Sakharov conditions

Sakharov conditions. In physical cosmology, a set of three necessary criteria that must be satisfied for a dynamical process to generate an observed imbalance between matter and antimatter in the universe, a phenomenon known as baryogenesis. First proposed in 1967 by Soviet physicist Andrei Sakharov, these conditions provide the foundational framework for explaining the origin of the baryon asymmetry observed in the cosmos. The conditions require processes that violate baryon number conservation, violate both C-symmetry and CP-symmetry, and occur outside of thermal equilibrium.

Overview

The central problem addressed by these criteria is the overwhelming empirical evidence, from observations such as those of the cosmic microwave background by missions like COBE and Planck (spacecraft), that the observable universe is composed almost entirely of matter. According to the principles of quantum field theory and the Standard Model, the Big Bang should have produced equal amounts of matter and antimatter, which would have subsequently annihilated. The conditions outline the essential physical mechanisms that allow a small initial asymmetry to be generated and then preserved, leading to the residual matter that forms galaxy clusters, stars, and planets. This framework connects deeply with theories of grand unification and electroweak physics.

The three conditions

The first condition is **baryon number violation**, a process that does not conserve the quantum number distinguishing quarks and leptons from their antiparticles. Such processes are predicted in theories beyond the Standard Model, such as those involving sphaleron transitions in the electroweak theory or the decay of X and Y bosons in GUT models. The second condition is **C-symmetry and CP-symmetry violation**, meaning the laws of physics must treat matter and antimatter differently, not just under charge conjugation but also under the combined operations of charge and parity. This has been observed in systems like the kaon and B meson systems studied at facilities like SLAC National Accelerator Laboratory and CERN. The third condition is **interactions out of thermal equilibrium**, which prevents reverse processes from erasing the generated asymmetry, often occurring during phase transitions like the electroweak symmetry breaking or in the decay of heavy particles like the right-handed neutrino.

Historical context and development

Andrei Sakharov formulated these principles in his 1967 paper, written during a period of intense work on both nuclear weapons and cosmology. His insight was influenced by earlier work on CP violation discovered by James Cronin and Val Fitch in 1964 through experiments on the neutral kaon system at Brookhaven National Laboratory. The conditions were initially a theoretical proposition, as the Standard Model of particle physics, then under development through the work of Sheldon Glashow, Steven Weinberg, and Abdus Salam, did not initially appear to satisfy all criteria sufficiently. The subsequent development of electroweak baryogenesis scenarios and the incorporation of ideas like leptogenesis, proposed by Fukugita and Yanagida, expanded the original framework.

Implications for cosmology

The conditions have profound implications for models of the early universe, tightly constraining viable theories of particle physics and cosmic inflation. They imply that the universe must have undergone epochs where the fundamental symmetries of nature were broken, such as during the electroweak epoch. Scenarios like electroweak baryogenesis tie the generation of asymmetry to the properties of the Higgs field and possible phase transitions. Furthermore, the conditions are central to theories of leptogenesis, where an asymmetry in leptons is converted to a baryon asymmetry via sphaleron processes, a mechanism often involving the decay of heavy right-handed neutrinos as suggested by the seesaw mechanism.

Tests and observational evidence

Direct experimental verification of the conditions is a major goal of modern particle physics and cosmology. Searches for proton decay, a signature of baryon number violation, are conducted in experiments like Super-Kamiokande in Japan and the planned Hyper-Kamiokande. Precision studies of CP violation continue at particle colliders such as the Large Hadron Collider at CERN and B-factories like Belle II at KEK. Observational cosmology provides indirect tests; measurements of the baryon-to-photon ratio from Wilkinson Microwave Anisotropy Probe data and constraints on primordial gravitational waves from experiments like BICEP and Keck Array can rule out or support specific baryogenesis models tied to early universe phase transitions.

Extensions and related concepts

The original framework has been extended to include concepts like leptogenesis and Affleck-Dine baryogenesis. In supersymmetry and string theory, new mechanisms involving fields like the axion or flat directions have been proposed. The conditions also relate to the study of topological defects such as cosmic strings and domain walls, which could have played a role in out-of-equilibrium dynamics. Furthermore, the exploration of anomalies in gauge theories, linked to the work of Gerard 't Hooft, has provided a deeper understanding of baryon number violation in the Standard Model itself, connecting Sakharov's criteria to fundamental aspects of quantum chromodynamics and the Standard Model. Category:Physical cosmology Category:Particle physics Category:Andrei Sakharov