Thermodynamic Evolution of the Universe

The evolution of the Universe, in the framework of the hot Big Bang model, can be conveniently described in terms of equilibrium thermodynamics, following the evolution of the number density of different kinds of particles and radiation. Certainly, this is not possible before the Planck era ( $\Pl{t}\sim\vu{10^{-43}}{s}$ or $\Pl{T}\sim\vu{10^{19}}{\GeV}$), where a quantum mechanical treatment of gravity is needed, but during much of the history of the Universe, conditions of thermodynamical equilibrium subsisted. The particles populating the Universe at a certain time, or, equivalently, at a certain energy, can be classified as being relativistic ($m \ll T$) or non-relativistic ($m \gtrsim T$) depending on their rest mass. At very early times all particles were relativistic and the Universe was radiation dominated. Due to the adiabatic expansion, the temperature decreases according to

$$t [\mr{s}] \sim \frac{1}{T^2[\MeV^2]}.$$

A given particle species drops out of thermodynamic equilibrium (``freeze out''), when the temperature dependent reaction rate $\Gamma \propto \ev{\sigma v}$ drops below the Hubble expansion parameter $H$. If this is the case, the abundances of these particles and antiparticles are no longer coupled to the thermal bath and they evolve differently from the photon abundance.

Several such phase transitions have occurred during the evolution of the Universe in the Big Bang model. As will be discussed in section 1.4.1 there are hints favouring the occurrence of a GUT (Grand Unified Theory) phase transition at $\sim 10^{14}$ to 10^16, after which fermions and bosons become fundamentally different particles and the very heavy gauge bosons $X$ and $Y$ decouple.

When the Universe is cooled down to 100 the electroweak transition occurs, $W$ and $Z$ bosons become massive through the Higgs mechanism and $SU(2)_L \otimes U(1)_Y$ breaks down to the $U(1)_{EM}$ symmetry. As will be seen in section 1.4.2, the order of this phase transition is crucial for a viable explanation of the baryonic asymmetry in the Universe.

Around $T\sim\vu{1}{\GeV}$ quarks and antiquarks annihilate, possibly with a slight excess of quarks. Subsequently, at $T\sim\vu{200}{\MeV}$, they get confined into mesons and baryons leading to a baryon-to-photon ratio of $10^{-10}$. The quark-antiquark asymmetry seems quite unnatural and we are going to study this issue in greater detail in the next sections.

When the Universe had a temperature of $T\sim\vu{1}{\MeV}$, neutrinos and antineutrinos ceased to interact with electrons and positrons and decoupled from the electromagnetic plasma. They are in principle detectable today at a lower temperature than the CMB, since the photons are slightly heated in later processes. Shortly afterwards, the temperature fell below the rest mass of the electron and the frequent annihilations of electron-positron pairs increased the number of photons.

At $T\sim\vu{0.1}{\MeV}$ nuclei formation starts to become energetically favourable. The abundances of the lightest elements in the Universe are predominantly determined by the conditions at this time ( $t\sim\vu{1}{s}$). A consistent picture has been developed to explain the observed abundances which goes under the name of primordial Big Bang nucleosynthesis.

The contribution to the energy density from radiation drops faster ( $\vi{\rho}{rad} \sim R^{-4}$) than that from matter ( $\vi{\rho}{m} \sim R^{-3}$), and therefore at a certain time both contributions are equal. This matter-radiation equality must have existed at about $T\sim\vu{1}{\eV}$, i.e. at a time 4 ×10^4, whereas today the energy density contribution of matter exceeds that of radiation by a factor 4000.

Only at about $t\sim\vu{1.5 \times 10^5}{yrs}$ nuclei and electrons could compound to neutral atoms in what is known as ``recombination'' (the choice of this term seems a bit inappropriate, since it is their first combination).

Since the photons are no longer scattered off free electrons, the Universe becomes transparent. Photons, after undergoing their ``last scattering'' at , propagate freely and can be detected now, redshifted, as the 3K CMB. The small temperature inhomogeneities ( $\delta T/T < 10^{-5}$ [17]) of the CMB are directly related to the matter density inhomogeneities which subsisted at the time of last scattering and are thought to be responsible for the formation of galaxies through gravitational clumping.