Reason for negligible chemical potentials of different particles in early universe For the early Universe at high temperatures, the chemical potential is assumed to be zero for all types of particles is negligible. Why is this true?
 A: In the current universe baryon and lepton number are conserved. This means that there are two chemical potentials, $\mu_B$ and $\mu_L$. We believe that the universe has a net-baryon density, and $\mu_B\neq 0$. We don't know the net lepton number of the universe, because the net lepton number of the neutrino background cannot be measured.
The net-baryon number of the universe is non-zero, but small. The current baryon-to-photon ratio is of order a few times $10^{-10}$. Compared to baryon (proton and neutron) rest mass the current temperature is essentially zero, so the current baryon chemical potential is a tiny amount larger than the baryon rest mass.
We can take this information and extrapolate to the past. In the past the universe was much hotter, but baryon and lepton number are conserved. At temperatures above $T\simeq 200$ MeV the baryon number is no longer in protons/neutrons, but in approximately massless quarks, which carry 1/3 baryon number. Since all species of particles (leptons, quarks, photons) are approximately massless, the total densities of quarks, leptons and photons are now comparable. This means that the conserved net-quark density is much smaller than the total density of quarks. This implies that $\mu_B<<T$, and the effect of $\mu_B$ on the pressure and energy density of the early universe can be ignored.
A: EDITED  after comment by KF Gauss , as I had not looked at the definition of chemical potential and just took the adjective meaning.

In thermodynamics, chemical potential of a species is energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant

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Chemical potential is assigned also to aggregates of subnuclear particles.

In recent years, thermal physics has applied the definition of chemical potential to systems in particle physics and its associated processes. For example, in a quark–gluon plasma or other QCD matter, at every point in space there is a chemical potential for photons, a chemical potential for electrons, a chemical potential for baryon number, electric charge, and so forth.


In the case of photons, photons are bosons and can very easily and rapidly appear or disappear. Therefore, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero. Since this process occurs extremely rapidly (at least, it occurs rapidly in the presence of dense charged matter), it is safe to assume that the photon chemical potential is never different from zero.


Electric charge is different because it is conserved, i.e. it can be neither created nor destroyed. It can, however, diffuse. The "chemical potential of electric charge" controls this diffusion: Electric charge, like anything else, will tend to diffuse from areas of higher chemical potential to areas of lower chemical potential. Other conserved quantities like baryon number are the same. In fact, each conserved quantity is associated with a chemical potential and a corresponding tendency to diffuse to equalize it out.


In the case of electrons, the behaviour depends on temperature and context. At low temperatures, with no positrons present, electrons cannot be created or destroyed. Therefore, there is an electron chemical potential that might vary in space, causing diffusion. At very high temperatures, however, electrons and positrons can spontaneously appear out of the vacuum (pair production), so the chemical potential of electrons by themselves becomes a less useful quantity than the chemical potential of the conserved quantities like (electrons minus positrons).

There is this similar question , whose answer has been accepted, with some calculations.
In this publication :

Properties of baryonic, electric and strangeness chemical potentials and some of their consequences in relativistic heavy ion collisions

Abstract

Analytic expressions are given for the baryonic, electric and strangeness chemical potentials which explicitly show the importance of various terms. Simple scaling relations connecting these chemical potentials are found. Applications to particle ratios and to fluctuations and related thermal properties such as the isothermal compressibility kappaT are illustrated. A possible divergence of kappaT is discussed.

In the introduction :

This paper focuses on the behavior and properties of the three chemical potentials $μ_B, μ_Q,μ_S$ (where B is baryon number, Q charge, S strangeness). Simple analytic expressions are developed for$μ_B, μ_Q,μ_S$, which explicitly show the importance of various quantities that appear. These expressions are then used to study particle ratios, particle asymmetries such as the baryon/antibaryon asymmetry, fluctuations and thermal properties of hadronic matter. Results based on a Hagedorn resonance gas model are developed. A possible divergence of the isothermal compressibility is discussed. The critical exponent associated with this divergence is related to properties of the vanishing of chemical potentials withTand the mass spectrum of excited states.

italics mine
So chemical potentials for species of particles can be calculated, and as far as I understand, for very high temperatures are assumed to be negligible mainly because of the way conservation laws constrain them, as these specific calculations show. It will depend at what time of the cosmological phase space the chemical potentials are assumed close enough to zero to be negligible.
