Andrei Sakharov (1921 - 1989)

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.]

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.)



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 have equal coupling constants, while at the GUT scale the strong, weak and electromagnetic coupling constants are all equal.  But 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.  A very interesting SM solution to the EW field equations shows up around 100 GeV!


The “sphaleron” (slick) state is a solution to the electroweak field equations that is valid at sufficiently high density and temperature. In this state, quarks can convert to antileptons, and antiquarks can convert to leptons. These are actual 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.





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 quarks and leptons. The problem is that “imagination” is about all you have to work with, at that era, the very beginning of the “hot Big Bang” itself.



BARYOGENESIS LEPTOGENESIS ORIGIN OF MATTER DARK ENERGY INFLATION Back