Thermodynamics in the early universeIn equilibrium, distribution functions have the form When m ~ T particles disappear because of Boltzmann supressionDecoupled particles: If particles are decoupled from other species their comoving number density is conserved. The momentum redshifts as p ~ 1/a

In equilibrium, In equilibrium neutrinos and anti-neutrinos are equal in number!However, the neutrino lepton number is not nearly as wellconstrained observationally as the baryon numberThe entropy density of a species with MB statistics is given byThis means that entropy is maximised when(true if processes like occur rapidly) It is possible that

Conditions for lepto (baryo) genesis (Sakharov conditions)CP-violation:Asymmetry between particles and antiparticlese.g. has other rate thanL-violation:Processes that can breaklepton number (e.g. )Non-equilibrium thermodynamics:In equilibrium always applies.Leptogenesis (more to come in the last lecture)

Non-equilibrium

Electroweak baryogenesisdoes not require new physics, does not work!SUSY electroweak baryogenesisrequires new physics, does not work in the MSSMGUT baryogenesisrequires plausible new physics, it workspossible problems with reheatingBaryogenesis via leptogenesisrequires plausible new physics, it worksDifferent possibilities:

Thermal evolution after the end of inflationTotal energy density

Temperature evolution of N(T)

In a radiation dominated universe the time-temperaturerelation is then of the form

The number and energy density for a given species, X, isgiven by the Boltzmann equationCe[f]: Elastic collisions, conserves particle number but energy exchange possible (e.g. ) [scattering equilibrium]Ci[f]: Inelastic collisions, changes particle number(e.g. ) [chemical equilibrium]Usually, Ce[f] >> Ci[f] so that one can assume that elasticscattering equilibrium always holds.

If this is true, then the form of f is always Fermi-Dirac orBose-Einstein, but with a possible chemical potential.

The inelastic reaction rate per particle for species X isParticle decouplingIn general, a species decouples from chemicalequlibrium when

After neutrino decoupling electron-positron annihilationtakes place (at T~me/3)Entropy is conserved because of equilibrium in thee+- e-- g plasma and thereforeThe neutrino temperature is unchanged by this because they are decoupled and therefore The prime example is the decoupling of light neutrinos (m < TD)

The baryon number left after baryogenesis is usually expressed in terms of the parameter hAccording to observations h ~ 10-10 and therefore theparameteris often usedFrom h the present baryon density can be found asBIG BANG NUCLEOSYNTHESIS

Immediately after the quark-hadron transition almost allbaryons are in pions. However, when the temperature hasdropped to a few MeV (T

n-p changing reactionsInteraction rate (the generic weak interaction rate)After that, neutrons decay freely with a lifetime of

However, before complete decay neutrons are bound innuclei.Nucleosynthesis should intuitively start when T ~ Eb (D) ~ 2.2 MeV via the reactionHowever, because of the high entropy it does not.Instead the nucleosynthesis starting point can be found fromthe conditionSince t(TBBN) ~ 50 s

At this temperature nucleosynthesis proceeds via the reactionnetworkThe mass gaps at A = 5 and 8 lead to small production of mass numbers 6 and 7, and almost no production of mass numbers above 8The gap at A = 5 can be spanned by the reactions

ABUNDANCES HAVE BEEN CALCULATEDUSING THE WELL-DOCUMENTED AND PUBLICLY AVAILABLE FORTRAN CODENUC.F, WRITTEN BY LAWRENCE KAWANO

The amounts of various elements produced depend on the physical conditions during nucleosynthesis, primarily the values of N(T) and h

Helium-4:Essentially all available neutrons are processedinto He-4, giving a mass fraction ofYp depends on h because TBBN changes with h

D, He-3:These elements are processed toproduce He-4. For higher h, TBBNis higher and they are processed more efficientlyLi-7:Non-monotonic dependence because of twodifferent production processesMuch lower abundance because of mass gap

Higher mass elements. Extremely low abundances

Confronting theory with observationsThe Solar abundance is Y = 0.28, but this is processed materialThe primordial value can in principle be found by measuringHe abundance in unprocessed (low metallicity) material.He-4 is extremely stable and is in general always produced,not destroyed, in astrophysical environmentsHe-4:

Extragalactic H-IIregions

I Zw 18 is the lowest metallicity H-II region known

Olive, Skillman & Steigman

Izotov & ThuanMost recent values:

Deuterium:Deuterium is weakly bound and thereforecan be assumed to be only destroyed inastrophysical environmentsPrimordial deuterium can be found either by measuringsolar system or ISM value and doing complex chemical evolution calculations

OR

Measuring D at high redshiftThe ISM value of

can be regarded as a firm lower bound on primordial D

1994:First measurements of D in high-redshift absorptionsystemsA very high D/H value was foundCarswell et al. 1994Songaila et al. 1994However, other measurementsfound much lower valuesBurles & Tytler 1996Burles & Tytler

Burles, Nollett & Turner 2001The discrepancy has been resolved in favour of a low deuterium value of roughly

Li-7:Lithium can be both produced and destroyedin astrophysical environments

Production is mainly by cosmic ray interactions

Destruction is in stellar interiorsOld, hot halo stars seem to be good probes ofthe primordial Li abundance because there hasbeen only limited Li destruction

Molaro et al. 1995Li-abundance in old halo stars in units ofSpite plateau

Li-7 abundances are easy to measure, but the derivationof primordial abundances is completely dominated by systematics

There is consistency between theory and observationsAll observed abundances fitwell with a single value of etaThis value is mainly determinedby the High-z deuteriummeasurementsThe overall best fit isBurles, Nollett & Turner 2001

This value of h translatesintoAnd from the HST valuefor hOne finds

BOUND ON THE RELATIVISTIC ENERGY DENSITY(NUMBER OF NEUTRINO SPECIES) FROM BBNThe weak decoupling temperature depends on the expansionrateAnd decoupling occurs whenN(T) is can be written as

Nn = 3Nn = 4Nn = 2Since The helium production is very sensitive to Nn

The bound using most recent deuterium measurements(Abazajian 2002)

Sterile neutrinos:If there are nA-ns oscillations in the early universe at T > Tdec,n then DNn>0However, DNn

n-p changing reactionsFLAVOUR DEPENDENCE OF THE BOUNDSMuon and tau neutrinos influence only the expansion rate.However, electron neutrinos directly influence theweak interaction rates, i.e. they shift the neutron-protonratioMore electron neutrinos shifts the balance towards more neutrons, and a higher relativistic energy density can be accomodated

Ways of producing more electron neutrinos: 1) A neutrino chemical potential2) Decay of massive particle into electron neutrinosIncreasing xne decreases n/p so that Nn can be much higher than 4Yahil 76, Langacker 82, Kang&Steigman 92, Lesgourgues&Pastor 99, Lesgourgues&Peloso 00, Hannestad 00, Orito et al. 00, Esposito et al. 00, Lesgourgues&Liddle 01, Zentner & Walker 01 BBN alone:

xne= 0.1xne= 0.2Allowed regionAllowed forxne= 0

If oscillations are taken into account these bounds becomemuch tighter:Oscillations between different flavours become importantonce the vacuum oscillation term dominates the matterpotential at a temperature ofFor nm-nt this occurs at T ~ 10 MeV >> TBBN, leading tocomplete equilibration before decoupling.For ne-nm,t the amount of equilibration depends completelyon the Solar neutrino mixing parameters.

Lunardini & Smirnov, hep-ph/0012056 (PRD), Dolgov et al., hep-ph/0201287Abazajian, Beacom & Bell, astro-ph/0203442, Wong hep-ph/0203180If all flavours equilibrate before BBN the bound on theflavour asymmetry becomes much stronger becausea large asymmetry in the muon or tau sector cannot bemasked by a small electron neutrino asymmetryDolgov et al., hep-ph/0201287SH 02

For the LMA solution the bound becomes equivalentto the electron neutrino bound for all speciesDolgov et al. 02

Using BBN to probe physics beyond the standard model

Non-standard physics can in general affect either

Expansion rate during BBN extra relativistic speciesmassive decaying particlesquintessence.

The interaction rates themselvesneutrino degeneracychanging fine structure constant.

Example:A changing fine-structure constant aMany theories with extra dimensions predict 4D-couplingconstants which are functions of the extra-dimensionalspace volume.Webb et al.:Report evidence for a change in a at the Da/a ~ 10-5 level in quasars at z ~ 3BBN constraint:BBN is useful because a changing a would changeall EM interaction rates and change nuclear abundanceBergstrm et al:Da/a < 0.05 at z ~ 1012