gravitational waves that record the early expansion.

The radiation era: thermal history and N_eff comes first. It derives the expansion rate H = 1.66√g* T²/M_Pl from the Friedmann equation and the energy density of relativistic species, sets out the two Planck-mass conventions, and explains entropy conservation and the yield Y = n/s by which relic abundances are carried to the present. It then defines N_eff, the effective number of neutrino species, and ΔN_eff for extra light species, including a hidden sector at its own temperature, and says how nucleosynthesis and the cosmic microwave background measure them. The program’s uses follow: row 10’s negative ΔN_eff from a closed dual space, and, in the retired candidate, the dropped factor (1.66√g*)³ in the Kibble yield, the dark-radiation bound ΔN_eff < 0.286 with the hidden temperature ratio ξ < 0.760, and freeze-out during nucleosynthesis.

A hidden sector at its own temperature follows a sector that exchanges no energy with ours. It keeps its own temperature T_h, and the ratio ξ = T_h/T is set at reheating or when the sectors last exchanged energy; afterwards each sector conserves its own entropy, so the ratio changes only when one sector’s heavy particles annihilate. The ratio fixes the dark radiation the sector adds, an excess growing as ξ⁴, and when by our clock its particles freeze out, and a portal such as a Higgs portal or kinetic mixing that brings the plasmas into contact erases it. The program met this physics only in the retired soliton candidate: the withdrawn manuscript #14 required ξ < 0.77, and round 3 corrected the bound to ξ < 0.760 [V].

Big Bang nucleosynthesis (BBN) is the formation of the light nuclei in the first minutes: neutron–proton freeze-out, the deuterium bottleneck and helium. The helium abundance measures the expansion rate at that time, and through it the radiation content and the strength of gravity together; deuterium measures the baryon density; and the abundances limit light particles, late decays and entropy release. The program dates row 10’s optional step in G_eff “before BBN”, and the round-3 referee found that the retired candidate’s light fermion ψ 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 (CMB) is the radiation released at recombination, when the universe became transparent. The page explains its blackbody spectrum and the acoustic peaks and damping tail of its anisotropies, and what they measure: the baryon and dark-matter densities, which calibrate the ruler of baryon-acoustic-oscillation surveys, and N_eff, through the damping and the phase shift that free-streaming neutrinos leave. The program’s uses are mostly the retired candidate’s record: Planck 2018’s N_eff interval behind the round-3 bound ΔN_eff < 0.286, and the dark-matter density at which the review’s abundance calculations aim. Row 10 names a planned experiment, CMB-S4, as its probe.

The relic yield Y = n/s and entropy dilution gives the measure by which a relic’s abundance is carried from the early universe to today: its number per unit entropy, fixed once the particles are no longer created or destroyed and converted to a present density through today’s entropy density s₀. It derives the Kibble yield n/s = p(T_c/M_Pl)³, with p = 104.31 for one defect per Hubble volume, the normalization whose dropped factor (1.66√g*)³ was the central error of the retired candidate, and explains entropy dilution: an entropy release, such as the decays that end a period of early matter domination, divides every yield fixed before it. At the candidate’s benchmark mass the monopoles could have made up the dark matter only with a dilution factor of at least 10³–10⁴ left free, and round-3 Decision 2 rejected that route because a free factor removes the mass prediction.

Inflation, reheating and entropy dilution covers how relics are thinned. Inflation dilutes relics formed before it; reheating starts the radiation era and decides whether a transition leaves defects at all; and a later period of early matter domination, ended by decays, divides every earlier yield by the entropy it releases, the mechanism the yield page sets out. The page records what a colder reheated hidden sector would have needed, a visible reheating temperature above v/ξ and a reheating mechanism that was never specified, and the isocurvature it could carry. In the program, inflation is the second reason the explanation of the monopole null result is dead, and dilution was route (b) for the soliton candidate, rejected in round-3 Decision 2 because a free dilution factor removes the mass prediction. The lab notebook’s polarization-genesis sketch also sets its decisive event at reheating.

Gravitational waves from phase transitions closes the section. It describes first-order transitions and their parameters, the three sources of the waves, the redshift of the peak frequency to today, f₀ = 1.65×10⁻⁵ Hz × (f*/H*) × (T*/100 GeV) × (g*/100)^{1/6} as the scripts code it, the amplitude, and the primordial background from inflation, whose spectrum maps the early expansion rate. The program met it twice: the retired candidate’s hidden transition, whose band the round-3 referee recomputed as 1.35×10⁵–2.47×10⁷ Hz and whose upper end ruling 5 moved to 3.2×10⁷ Hz; and the spectral step in the primordial background that the lab notebook predicted and version 1 dropped.

Boundaries#

The Friedmann equation and the homogeneous expansion are Friedmann cosmology and minisuperspace. The program’s own early-universe prediction is row 10: an early step in G_eff, derived from the conjugate gravity term on the duality dictionary. How defects form in a cooling universe and the monopole relic problem are in magnetic monopoles, with the Kibble mechanism and the monopole problem. Relic-abundance mechanisms are relic abundance mechanisms, with thermal freeze-out on a page of its own, and the production of a coherent light field is the misalignment mechanism. The retired candidate’s own thermal record is the hidden sector’s thermal history, its abundance is overproduction at the benchmark, and its obituary is Obituary: superheavy conjugate solitons.