Cosmology - 3/24/10 Chapter 20 Cosmology The Cosmological...

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3/24/10 1 Chapter 20 Cosmology The Cosmological Principle : the universe is homogeneous and isotropic on sufficiently large scales The universe looks pretty much like this everywhere – “walls” and “voids” are present but no larger structures are seen…. It follows that the Universe has no “edge” or center. But is the Universe the same at all times? Remember universal expansion (Hubble’s Law)? recession velocity = H o x distance Thus, the cosmological principle does not imply that the Universe is constant at all times (this was once thought, however, to be the case - Steady State Universe ). Universal expansion points to a beginning of the Universe and implies that the Universe is changing over time - more on this in Chapter 21
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3/24/10 2 Expansion of the Universe - Olbers’s Paradox -is the Universe infinite?? If so, every line of sight eventually hits a star and the sky is always bright. Number of stars goes up by r 2 for each shell, but brightness decreases for each shell by r 2 . Brightness per shell is a constant. The fact that sky is not uniformly bright indicates that either • the Universe has a finite size and/or • the Universe has a finite age + redshifting of light from distance sources reduces flux Newtonian Gravity in Cosmology What can we learn about the evolution of an expanding Universe by applying Newtonian gravity? Isotropy implies that the Universe is spherically symmetric from any point - spherical volume evolves under only its own influence. Consider mass m moving on the surface of a sphere with mass M(r) at position r m(d 2 r /dt 2 ) = -GM(r)m/r(t) 2 (20.13) Homogeneity ρ = constant R is the scale factor where R = r (t)/ r (t o ) As the Universe expands, any given mass occupies a larger volume ρ (t) = ρ o (R 3 o /R 3 (t)) One cannot be zero without the other. .. A Universe with matter cannot be static! To integrate the equation of motion, first multiply both sides by dR/dt This must be a constant (call it k) k can be either 0, +, or - Case 1: k = 0 R is proportional to t 2/3 The Universe expands at an ever decreasing rate! Borderline Universe or Marginally Bound
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3/24/10 3 Case 2: k > 0 This term becomes smaller when R increases, eventually reaching a point where R dot = 0. Expansion stops at R max . After R max is reached, Universe starts to collapse! Closed or Bound Universe Case 3: k < 0 If k is negative, then -k is positive and the right-hand side of 20.19 is always positive. As R increases, first term goes to zero and R dot 2 -k or R dot (-k) 1/2 Expansion continues forever! Open or Unbound Universe
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Cosmology - 3/24/10 Chapter 20 Cosmology The Cosmological...

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