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The Early Universe read chapter 13

The Early Universe read chapter 13. We have discussed Models such as the Big Bang and how the universe may have started from such an explosive event

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The Early Universe read chapter 13

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  1. The Early Universereadchapter 13 We have discussed Models such as the Big Bang and how the universe may have started from such an explosive event The observable universe today constrains the way things must have evolved just after the Big Bang-so we can build a history of the Early Universe

  2. Initially - size of universe was smaller Assuming matter+energy is constant at all epochs then of course the early universe had much denser matter & energy - hotter temperature Difficult to determine what conditions were -long before galaxies & stars formed, no sources which we can trace back that far

  3. In the early universe the high density caused elementary particles of all types to exchange energy & momentum Particles co-existed in an equilibrium defined by temperature…models assume early universe was in thermal equilibrium -supported by the black-body shape of the CMB spectrum

  4. Universe contains a mass density & energy density Present day- energy mostly CMB(CBR) photons, > 109 photons per matter particle Photons lost energy as universe expanded…now energy density in CBR small compared to matter density…the universe today is matter dominated Early universe had energy dominating …state of matter depended critically on temperature Will examine temperature & matter evolution as a function of time

  5. Recall the Friedmann eqns Describe evolution (into future) for scale factor based around mass/density A soln, for a given k,  is a model of the universe Also, recall we found so matter changes with 1/R2

  6. Friedmann Equation Physical interpretation… if there is more than a certain amount of matter in the universe, the attractive nature of gravity will ensure that the Universe recollapses • Scale factor as function of mass for future extrapolation…but how about backwards extrapolation, to a time when we had a high density of energy?

  7. The Friedmann Equations Photons carry energy & momentum - when they hit a particle they can impart some of that momentum to it - so photons exert a pressure For radiation-dominated era, need to incorporate photon energy and thus radiation pressure into Friedmann eqns, ie to understand how scale factor must have evolved

  8. The Friedmann Equations • Need to relate energy-density & scale factor R(t) • Taking either eqn for local energy density and solving it OR • following intuitive arguments like we used in last Tuesdays lecture • it turns out • (t)=(t1)[R(t1)/ R(t)]4 • , the energy density drops faster than just due to volume expansion of universe because cosmic redshift effects add in extra term • Scaling with energy more dramatic than that with mass!

  9. The Friedmann Equations In thermal equilibrium T4 gives us temperature-scale relation T(t)=T(t1)[R(t1)/ R(t)] or T(tthen)=T(tnow)[R(tnow)/ R(tthen)] using our previous relation gives T(tthen)=T(tnow)(1 + z) can measure temperature now and thus derive temperature in the past versus redshift and thus versus age or time after R(0). now then

  10. T=0s T=10-43 s The Beginning of Time - Planck Epoch Planck epochis t=10 -43 sec Think about the forces which dominate our life today GRAVITY ELECTROMAGNETISM WEAK FORCE STRONG FORCE Dominates Dominates chemical Dominate atomic reactions at large reactions distances We believe during this time all 4 forces composed a single force

  11. T=10-43 s T=0s The Beginning of Time Gravity not yet incorporated into QM -need a Theory of Everything Most of the time we can use one or the other, depending on what size-scale we are studying - as we consider t=0, need both to merge Theoretical models can (only) probe back to 10-43 sec after the Big Bang, -called the Planck time when the characteristic scale of the universe was ct=1.6x10-35m, the Planck length Planck epoch is t=10 -43 sec

  12. T=0s T=10-43 s The Beginning of Time - Planck Epoch Planck epochis t=10 -43 sec At end of Planck epoch gravitons fell out of equilibrium with the other particles and gravity decoupled from the other forces - first symmetry break

  13. Time Out Quantum field theory Waves (& hence allied particles) can be associated with a field A field can be mathematically represented as a quantity extended in space/time -strengths of fields related to # of associated particles present Fields have ripple-like fluctuations characterized by wavelength ofn associated particle Gravity is the field of the graviton (as-yet-undiscovered particle) Most important are field symmetries, quantities which are invariant under specific transformations (think back to SR, or of things like energy conservation laws) When conditions change & some symmetries stop we have spontaneous symmetry breaking

  14. Time Out Quantum field theory When conditions change and some symmetries stop we have spontaneous symmetry breaking Real life analogy…temperature changes cause phase transitions like the melting of ice Water has higher entropy and thus less symmetry than a crystalline solid o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ooo o o o o o oo o o o o o o o o o o o o o o o

  15. T=0-10-43 s The Beginning of Time - Planck Epoch Planck epochis t=10-43 sec Recap: At end of Planck epoch gravitons fell out of equilibrium with the other particles and gravity decoupled from the other forces - first symmetry break

  16. t=10 -43 sec --> t=10 -35 sec Unified Epoch Temperatures so high our understanding of matter is minimal Grand Unified Theories (GUTs) exist to try and describe the three unified forces -theories incomplete

  17. t=10 -43 sec --> t=10 -35 sec Unified Epoch These extreme conditions have not been reproduced in an accelerator - lack of direct verification means there are several GUT theories including supersymmetry, superstrings and supergravity We know current GUT models are not yet correct - they underpredict the lifetime of the proton Remnant of Unified Epoch is the excess of matter over anti-matter, process which left this is baryogenesis

  18. Pair Production During this epoch sub-atomic particles crashed together at relativistic speeds & interacted with photonsPhotons also collided & created particles (pair production) Threshold temperature for specific particle creation - temperature determines type of particles being produced by pair production proton/anti-proton production starts at T=1013K T = 2m0c2/3KB Mean energy/particle  temperature Higher temperatures favor production of more massive particles

  19. Matter/Anti-Matter At this epoch pair production/annihilation rates were in balance As universe expanded, cooled the temperature dropped & more types of particles stopped being createdAt some point the symmetry between matter/anti-matter must have been violated Currently 1 particle of matter per 1 billion photons, thus the excess of matter over anti-matter was 1 part in a billionThis slight imbalance resulted in all that we can see !!!Not yet a consensus as to why this is

  20. Quark Epoch End of the UNIFIED EPOCH at t=10 -35 sec - temperatures dropped,- strong force decoupled and we entered the Quark Epoch t=10 -35 sec --> t= 10 -6 sec - the Quark Epoch universe consisted of quarks & other particles/anti-particles temperatures dropped to 1015K at t~10-11 s - decoupling occurred After decoupling, all forces were separate - as they are today QM predicts electromagnetic & weak forces lose separate identities at very high temperatures/energies & merge into a single electroweak force Verified in particle accelerators!!!

  21. Inflation - a period of great expansion of the universe occurred during this epoch The freezing-out of the strong force may have liberated an enormous energy causing a period of rapid expansion called inflation In as small a time as 10-36s a piece of the universe the size of an atomic nucleus grew to the size of our solar system inflation caused size change of field ripples

  22. Inflation lasted only a small amount of time, but afterwards corners of the universe were widely separated Before inflation A&B could equilibrate, inflation pushed them apart and now we can see light from either, but light not yet reached one from another You can test inflation by comparing the amplitude of thespatial irregularities in the CMB spectrum with the predictions ofinflation Right now it’s looking pretty good

  23. The forces are distinct at low temperatures, but appear to merge at high temperatures

  24. T= 10-6 - 10-4 s Hadron Epoch After t= 10-6 sec - quarks condensed into hadrons (baryons & mesons) Baryon/anti-baryon pairs annihilated leaving photons, some unmatched baryons then remained Excess matter has survived with rest-mass intact

  25. Lepton Epoch At t= 10-4 sec - lighter particles associated with the weak force (e.g. electrons, neutrinos etc) gained domination, the lepton epoch T=2moc2/3KB (from equating rest-mass energy w/ mean energy of photon - the higher the temperature the more massive particles can be produced) Temperature continued to fall with particles of less & less mass dominating Universe now a soup of electrons, photons, neutrinos, positrons -particle interactions now occurring which change balance of protons/neutrons in the universe - protons start to dominate At t=1s T~1010K - density low enough that neutrinos stopped interacting & streamed freely across the universe At t~14 s T~ 5x109K, most leptons annihilated, but left enough electrons to balance the protons

  26. T=180s • 1+z=3.8x108 T=7x108K kT=6x104 eV NUCLEOSYNTHESIS ERA -when most of the H, He & a bit of Li were made i.e. 3 minutes after big bang • Universe has cooled down to 1 billion K • Filled with • Photons (i.e. parcels of electromagnetic radiation) • Protons (p) • Neutrons (n) • Electrons (e) • [also Neutrinos]

  27. T=180s • 1+z=3.8x108 T=7x108K kT=6x104 eV NUCLEOSYNTHESIS ERA Before * Photons * Electrons * Protons (1H+) * Neutrons * Neutrinos After * Photons * Nucleons (i.e 1H+, 2H+, 4He+, 7Li+) * Neutrinos Approximate time when the Planck distribution describing distribution of photon energies allows deuterium nucleus (2H+) to survive. Big Bang Nucleosynthesis (BBN) begins. This continues for a few hundred sec until most of the neutrons are contained within helium-4nuclei (4He2+) (though some are in 2H+, 3He2+, 7Li3+etc) After this time (BB + many hundred s) mean particle energies have dropped such that "building" of heavier nuclei (beyond 7Li3+) is no longer efficient. BBN stops.

  28. Big Bang Nucleosynthesis The three main "pillars" of evidence in support of Big Bang cosmology are * The Expansion of the Universe * The Cosmic Microwave Background (CMB) * The Abundances of the "Light" Elements We have now discussed the first two, here we discuss the third. By "light" elements, here we are primarily interested in 1H or p (Hydrogen) 2H (Deuterium) "fragile" 3H (Tritium) unstable 3He ("Helium-3") "fragile" 4He (Helium) 7Li (Lithium) "fragile" Note I am being rather "sloppy" in these notes. Obviously at the time of BBN, all these nuclei are fully stripped of electrons. Thus I should really be using 2H+ (known as a deutron) 4He++ etc etc Don't be confused by my sloppiness...

  29. BBN How did observed abundances of elements arise? Not until the 1940s was it was realized H & He were by far the most abundant elements in the universe - led to significant progress understanding nuclear reactions (WW II) Given our understanding of stellar nucleosynthesis & evolution, and given the age of the universe, it is not possible for stars (of any type) to have produced as much 4He as we see

  30. BBN How did observed abundances of elements arise? In the Big Bang ...? In 1948, Ralph Alpher (Hans Bethe) & George Gamow suggested that the during the early stages of the Big Bang, the densities & temperatures might also be sufficient to allow such thermonuclear reactions

  31. BB + 10-4 s revisit the past… At temperature ~ 1012 K, the universe a mixture of photons, electrons (e-), positrons (e+) neutrinos, anti-neutrinos & small fraction of neutrons (n) & protons (p) in thermal equilibrium. Mean thermal energy of the particles is kT ~ 86 MeV Difference in rest mass between a proton & neutron is [mp - mn]c2 = 1.3 MeV Thus neutrons (n) can be converted to protons (p) and vice versa mediated by electron neutrinos and antineutrinos The ratio of the number density of neutrons to protons is simply given by the Boltzmann equation: nn / np = EXP( - [mp - mn]c2 /kT ) i.e. for T = 1012 K, nn / np = 0.985 However, due to the intense radiation field, and (hence) e-, e+ density, fluid only contains ~ 5protons & 5neutrons for every 2x1010photons

  32. BB + 2 s protons & neutrons Due to expansion, temperature had fallen to ~ 1010 K. Reduced the mean energy of the photons below 1.02 MeV Pair production ceased… existing e- e+pairs were not replaced when they annihilated, thus proton-to-neutron & neutron-to-proton reactions were no longer possible. Ratio of the number density of neutrons to protons at this instant is simply given by the Boltzmann equation again: for T = 1010 K, nn / np = 0.223 protons dominate

  33. BB + 2-90 s Neutron Decay Once temperature has fallen to < 1010 K neutrons can no longer be created, but these (free) neutrons can decay Thus ratio of the numbers of neutrons to protons slowly decreases. However until the temperature falls below 109 K, the photon density & the mean particle energies are still too high for the products of nucleosythesisto survive.

  34. BB + 90 s Big Bang Nucleosynthesis (BBN) - 4He Production T dropped to ~109 K allowing protons & neutrons to combine, producing heavier nuclei. The primary reaction is of course the production of deuterium (2H): p + n converted to 2H + photon Can then build up the "mass-3" elements tritium (3H)& "Helium-3" (3He): 2H + n converted to 3H + photon 2H + p converted to 3He + photon 2H + 2H converted to 3H + p 2H + 2H converted to 3He + n 3He + n converted to 3H + p And thus (the relatively stable) "Helium-4" : 3He + n converted to 4He + photon 3He + 2H converted to 4He + p 3H + p converted to 4He + photon 3H + 2H converted to 4He + n

  35. BB + 700s The End of BBN Rates of reactions depend on baryon density & temperature (now fallen to ~108 K) These are falling as universe expands. BBN has effectively stopped Relative abundances produced in BBN can be used to measure baryon density then (and hence now) BBN makes specific predictions for 2H/1H ratio 3He/1H ratio 4He/1H ratio 7Li/1H ratio -can be compared to observations Note - though the 7Li/1H ratio is very small (~10-10), it serves as an important diagnostic since its prodution is a complex function of baryon density.

  36. Baryon Density Consistent results are obtained for a baryon density that corresponds to a current baryon density b = 2 - 5x10-31 g cm-3 Comparing this with the critical density c = 1.1x10-29 g cm-3 (for H0 = 75 km/s/Mpc) indicates that baryonic matter constitutes between 2% and 5% of the material needed to close the universe.

  37. BB + 5x1010 s (1.6x103yr) 1+z=1.7x104 T=3x104K kT=2.4 eV Radiation-Matter Equality The time when the energy densities of matter & radiation are equal. we made a crude estimate as to when the energy density in baryons equaled that in photons. There is disagreement between that value for z and that above simply because in the above we have taken into account our current estimates for the amount of non-baryonic dark matter in the universe. ContentsBefore & After * Photons * Electrons * Nucleons (i.e 1H+, 2H+, 4He+, 7Li+) * Neutrinos

  38. BB + 9x1012 s (2.8x105yr) 1+z=1100 T=3x103K kT=0.3 eV Recombination Contents*Before * Photons * Electrons * Nucleons (i.e 1H+, 2H+, 4He+, 7Li+) * Neutrinos After * Photons (leading to CMB) * Atoms (ie. 1H, 2H, 4He, 7Li) * Neutrinos The age when the radiation density had fallen sufficiently that electrons were able to become bound (& stay bound) to protons. NOTE Don't be distracted by the re used in the term "recombination". Protons and electrons were NEVER previous combined in the early universe. The term is used simple because the process is identical to that which occurs is other astrophysical situations (when the re is appropriate).

  39. BB + 9x1012 s (2.8x105yr) 1+z=1100 T=3x103K kT=0.3 eV Recombination Contents*Before * Photons * Electrons * Nucleons (i.e 1H+, 2H+, 4He+, 7Li+) * Neutrinos After * Photons (leading to CMB) * Atoms (ie. 1H, 2H, 4He, 7Li) * Neutrinos Photons no longer interact sufficiently with bound electrons, thus the universe becomes "transparent" to radiation. The binding energy for an electron in the ground-state of hydrogen is 13.6 eV. Thus recombination does not occur until the temperature has fallen sufficiently such that kT << 13.6 eV. The temperature at which this occurs is T~ 3x103K, when the scale factor was a factor R/R0 = 1/(1+z) ~ 9x10-4 of its current size.

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