How did matter form in the Universe, what is the origin of inertial mass of matter, why are quarks not free, why is there only matter around us, no antimatter?


For the first 30 microsec after the Big Bang the early Universe was a hot soup that contained the elementary primordial building blocks and in particular the light quarks now hidden in protons and neutrons, and beyond this electrons, neutrinos, and even strange quarks we come back to discuss below. Gluons which are akin to photons in that they provide the interaction between color charged quarks were very abundant as well. This primordial phase lasted as long as the temperature of the Universe was more than 100,000 times that expected to prevail in the center of the Sun.
To explain how it is possible that primordial matter has different constituents as compared to matter today we need to make a brief excursion into a better understanding what empty space is exactly. Is the vacuum really empty? Though devoid of matter, vacuum hosts a new phenomenon made possible by quantum physics, complex quantum fluctuations. This quantum structure of the empty space surrounding us is the cause why quarks cannot appear as free particles, they are contained inside bubbles we call nucleons. When we compress and heat many quark bubbles, at a temperature high enough the quantum structure dissolves allowing quarks to escape forming the primordial quark-gluon plasma.

The dominant matter mass-giving mechanism is popularly called quark confinement. Light quarks are compressed by the quantum vacuum structure into a small space domain a hundred times smaller than their natural `size'. That costs a lot of energy which is the nucleon mass. The remaining few percent of mass are than due to the fact that quarks also have inertial mass provided by the Higgs mechanism. Quantitatively, nucleons which provide practically all the mass of matter derive about 95% and in some interpretations up to 99% of their mass from the interaction of quarks with the confining vacuum.

One of interesting questions that reverberates in the research program is if the transformation of quark-gluon plasma into normal `hadronic' matter is a phase transition, akin to situation seen in superconductivity, the hot phase is quark conductive, the cold phase is a quark insulator. The drastic change in the local mobility of quarks supports the notion of a phase transition but detailed numerical model computations have in past years changed sides a few times on this issue and now they indicate that there is just a smooth rapid phase transformation, there is no discontinuity in the physical process. This result if past history is a guide could still change.

Let us now look at the `beginning of time', as far back as we can and count the available degrees of freedom, a well known procedure found in particle data booklet. Before the QGP era, when the Higgs vacuum was not frozen, all particles were nearly massless, possibly retaining mass at the scale we observe today for neutrinos. Later, by the Higgs mechanism, mass was given to many of the QGP era particles. Before the Higgs vacuum froze, the Universe was pushed apart by 28 bosonic and 90 fermionic degrees of freedom. Let us verify: the doublet of charged Higgs particles has 4=2 x 2=1+3$ degrees of freedom -- three will migrate to the longitudinal components of $W+-, Z$ when the electro-weak vacuum freezes and the EW symmetry breaking arises, while one is retained in the one single dynamical charge neutral Higgs component. In the massless stage, the SU(2) x U(1) theory has 4 x 2=8 gauge degrees of freedom where the first coefficient is the number of particles gamma, Z, W^+- and each massless gauge boson has two transverse polarizations. Adding in 8_c x 2_s=16 gluonic degrees of freedom we obtain 4+8+16=28 bosonic degrees of freedom, 14 times more than we count in today's world.

The count of the primordial fermionic degrees of freedom includes three f families, two spins s , particle-antiparticle duality. We have in each family of flavors a doublet of 2 x 3_c quarks, 1-lepton and 1/2 neutrinos (due left-handedness, not implemented counting spin). Thus we find that a total 7/8 x 3_f x 2_{p/a} x 2_s x (2 x 3+1_l+1/2-\nu)=7/8 x 90 fermionic degrees of freedom, that is 15 times the count of present day. The total number of massless non-interacting particles at a temperature above the top quark mass scale, referring by convention to bosonic degrees of freedom, is is g_{\rm SM}=28+90 x 7/8=106.75

As the temperature drops the respective mass scales emerge when m = T . At each such threshold less massive particles annihilate and disappear from the thermal Universe. The entropy originating in the now massive degree of freedom is shifted into the other, still present effectively massless degrees of freedom. During each of these `reorganization' periods the drop in temperature is slowed by the concentration of entropy in fewer degrees of freedom. Finally, after $e^+e^-$ annihilation there are no significant degrees of freedom remaining to annihilate and feed entropy into photons.

The question as to why the Universe is made of matter is one of the great unsolved mysteries of physics. In the standard big-bang model, the large primordial baryon and antibaryon abundance formed at hadronization of the deconfined quark-gluon plasma (QGP) disappears due to mutual annihilation, exposing a slight net baryon number observed today. Applying the knowledge of equations of state of hadronic matter derived from the study of high energy nuclear collisions we consider quantitatively this evolution epoch of the early Universe.

The observational evidence about the antimatter non-abundance in the Universe is supported by the highly homogeneous cosmic microwave background derived from the period of photon decoupling. This has been used to argue that the matter-antimatter domains on a scale smaller than the observable Universe are unlikely; others see need for further experimental study to confirm this result.

The current small value of the baryon-to-photon ratio is the result of this near complete annihilation of the large matter-antimatter abundance. Other than a (relatively) small increase in photons during nucleosynthesis and electron-ion recombination, eta, the baryon and photon numbers should be preserved back to the period of annihilation. Considering several observables, a range of eta is established, the latest WMAP result is eta = n_B/n_gamma = 6.1^{+0.3}_{-0.2} 10{-10}.

The importance of eta is that it allows to determine the value of entropy per baryon S/B in the Universe, which is conserved in adiabatic evolution. At present the entropy is dominated by photons, and nearly massless (decoupled) neutrinos. It is straightforward to compute the entropy densities of these species from the partition function, and then to convert \eta to S/B using the photon number density. We obtain a value of S/B = 8.0/eta=1.3 \pm 0.1 10^{10}, assuming a lower neutrino than photon temperature (photons are reheated by e^+e^-annihilation), and counting only left/right-handed neutrinos/antineutrinos.