THE BIG BANG. Ian Howley General Relativity Dr. Zdzislaw Musielak 8 December 2010

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1 THE BIG BANG Ian Howley General Relativity Dr. Zdzislaw Musielak 8 December

2 2

3 OUTLINE Early Theoretical Work and Observational Evidence Timeline of the Big Bang t=0 Shortcomings Inflation The Big Bang in the 21 st Century 3

4 HISTORICAL BACKGROUND G µν = R µν 1 2 Rgµν + Λg µν = κt µν Alexander Friedmann (Russian-Mathematician) Refutes Einstein s addition of the cosmological constant. Described how different models of the universe could be created based on Λ= ±1,0. - In particular he chose Λ= 0, which gives rise to a dynamic universe Georges Lemaître (Belgian-Priest/Physicist) Inspired by radioactive decay, he deduces the primeval atom model. - Lemaître is the first to describe a small, cataclysmic event that spurred the creation of our observable universe. 4

5 OBSERVATIONAL EVIDENCE Edwin Hubble Using the Mount Wilson observatory, he measures the redshifted velocity of nearby galaxies. They are found to obey the simple relation: v = H o d The current value of Ho based off data from HST is: H o = 70.6 ± 3.1 (km/s)/m pc 5

6 NUCLEOSYTHESIS Lemaître s Big Bang could not explain/account for the ratio of hydrogen to helium (10/1) found in the current universe. Alpher, Bethe, Gammow Provided the first rigorous mathematical derivations of the nuclear reactions occurring during the very early universe. They correctly predicted the H/He ratio, but could not foresee a means of producing heavier elements. Detractors of the BBT claimed Alpher had known the answer he needed to get, and made his calculations fit This put pressure on proponents of the BBT to provide a testable hypothesis. 6

7 COSMIC MICROWAVE BACKGROUND Alpher and Herman Predicted recombination, the point in time when the early universe was sufficiently cool so that plasma could no longer exist and neutral atoms were formed. They claimed the temperature for recombination was ~3,000 o C and that the universe would have reached this temperature 300,000 years after the big bang. Prior to this time light could not propagate through the foglike plasma. Hence, they predicted an echo of the Big Bang should still be propagating through the entire universe with a redshifted wavelength ~1mm. (Cosmic Microwave Background - CMB) 7

8 OBSERVATIONAL EVIDENCE CMB was not taken seriously, never searched for explicitly, and eventually found by accident. Penzias and Wilson Initially mistook noise in their radio antenna for pigeon white dielectric material. It was later proved to be the echo of the Big Bang as predicted by Alpher and Herman. COBE/WMAP - late 20 th century experiments to map the CMB. Found the temperature to be 2.7K to better than one part per million. 8

9 OBSERVATIONAL EVIDENCE 9

10 TIMELINE OF THE BIG BANG t=0.01s - T=10 11 K, photons, neutrinos, antineutrinos, and e-p pairs. - small amounts of protons, neutrons, and electrons. - radiation is dominant. t=0.12s - T=3x10 10 K. - neutron-proton ratio (2/3) is decreasing as n + ν e p + e becomes more one directional. - No nucleosynthesis yet. t=1.1s - T=10 10 K. - ν ν e + e or γγ has ended, and the role of neutrinos is diminished. - neutron-proton ratio (1/3). 10

11 TIMELINE OF THE BIG BANG t=13s - T=3x10 9 K. - Heat produced from e - e + annihilation has slowed the rate of cooling - neutron-proton ration (1/5). - Stable Helium nuclei are formed. Unstable deuterium, tritium, and 3 He are also formed. t=3min - T=10 9 K, universe is mostly photons and neutrinos. - All light nuclei can be formed except deuterium. - Matter already reigns over antimatter, why the universe chose matter is not addressed by the Big Bang. t=35min - T=3x10 8 K. - Density of matter (being only nuclei still) is small compared to the density of photons and neutrinos. 11

12 t =O To understand the behavior of the universe at t=0, we consider the Robertson-Walker metric: ds 2 = cdt 2 R(t) 2 dr 2 1 kr 2 + r2 (dθ 2 + sin 2 θdφ 2 ) Where R is the radius of the universe, and k the parameter describing the curvature with values k=0,±1. Einstein s equation for each value of k become: (1) Ṙ 2 = c 2 + 8πG 3 Ṙ 2 = 8πG 3 Ṙ 2 = c 2 + 8πG 3 R 2 c 2 R 2 c 2 R 2 c 2 (2) 12

13 t =O, PURE RADIATION CASE The early universe was radiation dominated (as opposed to matter). For this case we have p = 1 (see HW# 78). Where the energy density, ε, varies as R Equations (2) then all reduce in the same way to: Integrating we may find: Ṙ 2 =2u 0 R 4 0R 2 R(t) =(8u 0 ) 1 4 R0 t 1 2 This tells us that during the early radiation dominated universe, R varied with t 1/2. 13

14 PROBLEMS The BBT cannot or does not provide answers to the following questions: - Singularity - What banged? What happened before t=0? Before s, the BBT breaks down since GR would be replaced by quantum gravity. - Flatness - General Relativity says our universe is non-euclidean, yet we observe it to be flat over cm. Why is it so nearly Euclidean? - Horizon - At t=0, why did all space start expanding simultaneously? What said go? - Homogeneity - Over a distance of ly, the universe is completely homogenous to 1/1,000. Yet galaxies cluster forming inhomogeneities over distances of 10 8 ly - Uniqueness - What I am really interested in is whether God could have created the world differently. - A. Einstein. 14

15 FLATNESS/HOMOGENEITY The ratio of energy density to critical density of the universe is defined as Ω - Ω <1 universe expands forever - Ω >1 universe The current accepted value of Ω is.1<ω<2. If we extrapolate backwards we find: Ω(1s) 1 = O(10 16 ) Ω(10 43 s) 1 = O(10 60 ) The BBT has difficulty explaining these absurdly small numbers 15

16 INFLATION (QUALITATIVE) Guth From the moment of the Big Bang until s, the universe doubled in size every s - This equates to 100 doublings or a factor of Advantages: - Rapid early inflation of the universe could explain the large scale homogeneity of the universe. - Small inhomogeneities would have been expanded and exaggerated, possibly providing the variations needed for galaxies and other large scale structure. 16

17 INFLATION (QUALITATIVE) 17

18 INFLATION slightly less(qualitative) Grand Unified Theories predict a critical phase transition for the universe at K (like the units matter...) Below this temperature the Higgs field acquires a non-zero expectation (vacuum) value. (Spontaneous Symmetry Breaking) Other impurities or defects in the field give rise to magnetic monopoles(mass ~10 16 x the proton), and domain walls (2d singularity) 18

19 INFLATION (QUANTITATIVE?) As in class we have for the energy momentum tensor: T µν =( + p)u µ u ν pg µν L the Lagrangian has a potential V of the scalar field L = 1 2 µφ µ φ V (φ) With this Lagrangian the stress tensor becomes: Tµ ν = diag(, p, p, p ) where, = 1 2 φ 2 + V (φ) ; p = 1 2 φ 2 V (φ) To find one of the few exact inflationary solutions we take the potential: V (φ) =V 0 + Aφ 2 + Bφ 5 + Cφ 6 And by using Einstein s equation we can find: R(t) =Ae nt (e nt + ξ) 2/9 exp{ 2 9 ent (e nt + ξ) 2 } 19

20 BIG BANG IN THE 21 ST CENTURY Loop Quantum Gravity , Ashtekar - A possible reconciliation of GR and Quantum. Quantizes space-time, without needing 11 dimensions a la string theory. The Big Bounce Bojowald - Predicts an oscillating universe where a big bang is followed by periods of expansion, retraction, a big crunch, and the process repeats - In contrast to detailed quantitative calculations, a proof of the inability to obtain certain precise predictions in a solvable model can be taken as a more reliable result. - Current observations cannot constrain values that enter the post-big bang era as highly suppressed quantum fluctuations from before the big bang. 20

21 SUMMARY The Big Bang Theory is likely the most important cosmological theory to date. Observational evidence assures that 13.7 billion years ago the visible universe was in a dense, homogeneous, rapidly expanding state. There are several shortcomings of the BBT that have been addressed by later, valid (though not flawless) theories, ie Inflation. We are closing in on understanding what banged, and why it banged. The role of charge-parity violation may help explain the matter asymmetry. Discovery and measurement of SUSY and/or the Higgs could provide crucial pieces of evidence towards understanding the early universe. 21

22 BIG BANG 22

23 REFERENCES An Introduction to Mathematical Cosmology. JN Islam. Cambridge Press, Big Bang, The Origin of the Universe. S. Singh. First Harper Perennial, The Inflationary Universe. A. Guth and PJ Steinhardt Particle Physics and Inflationary Cosmology. A. Linde. Physics Today, September Quantum Nature of the Big Bang. A Ashtekar. PRL 96, (2006) What happened before the Big Bang? M Bojowald. Nature Physics, vol. 3, Aug

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