Topic 3. Evidence for the Big Bang

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1 Topic 3 Primordial nucleosynthesis Evidence for the Big Bang! Back in the 1920s it was generally thought that the Universe was infinite! However a number of experimental observations started to question this, namely: Red shift and Hubble s Law Olber s Paradox Radio sources Existence of CMBR

2 Red shift and Hubble s Law! We have already discussed red shift in the context of spectral lines (Topic 2)! Crucially Hubble discovered that the recessional velocity (and hence red shift) of galaxies increases linearly with their distance from us according to the famous Hubble Law V = H 0 d where H 0 = 69.3 ±0.8 (km/s)/mpc and 1/H 0 = Age of Universe Olbers paradox! Steady state Universe is: infinite, isotropic or uniform (sky looks the same in all directions), homogeneous (our location in the Universe isn t special) and is not expanding! Therefore an observer choosing to look in any direction should eventually see a star! This would lead to a night sky that is uniformly bright (as a star s surface)! This is not the case and so the assumption that the Universe is infinite must be flawed

3 Radio sources! Based on observations of radio sources of different strengths (so-called 2C and 3C surveys)! The number of radio sources versus source strength concludes that the Universe has evolved from a denser place in the past! This again appears to rule out the so-called Steady State Universe and gives support for the Big Bang Theory Cosmic Microwave Background! CMBR was predicted as early as 1949 by Alpher and Herman (Gamow group) as a remnant heat left over from the very hot and dense initial Universe! They predicted that after the Big Bang the Universe should glow in the gamma ray part of the spectrum! This will subsequently cool as the Universe expands shifting the wavelength of this last light to a temperature of ~5K! Eventually observed in 1965 by Penzias and Wilson! The CMBR is now a very powerful tool for cosmologists! Recent experiments such as COBE and WMAP have measured the CMBR anisotropies at the 10-5 level! Gives us information on Big Bang, Dark Matter, etc.

4 αβγ theory (Origin of Chemical Elements)! Actually Alpher & Gamow: Bethe included (by Gamow) as a joke! Proposed an early Universe that was hot and dense! Assumed that the Early Universe consisted only of neutrons! As the temperature fell neutron decay to protons was possible! Subsequently they proposed a single process for all elemental abundances in the Universe - that of neutron capture! Protons via β-decay: n p + e - + ν e! First step: p + n 2 H + γ αβγ theory ν e ν e

5 αβγ theory - abundances! Successive neutron capture creates heavier elements! At each step the progress controlled by the balance between the rate of production and the rate of destruction! By setting up and solving a sequence of differential equations of this type, a distribution could be produced in reasonable agreement with the trend of the observed abundances For these calculations capture cross-sections measured at Los Alamos during World War II were used (1 MeV neutrons =10 10 K) dn A /dt = F(S,T)[σ A-1 N A-1 - σ A N A ] F is collision frequency (function of thermodynamic state variables) N A is the no. of atoms with atomic no. A σ A is the neutron capture cross-section Cross-sections (quick revision)! Consider the simple case in which a beam of particles is incident on nuclei of some type, then the cross-section is the probability of a particular process occurring per target nucleus, per incident particle! The total area blocked out is the (number of nuclei per unit volume) x (the volume) x (σ). Thus the fraction of the beam which is removed by the reaction is: dn/n = - nσ dx where n = number density x beam area Integration yields N = N 0 exp(- nσx) or N = N 0 exp(- x /λ ) where λ is the mean free path! In neutron capture the rate at which the reaction is occurring depends upon the relative velocity v of the particles and target nuclei and is given by the product of particle density, the relative velocity, the cross section and the total number of target nuclei.! We shall discuss neutron capture further in understanding the production of elements heavier than Iron

6 αβγ theory - success and failure! Abundance for He agrees well with observation! By splitting the elements into 15 groups by atomic weight and using an average cross-section for each group gives a reasonable fit to abundance data! BUT predicted abundances for heavier elements were incorrect! Problem getting past A=4 due to lack of stable elements with A=5, 8! Results carved the way for calculations of thermonuclear fusion! Discussion is relevant to neutron capture topic later This is an extract from the Chart of nuclides Big Bang: Underlying principles I! Universe expanded some 14 billion years ago from a singularity! At extremely high temperatures elementary particles can simply be created from thermal energy kt = mc 2 (essentially E = mc 2 )! After the BB the Universe expands and cools! As temperatures fall below the threshold temperature for particle production then annilihilation rate > creation rate

7 Big Bang; Underlying Principles II! Normal physics laws (including standard model of particle physics)! Small matter-antimatter asymmetry! Gravitation described by General Relativity! Cosmological principal (Universe is homeogeneous and isotropic) Robertson- Walker metric! Expansion of the Universe is governed by field equations of GR The Big Bang Time Space

8 Time Key events after Big Bang Temp/Energy Event s kt = ev Planck era, quantum gravity, prior to this all forces one, gravity first to decouple, many exotic particles s kt = ev Inflation starts, Strong nuclear force decouples s s T = K K Free electrons, quarks, photons, neutrinos all strongly interacting 10-4 s s T = K K Free electrons, protons, neutrons, photons, neutrinos all strongly interacting Key events after Big Bang Time Temp/Energy Event 10 1 s T = K Neutrinos decouple from the cosmic plasma (cross-section falls dramatically) 10 2 s T = 7.5-6x10 9 K Pair production of e + e - ceases 10 2 s kt = 0.8 MeV Proton:neutron ratio is frozen Next 300 s Next 10 3 s Thermal energy still high enough to photodissociate atoms Neutron decay continues, n:p ratio changing Primordial nucleosynthesis starts Note ions not atoms due to mean thermal energy

9 Key events after Big Bang Time Temp/Energy Event ~ 10 3 s to 400,000 years 380,000 years T ~ 10 8 or 9 K to T = 3000 K T = 3000 K Dark ages : Universe is a sea of free nuclei, electrons and photons. Photons Thomson scatter off electrons so Universe remains opaque to photons. Physics in this period is less well-established. Photons can no longer ionize, photons decouple, last scattering surface. Origin of CMBR. Fundamental forces

10 Cosmic Microwave Background Cosmic Microwave Background Very close to a perfect thermal (Black Body) spectrum with a temperature of 2.7K

11 The neutron:proton ratio! The main 3 reactions involved in determining the number of protons and neutrons in the early Universe are: (i) n + e + p + ν e (+ 1.8 MeV) (ii) p + e - (+0.8MeV) n + ν e (iii) n p + e - + ν e (+ 0.8 MeV)! Note that reaction (ii) is endothermic in a leftright direction i.e. requires energy into the system (KE of incoming particles) in order to proceed The neutron:proton ratio! At T > K, kt > 1 MeV, t < 1 s, reactions (i) and (ii) maintain protons and neutrons in thermal equilibrium When kt >> m n m p = Δm, protons and neutrons are nearly equal in number When Δm becomes significant compared to kt, the neutron-proton ratio is given by the Boltzmann factor exp( Δmc 2 /kt)! At T ~ K, kt ~ 0.8 MeV, t ~ 1 s, the reaction rates for (i) and (ii) become slow compared to the expansion rate of the universe neutrinos decouple (weak interaction rate slow compared to expansion rate) e + e pair creation suppressed (γ energies drop below MeV) neutron:proton ratio freezes out! Below this temperature only reaction (iii) continues

12 The neutron:proton ratio! We use the Boltzmann distribution to estimate the n:p ratio at this point! hence N m 3 $ 2 exp mc 2 ' & ) % k B T ( 3 N " n = m % 2 " n N $ p # m ' exp (m n m p )c 2 % $ ' p & # k B T &! where kt = 0.8 MeV and (m n - m p ) = 1.3 MeV/c 2 This yields a value of N n :N p ~ 0.2 Primordial nucleosynthesis! At this point kt is too high for primordial nucleosynthesis to start (formation of nuclei) due to dissociation! Therefore reaction (iii) continues in the left-right direction this is neutron decay! After a further 300 seconds primordial nucleosynthesis starts p + n 2 H + γ 2 H + 2 H 3 He + n 2 H + 2 H 3 H + p 3 H + 2 H 4 He + n 3 He + 2 H 4 He + p 2 H + 2 H 4 He 3 He + 4 He 7 Be + γ 3 H + 4 He 7 Li + γ 7 Be + n 7 Li + p 7 Li + p 2 4 He Note: ions not atoms

13 Solved problem! If the neutron:proton ratio starts at 0.2 and the neutron continues to decay for a further 300 seconds what is the neutron:proton ratio at the end of this period given that the neutron s lifetime is 890 seconds?! The neutron s lifetime is 890 seconds therefore in 300 seconds: N $ = exp t ' $ & ) = exp 300 ' & ) = N 0 % τ ( % 890(! Therefore the fraction of neutrons that have decayed = 0.286! Next we write N n (1 d) N p N " n N % where = 0.2 and d=0.286 to give n = N $ p # N ' p & " $ # N n N p % ' & t= 300s = N n (1 d) = N p + dn n 1+ d N n t= 300s N p Abundances vs time Note that a neutron:proton ratio of 0.135:1 is equivalent to 12:88 Assuming that the 12 neutrons go to forming 4 He we would expect 76% Hydrogen ( 1 H) and 24% Helium ( 4 He) - in excellent agreement with observation

14 Modern day abundances! Comparison of modern day elemental abundances from primordial nucleosynthesis can also give important cosmological information such as the baryon density or the baryon to photon ratio! Concordance with CMB is important check on theory Summary! Big Bang Nucleosynthesis (BBNS) successfully predicts the production of light elements shortly after the Big Bang! The thermal history of the early Universe and nuclear physics are used to explain the sequence of events! Light element abundances can be accurately predicted and related to cosmological parameters

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