Cosmology - Chapter 20 Cosmology The Cosmological Principle...

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Chapter 20 Cosmology
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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?
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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 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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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 the 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
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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 – A spherical volume evolves under 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! Equation of motion
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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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Case 2: k > 0 This term becomes smaller when R increases, eventually reaching a point where R dot = 0. Expansion stops at R max . 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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How does the presence of Gravity in an expanding Universe affect the relationship between the Hubble Time (1/H o ) and the true age of the Universe? The Universe was expanding faster in the
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Cosmology - Chapter 20 Cosmology The Cosmological Principle...

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