Sakharov conditions
/ SAH-kuh-rof /
If the early universe started out perfectly balanced between matter and antimatter, what would it take to end up with the lopsided, matter-dominated cosmos we live in? In 1967 the Soviet physicist Andrei Sakharov answered this with a beautifully simple recipe: three conditions that any process must satisfy in order to generate an excess of matter from a symmetric start. They are like the minimum ingredients for a cake — leave any one out and you cannot bake the imbalance.
The three conditions are these. First, baryon number must not be perfectly conserved — there has to be some process that can change the net count of matter particles, otherwise the total can never shift away from zero. Second, both C symmetry and the combined CP symmetry must be violated — without CP violation, every matter-making process would be exactly balanced by an equal antimatter-making process, and the books would stay even. Third, the universe must pass through a period out of thermal equilibrium — in perfect equilibrium, any reaction that builds an excess runs equally in reverse and erases it, so the imbalance can only survive if conditions are changing fast enough (as during cosmic expansion or a phase transition). All three together can let a symmetric universe drift to a matter-dominated one.
The Sakharov conditions are the master checklist for any theory of why matter exists. They tell us exactly what new physics must provide. Remarkably, the Standard Model in principle contains all three ingredients — baryon number can change through a subtle quantum effect, CP is violated via the CKM phase, and the early universe was expanding — yet quantitatively each falls far short of what is needed. That gap is precisely why physicists pursue ideas like leptogenesis and new sources of CP violation. The honest caveat is that satisfying the conditions is necessary but not sufficient: meeting them does not by itself guarantee the right size of asymmetry, which is where the real difficulty lies.
The Standard Model technically ticks all three Sakharov boxes — it has baryon-number-changing quantum processes, CP violation through the CKM phase, and an expanding early universe — yet the CP violation is so tiny that the predicted matter excess comes out roughly a billion times smaller than observed.
All three ingredients present, but the recipe falls a billionfold short.
Meeting the Sakharov conditions is necessary but not sufficient; a theory can satisfy all three and still produce far too little asymmetry, which is exactly the situation the Standard Model finds itself in.