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Modelling and Measuring the Universe

This lecture discusses the expansion of the universe, Einstein's theory of general relativity, and the Friedmann equation for describing the universe. It also explores how to model and measure the universe, the matter contents of the universe, and the effect of curvature. The lecture highlights key questions about the scale factor, age of the universe, energy density, and distances of objects with redshift. Various types of universes are examined, including those with matter, radiation, dark energy, and curvature. The lecture concludes by discussing the "benchmark" model of the universe and the evidence from observations.

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Modelling and Measuring the Universe

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  1. Volker Beckmann Joint Center for Astrophysics, University of Maryland, Baltimore County & NASA Goddard Space Flight Center, Astrophysics Science Division UMBC, November 2nd, 2006 Modelling and measuring the Universe Summary

  2. The first part of the lecture - Universe is expanding (Hubble relation) - Newton’s not enough: Einstein’s idea about space-time - General relativity for curved space-time - Four equations to describe the expanding/contracting universe

  3. The second part of the lecture - How to model the Universe - the Friedmann equation as a function of density parameters - Matter-, radiation-, lambda-, curvature- only universe - mixed-component universes - the important times in history: ar,m and a m,

  4. The second part of the lecture • - How to measure the Universe • - the Friedmann equation expressed in a Taylor series: H0 and q0 (deceleration parameter) • - luminosity distance, angular size distance • distance ladder: parallax, Cepheids, SuperNova Type Ia • - results from the SuperNova measurements

  5. The second part of the lecture - What is the matter contents of the Universe? - matter in stars - matter between stars - matter in galaxy clusters - dark matter

  6. The effect of curvature

  7. Density parameter  and curvature

  8. The effect of curvature Scale factor a(t) in an empty universe

  9. The effect of curvature Spatially flat Universe Our key questions for any type of Universe: Scale factor a(t) ? What is the age of the Universe t0 ? Energy density (t) ? Distance of an object with redshift z ?

  10. The effect of curvature What happens in a flat universe ? One component only ?

  11. The effect of curvature

  12. The effect of curvature

  13. The effect of curvature Spatially flat Universe with matter only aka Einstein-de Sitter Universe Willem de Sitter (1872 - 1934) Our key questions for any type of Universe: Scale factor a(t) ? What is the age of the Universe t0 ? Energy density (t) ? Distance of an object with redshift z ?

  14. The effect of curvature

  15. The effect of curvature empty universe Scale factor a(t) in a matter-only (nonrelativistic) universe

  16. The effect of curvature Scale factor a(t) in a radiation-only universe Matter (top) & empty (bottom) universe

  17. The effect of curvature Spatially flat Universe with dark energy only Our key questions for any type of Universe: Scale factor a(t) ? What is the age of the Universe t0 ? Energy density (t) ? Distance of an object with redshift z ?

  18. The effect of curvature Matter, empty, radiation only universe Scale factor a(t) in a lambda-only universe

  19. The effect of curvature Scale factor a(t) in a flat, single component universe

  20. The effect of curvature

  21. The effect of curvature Universe with matter and curvature only

  22. The effect of curvature Universe with matter and curvature only

  23. The effect of curvature Universe with matter and curvature only

  24. Curved, matter dominated Universe 0 < 1  = -1 Big Chill (a  t) 0 = 1  = 0 Big Chill (a  t2/3) 0 > 1  = -1 Big Crunch

  25. The effect of curvature Universe with matter and curvature only What is a(t) ?

  26. The effect of curvature Universe with matter and  (matter + cosmological constant, no curvature) What values for  in order to get a flat Universe?

  27. Possible universes containing matter and dark energy Abbe George Lemaître (1894-1966) and Albert Einstein in Pasadena 1933

  28. The effect of curvature Universe with matter, , and curvature (matter + cosmological constant + curvature) 0 = m,0 +  ,0

  29. The effect of curvature Flat Universe with matter, radiation (e.g. at a ~ arm) 0 = m,0 +  r,0

  30. The effect of curvature Describing the real Universe - the “benchmark” model 0 = L + m,0 +  r,0 = 1.02 ± 0.02 (Spergel et al. 2003, ApJS, 148, 175)

  31. The effect of curvature The “benchmark” model 0 = L + m,0 +  r,0 = 1.02 ± 0.02 (Spergel et al. 2003, ApJS, 148, 175) “The Universe is flat and full of stuff we cannot see”

  32. The effect of curvature The “benchmark” model Important Epochs in our Universe: “The Universe is flat and full of stuff we cannot see - and we are even dominated by dark energy right now”

  33. The effect of curvature The “benchmark” model • Some key questions: • - Why, out of all possible combinations, we have • 0 =  + m,0 +  r,0 = 1.0 ? • Why is  ~ 1 ? • What is the dark matter? • What is the dark energy? • - What is the evidence from observations for the benchmark model? “The Universe is flat and full of stuff we cannot see”

  34. How do we verify our models with observations? Hubble Space Telescope Credit: NASA/STS-82

  35. The effect of curvature Taylor Series A one-dimensional Taylor series is an expansion of a real function f(x) about a point x==a is given by Brook Taylor (1685 - 1731)

  36. The effect of curvature Scale factor as Taylor Series qo = deceleration parameter

  37. The effect of curvature Deceleration parameter q0

  38. The effect of curvature How to measure distance Measure flux to derive the luminosity distance Measure angular size to derive angular size distance M101 (Credits: George Jacoby, Bruce Bohannan, Mark Hanna, NOAO)

  39. The effect of curvature Luminosity Distance In a nearly flat universe: • How to determine a(t) : • determine the flux of objects with known luminosity to get luminosity distance • - for nearly flat: dL = dp(t0) (1+z) • measure the redshift • determine Ho in the local Universe •  qo

  40. The effect of curvature Angular Diameter Distance dA = length /  = dL / (1+z)2 For nearly flat universe: dA = dp(t0) / (1+z)

  41. The effect of curvature Angular Diameter Distance dA = l /  Credits: Adam Block

  42. The effect of curvature Measuring Distances - Standard Candles

  43. The effect of curvature Cepheids as standard candles Henrietta Leavitt

  44. The effect of curvature Cepheids as standard candles Large Magellanic Cloud (Credit: NOAO) M31 (Andromeda galaxy) Credit: Galex

  45. The effect of curvature Cepheids as standard candles Hipparcos astrometric satellite(Credit: ESA) Hubble Space Telescope Credit: NASA/STS-82

  46. The effect of curvature For nearly flat Universe: Credit: Adam Block

  47. Simulation of galaxy merging

  48. Super Nova types - distinguish by spectra and/or lightcurves

  49. Super Nova Type II - “core collapse” Super Nova

  50. A white dwarf in NGC 2440 (Credits: Hubble Space Telescope)

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