Andrei Sakharov (1921 - 1989): "... Like faint glimmers of light in the dark, we have emerged for a moment from the nothingness of the dark unconsciousness of material existence. We must make good the demands of reason and create a life worthy of ourselves and of the goals we only dimly perceive."

The very early universe could have consisted only of bosons. Bosons can create fermion-antifermion pairs at high energy density, but they would presumably rapidly annihilate back to bosons. Yet we live in a universe where dark matter, baryons and leptons do exist, with no antiparticle counterparts anywhere, and the ratio, for example, of baryons to photons is around 6 × 10⁻¹⁰. Because the amount of dark matter is comparable to the amount of baryons, it is tempting to think they have a common origin. In order to be “frozen in,” matter must have originated within the first 10⁻¹² sec of the universe. [In what follows, we use B for baryon number instead of our usual A.]

There are three vital discrete symmetry operations in fundamental physics. The charge conjugation operator C changes the sign of a particle's charge, or other additive quantum numbers. The parity operator P changes the parity of a state or particle. The time reversal operator T changes the direction of time. These operators are vital to fundamental physics because ALL PHYSICAL SYSTEMS must be invariant under the combined operation of P, C and T. That is, for any meaningful Hamiltonian H, [PCT,H] = 0. In order for a process to produce more particles than antiparticles, the process must fail to commute with CP. This is not a problem because it can and will still commute with PCT. However, one of the big unsolved problems in physics is that in the Standard Model, there is nothing that would conserve CP. And yet nearly every strong process that has ever been studied conserves CP! This is the main stumbling block in applying the Standard Model to processes that create excess leptons and quarks from the decay of heavy bosons.  Another mystery is that there is nothing known in theoretical physics that would require conservation of baryon number B or lepton number L, yet we do not see (for example) protons decay... they seem to be stable, at least for 10³⁵ or more years!  This is  not a problem for the Standard Model because it conserves only B -  L, not B or L individually!

Sakharov Conditions for Fermion Synthesis: • There must be processes that directly violate conservation of B and L. • There must be both C- and CP-violating processes. • The interactions must occur beyond thermal equilibrium.
(For example C-violating processes could produce excess “handedness,” but direct CP violation is needed to generate excess fermions.)


Since the early 1970s, theorists have sought descriptions which unify the strong interaction with the electroweak interaction, and even more ambitions descriptions which include gravity. The record so far is a record of total, absolute and complete failure.  Such ideas seem misguided, and tend to muddle efforts to imagine processes that could result in net amounts of dark and ordinary matter.

The usual suggestions for generating leptons go beyond the Standard model, which may or may not be surprising, but we would probably need to go beyond the Standard model anyhow, at some point.



There are high energy electroweak processes in the Standard Model that, for example, convert anti-leptons to quarks, but in those nonperturbative processes, B - L is conserved. There is a consensus that not nearly enough CP violating processes are known to understand fermion production in the early universe. In fact the estimate based on existing CP-violating processes is about 10 powers of 10 too small! One suggested solution is to concentrate on generating leptons and depend upon B - L conserving processes to convert many leptons to quarks. However, what about dark matter? It is highly suggestive that Ω_b/Ω_dm is about 0.2. Presumably dark matter and baryons need a unified theory of their origins... difficult to accomplish when the nature of dark matter is unknown! Two energy scales of interest in trying to think up processes are the Planck Scale, about 2.4 × 10¹⁸ GeV, and the “Grand Unification” scale of about 2 × 10¹⁶ GeV. At the Planck scale all four interactions might have equal coupling constants, while at the GUT scale the strong, weak and electromagnetic coupling constants might all be equal.  Or not.  And essentially nothing is known about these regions.   It's not surprising, then, that a lot of attention has been directed to the electroweak scale of only 250 GeV, and to the consequences of the breaking of electroweak symmetry.  This is the only actual "unification" transition we have ever seen!  A very interesting SM solution to the EW field equations shows up around 100 GeV!


The “sphaleron” (slick) state is a formal solution to the electroweak field equations that is valid at sufficiently high density and temperature. In this state, quarks can convert to antileptons, but antiquarks can not convert to leptons. These are actual legitimate SM processes conserving B - L. If the whole process is viewed as a first-order phase transition, resulting from broken EW symmetry, the basic idea would work extremely well... if there were enough CP-violating processes known.  But there are not.  Also the Higgs plays a key role in such phase transitions, and not enough is known about the Higgs currently to hope to do realistic calculations.

Recent calculations (2024) are strongly suggesting that the origins of matter occur in several stages, some of which come along fairly late in the early history of the universe, and not from the hypothetical very early "baryogenesis" and "leptogenesis" processes. This would mean that the early processes needed to produce far less matter than previously thought. Time will tell.

A very popular time to attribute the origin of matter to is the era immediately following the collapse of the inflation field into particles. At first these would be bosons of huge mass, but after a cascade of very rapid decays as the universe reheated, it is tempting to imagine processes that create excess quarks and leptons. The problem is that “imagination” is about all you have to work with, at that era, the very beginning of the so-called “hot Big Bang” itself.

It is not surprising that understanding the origin of quarks and leptons brings us face to face with two of the big unsolved problems of physics, the Strong CP problem and the conservation of B and L. No one currently has any idea of what hidden physics principles result in the observed near-perfect conservation of CP, B and L!!


BARYOGENESIS LEPTOGENESIS ORIGIN OF MATTER DARK ENERGY INFLATION
STRINGS????
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