Big Bang Nucleosynthesis Subir Sarkar xford hysics TM v Introduction v Physical context v Nuclear reactions v Primordial abundances v Cross-check with CMB v Constraints on fundamental physics Master class, The Ninth Quantum Universe Symposium, Groningen, 17 April 2019 The universe is made mainly of hydrogen (~75%) and helium (~25%) + traces of heavier elements Where did all the elements come from? :547,1957 29 ---------------------------------- -------------------------------- Neutron-star mergers (‘kilonova’) Burbidge, Burbidge, Fowler & Hoyle, RMP George Gamow is generally credited with having founded the theory of primordial nucleosynthesis and, as a corollary, predicted the temperature of the relic radiation The real story is that while Gamow had brilliant ideas, he could not calculate too well, so enlisted the help of graduate student Ralph Alpher and posdoc Robert Herman … Ref. 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”! 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) that neutrons and protons are in chemical equilibrium in the hot early universe Ralph Alpher was belatedly awarded the US National Medal of Science (2005): “For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory” The Standard Model of the Early Universe Radiation-dominated plasma in thermal equilibrium (very close to Einstein-deSitter: Wm=1, Wk=0, WL=0) Number density: Energy density: Entropy density: where, the number of relativistic degrees of freedom sum over all bosons and fermions with appropriate weight: number energy Knowing the equation of state, we can solve the Friedman equation … For matter: ⇒ ⇒ ➪ Hence ⇒ For radiation: ⇒ So radiation will dominate over all other components as we go to early times ⇒ Radiation-dominated era But at the matter density will come to dominate Note that during matter-domination too Evolution of different energy components matter-radiation equality -4 ρr ~ a log (r) -3 ρm ~ a present epoch ρΛ -4 0 log(a) Very recently (at z~1) the expansion has supposedly become dominated 2 2 2 by a ‘cosmological constant’: Λ ~ 2 H0 ⇒ ρΛ ~ 2 H0 MP This creates a severe ‘why now?’ problem as ρΛ << ρm,r at earlier epochs In the absence of dissipative processes (e.g. phase transitions which generate entropy) the comoving entropy is conserved: ⇒ i.e. The dynamics is governed by the Friedmann equation: Integrating this gives the time-temperature relationship: t (s) = 2.42 g-1/2 (T/MeV)-2 So we can work out when events of physical significance occurred in our past (according to the Standard Model of particle physics) The Standard Model of the Early Universe History of g (T) The phAse diAgrAm of the StAndArd Model (bAsed on A dimensionAlly reduced SU (2)L theory with quArks And leptons, with the AbeliAn hyperchArge symmetry U (1)Y neglected). The 1st-order trAnsition line ends At the 2nd-order endpoint: 2 mH ≃ 72 ± 2 GeV/c , kBTE ≃ 110 GeV; for higher Higgs mAss it is A ‘crossover’ Rummukainen et al, Nucl.Phys.B532:283,1998 To construct our thermal history we must then count all boson and fermion species contributing to the number of relativistic degrees of freedom … and take into account our understanding of (possible) phase transitions Quark-hadron ‘cross-over’ Borsanyi et al, Nature 539:69,2016 Favoured value of quark-hadron (de) confinement transition The Cosmic Microwave Background Spectrum This perfect blackbody is testimony to our hot, dense past and directly demonstrates that the expansion was indeed adiabatic (with negligible energy release) back at least to t ~ 1 day … we can go back further to t ~ 1 s by studying element synthesis The blackbody temperature can be used as a clock (assuming adiabatic expansion: aT = constant), so our thermal history can be reconstructed Nucleosynthesis (Re)combination The furthest we ‘see’ directly is back to t ~ 1 s when light elements were synthesised (the small fluctuations in CMB temperature must have been generated much earlier) 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 << 1 s − n+νe ↔ p +e n-p weak equilibrium: + neutron-to-proton ratio: p +νe ↔ n + e 1/3 t T "G /G2 # τweak(n ↔ p) ≥ ⇒ $ N F % Weak freeze-out: Tf ~ 1 MeV, tf ~ 1 s universe freeze-out & ' which fixes: n p = e−(mn −mp )/Tf ≈1 6 Deuterium bottleneck: T ~ 1 → 0.07 MeV D created by but destroyed by high-E photon tail: so nucleosynthesis halted until: Tnuc ~ ΔD/-ln(η) Element synthesis: Tnuc ~ 0.07 MeV, tnuc ~ 3 min (meanwhile n/p ➛ 1/7 through neutron β-decay) 4 3 7 6 7 -5 nearly all n ➛ He (YP ~ 25% by mass) + left-over traces of D, He, Li (with Li/ Li ~ 10 ) No heavier nuclei formed in standard, homogeneous hot Big Bang … must wait for stars to form after a ~billion years and synthesise all the other nuclei in the universe (s-process, r-process, …) v Computer code by Wagoner (1969, 1973) .. updated by Kawano (1992), other codes: PArthENoPE (2007), AlterBBN (2012) v Coulomb & radiative corrections, ν heating et cetera (Dicus et al 1982) v Nucleon recoil corrections (Seckel 1993) v Covariance matrix of correlated uncertainties (Fiorentini et al 1998) v Updated nuclear cross-sections (NACRE 2003) The ‘first three minutes’ • Time < 15 s, Temperature > 3 x 109 K –universe 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 109 K –Still too hot for Deuterium to survive –Cool enough for Helium to survive, but too few building blocks • Time = 3 min, Temperature = 109 K –Deuterium survives and is quickly fused into He –no stable nuclei with 5 or 8 nucleons, and this restricts formation of elements heavier than Helium –trace amounts of Lithium are formed • Time = 35 min, Temperature = 3 x 107 K –nucleosynthesis essentially complete (still hot enough to fuse He, but density too low for appreciable fusion) Model makes predictions about the relative abundances of the light elements 2H, 3He, 4He and 7Li, as a function of the nucleon density Primodial versus Stellar Nucleosynthesis • Timescale – Stellar Nucleosynthesis (SN): billions of years – Primordial Nucleosynthesis (PN): minutes • Temperature evolution 9Be – SN: slow increase over time – PN: rapid cooling 7Li 6Li • Density 3 – SN: 100 g/cm 4He -5 3 – PN: 10 g/cm (like air!) 3He 2H no stable nuclei • Photon to baryon ratio 1H – SN: less than 1 photon per baryon – PN: billions of photons per baryon 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 (much) longer timescale The neutron lifetime normalises the “weak” interaction rate: τn = 880.0 ± 0.9 s (has recently dropped in value by 5σ because of one new measurement!) Uncertainties in synthesized abundances are correlated … estimate using Monte Carlo (Smith, Kawano, Malaney 1993; Krauss, Kernan 1994; Cyburt, Fields, Olive 2004) NEUTRON LIFETIME MEASUREMENT The neutron lifetime cannot be USING MAGNETICALLY TRAPPED accurately computed theoretically ULTRACOLD NEUTRONS (even knowing the weak interaction coupling GF very well) because there are corrections due to the strong interactions (which alter gA/gV away from unity) .. so it has to be measured experimentally Linear propagation of errors → → errors of propagation Linear covariance matrix (in (in agreement with Monte Carlo results) Carlo with Monte Fiorentini, Lisi, Sarkar, Villante, Phys.Rev.D58:063506,1998 BBN Predictions line widths ⇒ theoretical uncertainties (neutron lifetime, nuclear #-sections) Nucleosynthesis without a computer ⇒ … but general solution is: source sink :504,1991 378 ApJ , If … then abundances approach equilibrium values StarkmAn Freeze-out occurs when: ⇒ , HAll, Examine reAction network to identify the largest ‘source’ and ‘sink’ terms Esmailzadeh obtAin D, 3He And 7Li to , …………. within A fActor of ~2 of analytic exact numerical solution, solution and 4He to within A few % Dimopoulos … can use this formalism to determine joint dependence of abundances on expansion rate as well as baryon-to-photon ratio and so: ⇒ … can therefore employ simple χ2 statistics to determine best-fit values and uncertainties (faster than Monte Carlo + Maximum Likelihood) Lisi, Sarkar, Villante, Phys.Rev.D59:123520,1999 Inferring primordial abundances Observations of the light elements He and Li • Helium Abundance –measured in extragalactic HII regions with lowest observed abundances of heavier elements such as Oxygen and Nitrogen (i.e. smallest level of contamination from stellar nucleosynthesis) • Lithium Abundance –measured in halo Pop II stars –Lithium is easily destroyed hence observe the transition from low mass stars (low surface temp) whose core material is well mixed by convection, to higher mass stars (higher surface temp) where mixing of core is not efficient For a quantity of such fundamental cosmological importance, relatively little effort has been spent on measuring the primordial helium abundance Recent reevaluations