Sarkar BBN

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DPG Physics school Astroparticle Physics,

Physikzentrum Bad Honnef, 20-25 Sept 2009

Subir Sarkar

Big Bang

Nucleosynthesis


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The universe is made mainly of hydrogen (~75%)and helium (~25%) + traces of heavier elements


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Big Bang ! Stars/Supernovae !

Where did all the elements come from?


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George Gamow is generally credited with having founded the theory of primordialnucleosynthesis and, as a corollary, predicted the temperature of the relic radiation


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The real story is that while Gamow had brilliant ideas, he could not calculate very well, so

enlisted the help of a graduate student Ralph Alpher (who worked with Robert Herman)

1) was published on 1 April 1948 including Bethe (who had nothing to do with it)but leaving out Herman because he stubbornly refused to change his name to Delter!


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The modern theory of primordial nucleosynthesis is based essentially on this paper

which followed the crucial observation by Hayashi (Prog. Theoret. Phys.5:224,1950)thatneutrons and protons were in chemical equilibrium in the hot early universe

Alphers achievement was finally recognized when he wasawarded the US National Medal of Science in 2005:

"For his unprecedented work in the areas of nucleosynthesis, for theprediction that universe expansion leaves behind background radiation,

and for providing the model for the Big Bang theory."


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(See lectures by Prof Gerhard Brner)


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In the absence of dissipative processes (e.g. phase transitions whichgenerate entropy) the comoving entropy is conserved:

i.e.

Integrating this gives the time-temperature relationship: t(s) = 2.42g-1/2 (T/MeV)-2

So we can work out when events of physical significance occurredin our past (according to the Standard Model of particle physics)

aa2=

8GN

3

The dynamics is governed by the Friedmann equation:


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To get this right we need to count all the bosons and fermionscontributing to the relativistic degrees of freedom and take into

account our uncertain knowledge of possible phase transitions

quark-hadron (de)confinement transition


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The Cosmic Microwave

Background Spectrum

Thisperfectblackbody is testimony to our hot, dense past and directly demonstrates that the expansion was adiabatic (with negligible energy release) back at least to t~ 1 day

we can go backfurther to t~ 1 sby studying element synthesis

See lecture by Prof Paolo de Bernadis


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Weak interactions and nuclear reactions in expanding, cooling universe(Hayashi 1950, Alpher, Follin & Herman 1953, Peebles 1966, Wagoner, Fowler & Hoyle 1967)

Dramatis personae:Radiation (dominates)Matter baryon-to-photon ratio (only free parameter)

Initial conditions:T>> 1 MeV, t


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Computer code byWagoner (1969, 1973) .. updated by Kawano (1992)

Coulomb & radiative corrections, heating et cetera(Dicuset al1982)

Nucleon recoil corrections (Seckel 1993)

Covariance matrix of correlated uncertainties (Fiorentiniet al1998)

Updated nuclear cross-sections (NACRE 2003)


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The first three minutes


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Time < 15 s, Temperature > 3 x 109 Kuniverse is soup of protons, electrons and other particles so hot that

nuclei are blasted apart by high energy photons as soon as they form

Time = 15 s, Temperature = 3 x 10

9

K

Still too hot for Deuterium to surviveCool enough for Helium to survive, but too few building blocks

Time = 3 min, Temperature = 109 KDeuterium survives and is quickly fused into Heno stable nuclei with 5 or 8 nucleons, and this restricts formation of

elements heavier than Heliumtrace amounts of Lithium are formed

Time = 35 min, Temperature = 3 x 107 Knucleosynthesis essentially completeStill hot enough to fuse He, but density too low for appreciable fusionModel makes precise predictions about the relative abundances of the

light elements 2H, 3He, 4He and 7Li, as a function of the nucleon density


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Primodial versus Stellar Nucleosynthesis Timescale

Stellar Nucleosynthesis (SN): billions of years

Primordial Nucleosynthesis (PN): minutes

Temperature evolution SN: slow increase over time PN: rapid cooling

Density SN: 100 g/cm3 PN: 10-5 g/cm3 (like air!)

Photon to baryon ratio SN: less than 1 photon per baryon PN: billions of photons per baryon 1H

2H

3He

4He

6Li

7Li

9Be

no stable nuclei !

The lack of stable elements with masses 5 and 8 make it hard for BBN(2-body processes, short time-scale) to synthesise elements beyond helium

this can be happen only in stars, on a longer timescale


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Uncertainties in synthesized abundances arecorrelated estimate using Monte Carlo methods(Krauss & Romanelli 1988; Smith, Kawano & Malaney 1993; Krauss & Kernan 1994; Cyburt, Fields & Olive 2004)

The neutron lifetime normalises the weak interaction rate: n = 885.7 0.8 s(a recent measurement is 6.5lower notincluded by the PDG in the average)

Courtesey:

KeithOlive


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Linear propagation of errors covariance matrix (inagreementwith Monte Carlo results)

Fiorentini, Lisi, Sarkar & Villante (1998)


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BBN Predictionsline widths theoretical uncertainties (neutron lifetime, nuclear cross sections)

Courtesey:KeithOlive


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Nucleosynthesis without a computer

If then abundances approach equilibrium values

but general solution is:

Freeze-out occurs when:

Examine reaction networkto identify the largest

source and sink terms

obtain D, 3He and 7Li towithin a factor of ~2 of

exact numerical solution,and 4He to within a few %

source sink

...analyticsolution

Dimopoulos, Esmailzadeh, Hall & Starkman (1988)


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can use this formalism to determinejointdependence ofabundances on expansion rate as well as baryon-to-photon ratio

and so:

can therefore employ simple 2 statistics to determine best-fit valuesand uncertainties (faster than Monte Carlo + Maximum Likelihood)

Lisi, Sarkar & Villante (2000)


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Inferring primordial abundances


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Courtesey:

KeithOlive


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Courtesey:Keit

hOlive

For a quantity of such fundamental cosmological importance, relatively

little effort has been spent on measuring the primordial helium abundance


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Olive & Skillman (2004)

This is the value (and uncertainty) presently recommended by the PDG


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Primordial deuterium?... is easily destroyed in starsLook in QuasarAbsorption Systems

- low density clouds of gas seen inabsorption along the lines of sight

to distant quasars (when universewas only ~10% of its present age)The difference between H and D

nuclei causes asmallchange in theenergies of electron transitions,shifting their absorption lines apartand enabling D/H to be measured

But: Hard to find clean systems Do not resolve clouds Dispersion/systematics?


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W. M. Keck ObservatorySpectra with the necessary

resolution for such distantobjectscan be obtained

with 10m-class telescopes this has revolutionisedthe determination of theprimordial D abundance


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Courtesey:Ke

ithOlive

The observed scatter isnotconsistent with fluctuations about an average value!


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Observe in primitive (Pop II) stars: (most abundant isotope is 7Li)- Li-Fe correlation mild evolution- Transition from low mass/surface temp stars (core well mixed byconvection) to higher mass/temp stars (mixing of core is not efficient)

Primordial Lithium?

Courtesey:Keith

Olive

Plateau at low Fe (high T) constant abundance at early epochs so infer observed 7Li plateau is primordial (Spite & Spite 1982)


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Inferredprimordial abundances

4He observed in extragalactic HII regions:

2H observed in quasar absorption systems (and ISM):

7Li observed in atmospheres of dwarf halo stars:

Systematic errors have been re-evaluated based on scatter in data for details seeReview of Particle Physics (Fields & Sarkar, Phys. Lett. 667, 1, 2008)

(3He can be both created & destroyed in stars soprimordial abundancecannotbe reliably estimated)


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is in agreement withallowing for large systematic uncertainties

in the inferred elemental abundances

Confirms and sharpens the case for(two kinds of) dark matterBaryonic Dark Matter:warm-hot IGM, Ly- , X-ray gas

+Non-baryonic dark matter:

neutralino? axion?

BBN versus CMBCMB

!BBN

!

Particle data Group: Fields & Sarkar (2008)


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Another argument comes from considerations of structure formation in the universe


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Perturbations in metric (generated during inflation)

induce perturbations in photons and (dark) matter

These perturbations begin to grow through

gravitational instability after matter domination


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Before recombination, the primordial fluctuations just excite sound waves in theplasma, but can start growing already in the sea of collisionless dark matter

These sound waves leave an imprint on the last scattering surface of the CMB as the

universe turns neutral and transparent sensitive to the baryon/CDM densities

Co

urteseyDavidSpergel

For a statistically isotropic gaussianrandom field, the angular power

spectrum can be constructed bydecomposing in spherical harmonics:


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H

u,

Sugiyama,

Silk[astro-p

h/9604166]


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The Cosmic Microwave Backgroundprovide independentmeasure of

Acoustic oscillations in (coupled)photon-baryon fluids imprintfeatures at small angles (< 1

o) in

angular power spectrumDetailed peak positions, heights, sensitive to cosmological parameterse.g. 2nd/1st peak baryon density

T!

2

Bh!

Bond & Efstathiou (1984)

Dodelson & Hu (2003)

WMAP-5 best-fit:


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in more detail

Predict BBN abundances with

WMAP determination ofCMB(blue)compare with observations (yellow)

D agreement excellent, 4He also OK But 7Li isdiscrepant

- systematic errors inobservations?

- theoretical uncertainties? - new physics (e.g. decaying

relic particles)? this hasadditional motivation from theobservation that 6Li has also

been observed with anabundance > 104 times higher

than expected!Cyburt, Fields & Olive (2008)


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Ryan, Beers, Olive, Fields & Norris (2000)


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Systematic Errors in the inferred Lithium abundanceObservational systematics

Measure Li I absorption line(s) to infer 7Li/H Teffcritical (mostly Li II) But required shift in T scale is ~500 K - very unlikely

Melendez & Ramirez (2004); Fields, Olive & Vangioni-Flam (2005)

Astrophysical systematics

Stellar depletion over ~1010 yr if Li burned need to correct LipupwardBut no scatter seen around Spite plateau - also 6Li preserved

Ryanet al (2000)Nuclear Systematics

7Li production channel - 3He (,) 7Be - normalization error?But same reaction also key for Solar neutrinos standard Solar model OK!

Cyburt, Fields & Olive (2004)


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Recently a primordial plateau in 6Li has indeed been detectedwith 6Li/7Li ~ 0.1 (cf. standard expectation 6Li/7Li ~ 10-5)

Coupled with the fact that the 7Li abundance is ~3 timessmaller thanexpected, this has refocussed interest onnon-standard BBN

(Nissen et al 1999; Asplund et al 2001, 2004)


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However the detection of6Li isbased on fits to the line shape

need more data to establish thereality of a 6Li plateau!

Lambert (2005)

Also stars in which 6Li isdetected are close to the

main-sequence turn-offin the H-R diagram


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Does the Lithium anomaly imply new physics?

Jedamzik (2000, 2004)


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Extensions of the Standard Modelpredict new (typically)unstable particles,which would have been created

(thermally) in the early Universe,e.g. TeV mass gravitinos in supergravity

(Weinberg 1982; Khlopov & Linde 1983; Ellis,Nanopoulos & Sarkar 1985; Reno & Seckel 1988)The high energy photons would

have photo-dissociated the

synthesized elements

severe

limitson the decaying particle abundanceThis requires that highest temperaturereached in our past (after inflation) was< 108 GeV - constraint on baryogenesis!

BBN and decaying particles

Massxrelicabun

dance(GeV)

Cyburt et al2003

particle lifetime (s)


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Bailly, Jedamzik & Moultaka 2008

May be possible to solve both lithiumproblems with relic decaying particlehaving suitable abundance/lifetimee.g. gluino in split supersymmetry, supersymmetric stau Next-to-LSP(with gravitino LSP),


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Arvinataki, Davis, Graham, Pierce & Walker (2005)

Gluino in split supersymmetry

A small number of these would survive annihilation in the early universe anddecay during nucleosynthesis stringent bound from overproduction of D + 3He

This would require supersymmetry breaking scale to be < 1010 GeV

If mass scale of SUSY scalar superpartners is raised well above a TeV (to evadevarious problems with weak scale SUSY breaking), then predict long-lived gluinos

Th l b h d i bl li i l i


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There may also be newcharged quasi-stable relic particles inNature which would formbound states with 4He

Although the

4

He (D,

)

6

Li reaction is normally highlysuppressed, this is not so for the bound state

Pospelov (2006) Thus the lithium anomaly may be due to supersymmetric

particles (e.g. stau) which catalyse relevant nuclear reactions if so these could be seen soon at the LHC!


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There is something fascinating about science. One gets such wholesomereturns of conjectures out of such trifling investment of fact.

Mark Twain

E l N i C i


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Element abundances sensitive toexpansion history during BBN

observed values constrainrelativistic energy density

(Hoyle & Taylor 1964, Peebles 1966; Shvartsman1969; Steigman, Schramm, & Gunn 1977)

Pre-CMB:4He as probe, other elements give With from CMB: All abundances can be used 4He still sharpest probe D competitive if measured to 3% Cyburt, Fields, Olive & Skillman (2005);

Lisi, Sarkar & Villante (1999),

Example: Neutrino Counting

so singlet neutrino (cf. LSND) isallowedN N 3 < 1.5

@ 95% c.l.

E l F d l li


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Note n-pmass difference is sensitive to both em and strong interactions,

while freeze-out temp is sensitive to weak interactions and gravity, hence4He abundance isexponentially sensitive toallcoupling strengthsConversely obtain bound of < few % on any additional contribution toenergy density driving expansion e.g. rules out ofO(H2)always

(since this would correspond to a large renormalisation of GN)

Example: Fundamental couplings


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C

ourtesey:KeithOlive

In fundamental theories e.g. string theory, the physical constants do vary withtime but the BBN constraint says that this must have stopped before t ~ 0.1 s

S


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Summary

Observational inferences about the primordially synthesised

abundances of D,4

He and7

Li presently provide thedeepestprobe ofthe Big Bang, based on anestablished physical theoryThe overall concordance between the inferred primordial abundances of D and4He with the predictions of the standard cosmology requires most of the matterin the universe to be non-baryonic,and enables constraints to be placed on any

deviations from the usual expansion history (e.g. new neutrinos or dark energy)Anomalies in the abundances of6Li and 7Li have been interpreted as

indications for new physics beyond the Standard Model (viz.unstable supersymmetric particles) need better understanding of

the astrophysical processing of lithium to investigate this furtherNucleosynthesis marked the beginning of the development of modern cosmology and it is still the final observational frontier as we look back to the Big Bang!

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