Lecture 11. The standard Model

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5 Lecture 11 The standard Model

6 Standard Model The standard model assumes that the universe is filled with matter and other forms of energy (photons) but that matter is dominant today. The standard model assumes that the cosmological principle is valid The standard model must incorporate: The Hubble expansion The Cosmic Microwave Background The ratio of light elements The large scale structure of the universe

7 Cosmological Principle The universe is homogeneous and isotropic on large scales

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9 Distances in the Univese Earth to sun = 93,000,000 miles = 8 light minutes = 1.5x 10-5 light years Earth to Alpha Centauri = 4.37 light years Earth center of Milky Way = 8Kpc = 26,080 light years Earth to Andromeda Galaxy = 778 Kpc = 2.54 million light years Earth to Coma cluster = 99 Mpc = 321 million light years

10 Hubble Flow v = H 0 d H 0 = 70 Km/s/Mpc (units of 1/time) Means in 1 second, an object 1Mpc distant will become an addition 70 km distant As a fractional growth: H 0 = 2.3 X /s Universe is 4 x seconds old

11 Microwave Background Formed when the universe was ~ 350,000 years old, at a temperature of ~ 3000 Kelvin Universe transitioned from opaque plasma to transparent gas Photons travel unimpeded since that time, but redshifted by 1000 to today seen as temperature of ~ 3 Kelvin

12 Ratio of the light elements When the universe was a few minutes old, the density and temperature were appropriate for nuclear fusion to occur Hydrogen (H) fused into deuterium (D) and then Helium (He) Then the universe cooled, and the fusion stopped, leaving the universe ~ 90% H and 10% He, which is what we measure today

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14 Large scale structure At the time the CMB formed, the universe was relatively uniform in density Over time areas with slightly more mass condensed, and structures formed Large scale structure means larger then galaxies scale

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18 Observational Comsology Observational cosmology is the attempt to measure the values associated with these models

19 Back to the Standard model The model assumes that: 1: gravity is the only force relevant on cosmological scales 2: Gravity is dominated by mass today

20 This means the universe is a battle between expansion (kinetic energy) and contraction (gravitational attraction) and that their inequality (if it exists) cause a curvature of space:

21 Contraction - expansion = curvature

22 Contraction (gravity) - expansion = curvature - (Hubble flow) = curvature

23 Contraction - expansion = curvature (gravity) - (Hubble flow) = curvature (Kinetic energy) (potential energy) = fate

24 Contraction - expansion = curvature (gravity) - (Hubble flow) = curvature (Kinetic energy) (potential energy) = fate If gravity wins: universe will collapse (closed) If expansion wins: universe will expand forever (open) (eventually reaching a constant speed) If a tie we call that a critical universe expands forever ( approaching zero speed ininfinite time)

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26 Contraction (gravity) - expansion = curvature - (Hubble flow) = curvature

27 Contraction (gravity) - expansion = curvature - (Hubble flow) = curvature Measure the density of the universe Measure the Hubble constant Measure the curvature

28 Standard Model Basics K = curvature k = +1, positive curvature, closed universe (re-collapse) k = 0, flat curvature, open universe (expand forever) k = -1, negative curvature, open universe

29 Ω Ω = ρ/ρ crit where ρ crit is the density necessary to balance expansion and collapse (depends upon H 0 ) When ρ = ρ crit ; Ω = 1 (by definition); k = 0;

30 Ω and curvature if k = 0, Ω = 1 for all time if k = +1, Ω > 1 for all time, but changes if k = -1, Ω,< 1 for all time, but changes

31 Rules for Standard Cosmology Standard cosmology means mass dominates over energy, and the cosmological constant = 0 Three cases: k = -1, neg curve, Ω < 1, expand forever, infinite k = 0, flat curve, Ω = 1, expand forever, infinite k =+1, pos curve, Ω > 1, collapses, finite

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33 Standard Cosmology

34 Standard Cosmology

35 This is how your phone camera works (not an astronomical camera)

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