Particle Physics and Cosmology Baryon asymmetry Boltzmann equation

Particle Physics and Cosmology Baryon asymmetry

Boltzmann equation in terms of cross section.

dimensionless inverse temperature m : particle mass small x : particle is relativistic large x : particle is non-relativistic dimensionless time variable in units of particle mass m x<3 x>3

particle number per entropy

cold relic fraction not necessarily order one !

cold relic abundance , mass and cross section m (m, σA ) inversely proportional to cross section , plus logarithmic dependence of xf

baryon relics in baryon symmetric Universe observed : Y = η ≈ 10 -10

baryons : the matter of stars and humans Ωb = 0. 045

Abundancies of primordial light elements from nucleosynthesis A. Coc

primordial abundances for three GUT models He present observations : 1σ D Li T. Dent, S. Stern, …

present baryon number

anti-baryons in baryon asymmetric Universe

conserved baryon asymmetry no baryon number violating processes in standard model of particle physics at energy below 1 Ge. V baryon asymmetry must exist at T = 1 Ge. V

high temperature baryon problem

baryon number violation in standard model baryon number is global symmetry of interactions in the standard model n violated by quantum anomaly ( no anomalies n possible for local symmetries : corresponding charge , like electric charge , exactly conserved ) n sphaleron processes generate strong baryon number violating processes at temperatures above 100 -200 Ge. V

baryon number violation in standard model no chemical potential for baryon number

thermal equilibrium in absence of chemical potential

baryogenesis

Sakharov’s conditions for baryogenesis 1) 2) 3) 4) baryon number violation interactions charge conjugation violating interactions CP – violating interactions non – equilibrium process

baryon number violating process in Grand Unified Theories ( GUT )

baryon number violating process in Grand Unified Theories ( GUT )

not good enough : B asymmetry will be washed out later by sphaleron processes no B-L asymmetry is produced

leptogenesis or late baryogenesis

leptogenesis n B – L is conserved quantum number in standard model n sphaleron processes transmute lepton asymmetry into baryon asymmetry a fraction of primordial B-L asymmetry appears as baryon asymmetry n ( B-L ) n primordial asymmetry protected from wash out by sphaleron processes

leptogenesis non – equilibrium decay of heavy neutrinos n non – equilibrium production after inflation during entropy production of the Universe n

baryogenesis during electroweak phase transition ?

Sakharov’s conditions for baryogenesis during electroweak phase transition 1) 2) 3) 4) baryon number violation interactions ☺ charge conjugation violating interactions ☺ CP – violating interactions ☺ non – equilibrium process ☺

cosmological phase transitions

cosmological phase transitions

first order cosmological phase transitions

chaos in the Universe

baryogenesis during electroweak phase transition strongly first order electroweak phase transition can generate baryon asymmetry if CP violation is sufficiently strong n no efficient baryogenesis for weak first order phase transition, second order phase transition or crossover n presumably too little CP violation in SM ( not definitely settled ) n

electroweak “phase transition “ in standard model is crossover ! perhaps strong first order transition in supersymmetric extensions of standard model

standard model of particle physics and cosmology n no candidate for dark matter n no baryon asymmetry n no massive neutrinos

standard model of particle physics and cosmology prediction : present Universe consists of photons and massless neutrinos