Sakharov conditions

Sakharov conditions
NASA / WMAP Science Team · Public domain · source
Name	Andrei Sakharov
Birth date	1921-05-21
Death date	1989-12-14
Nationality	Soviet
Known for	Development of conditions for baryogenesis

Sakharov conditions are the three criteria formulated by Andrei Sakharov in 1967 that define necessary requirements for generating a baryon asymmetry in the early Universe. These conditions connect particle physics, field theory, and cosmology, influencing research programs in Grand Unified Theory, Electroweak theory, and beyond‑Standard Model proposals. Their relevance spans theoretical frameworks from Big Bang scenarios to experimental probes at facilities like the Large Hadron Collider and observational programs such as WMAP and Planck.

Overview

Sakharov presented his criteria in a paper while at the Soviet Academy of Sciences addressing the cosmological excess of baryons relative to antibaryons after the Big Bang Nucleosynthesis epoch. The conditions require violation of discrete symmetries and departure from thermal equilibrium, linking violations of charge conjugation symmetry and parity symmetry with processes in high‑energy environments such as those in Grand Unified Theory phase transitions or during the Electroweak phase transition. Influential contexts that have tested or extended Sakharov's ideas include analyses in Quantum Field Theory, studies of CP violation in Kaon and B meson systems, and application to scenarios like leptogenesis and baryogenesis via heavy particle decays studied in frameworks including SU(5), SO(10), and Left–Right symmetric models.

The Three Sakharov Conditions

Sakharov enumerated three necessary ingredients: (1) baryon number nonconservation, (2) C and CP violation, and (3) a departure from thermal equilibrium. Baryon number violation appears in models with sphaleron processes in the Electroweak theory and in baryon‑violating operators emerging from Grand Unified Theorys such as SU(5), SO(10), and E6. C and CP violation were empirically established in experiments with neutral kaons and later in B factory studies at KEK and SLAC National Accelerator Laboratory confirming CP asymmetries tied to the Cabibbo–Kobayashi–Maskawa matrix parameters. Departure from thermal equilibrium can occur in first‑order phase transitions, nonthermal particle production during inflationary reheating, or out‑of‑equilibrium decays of heavy states as considered in scenarios involving heavy Majorana neutrinos and right-handed neutrino models.

Theoretical Implications in Cosmology

Sakharov's criteria shape model building in cosmology, affecting theories of inflation, reheating, and phase transition dynamics. In inflationary cosmology, baryogenesis mechanisms must contend with dilution by cosmological inflation and rely on post‑inflationary dynamics such as preheating or reheating studied in the contexts of chaotic inflation, new inflation, and hybrid inflation. In electroweak baryogenesis, the nature of the Electroweak phase transition — whether strongly first order as in extensions like the Minimal Supersymmetric Standard Model or the Two-Higgs-Doublet model — determines viability. Alternative frameworks include Affleck–Dine mechanisms in supersymmetric settings, baryogenesis from primordial black hole evaporation, and baryon asymmetry generation in string theory inspired constructions including brane cosmology and heterotic string compactifications.

Mechanisms and Models for Baryogenesis

Mechanisms that implement Sakharov's conditions include: electroweak baryogenesis driven by sphaleron transitions and CP‑violating sources in extended scalar sectors; thermal leptogenesis where out‑of‑equilibrium decays of heavy Majorana neutrinos produce a lepton asymmetry converted to baryons by sphalerons; GUT baryogenesis from the decays of heavy X and Y gauge bosons in SU(5) or scalar decays in SO(10); the Affleck–Dine scenario relying on scalar condensates in supersymmetry; models invoking CPT violation or Lorentz violation as in some quantum gravity inspired proposals; and mechanisms within extra-dimensional frameworks or grand unification schemes that exploit new sources of CP violation. Each mechanism interacts with particle sectors studied at colliders such as the Large Hadron Collider, flavor experiments like LHCb, neutrino facilities including IceCube and DUNE, and precision measurements from projects like MEG and Mu2e.

Experimental and Observational Constraints

Empirical constraints derive from measurements of the baryon asymmetry parameter from cosmic microwave background observations by COBE, WMAP, and Planck; light element abundances from Big Bang nucleosynthesis compared with spectroscopic studies of quasar absorption systems and metal‑poor stars; limits on proton decay from Super-Kamiokande and planned detectors like Hyper-Kamiokande and DUNE that constrain GUT baryogenesis; CP violation measurements in Kaon experiments such as NA62 and B physics results from Belle II and BaBar that restrict model parameters; collider searches at the Large Hadron Collider and precision electroweak constraints from LEP and Tevatron; neutrino mass and mixing bounds from KamLAND, SNO, and MINOS that inform leptogenesis; and gravitational wave signatures from first‑order phase transitions targeted by observatories like LISA and pulsar timing arrays including NANOGrav. Together these observations narrow viable implementations of the Sakharov criteria and guide future experimental programs at facilities such as CERN, Fermilab, J-PARC, and astronomical surveys like LSST.

Category:Physical cosmology