Ay21_Lec03_models

Ay21_Lec03_models - Ay 21 Lecture 3 An Overview...

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Ay 21 - Lecture 3 Global Geometry and Dynamics of the Universe, Part II An Overview: • Cosmological Equations of State • Computing cosmological models – Various examples • Distances in cosmology • Basics of cosmological tests • Horizons Recall the definitions of the cosmological parameters: The Friedmann Eqn. is now: and if ! k = 0, then: Solving The Friedmann Equation In order to solve it, we also need to define the behavior of mass/energy density " ( R ) of any given mass/energy component, which is generally expressed through the equation of state , often written as a relation between pressure and density: P = w !
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The EOS Parameter W • Defined by the equation p = w ! • Often called by itself the “equation of state” – Note: this is not necessarily the best way to describe the matter/energy density; it implies a fluid of some kind… This may be OK for the matter and radiation we know, but maybe it is not an optimal description for the dark energy • Special values: w = 0 means p = 0, e.g., non-relativistic matter w = 1/3 is radiation or relativistic matter w = -1 looks just like a cosmological constant … but it can have in principle any value, and it can be changing in redshift Equation of State (EOS) Some simple EOS we can consider: • “Matter”, “dust”, “galaxies” • Radiation • “Cosmological Constant” 0 = P 1 3 2 c P = 2 2 c P " = 3 Each will lead to a different evolution in redshift, and recall the basic GR paradigm: In reality, the universe contains a mix of these components, and maybe others as well… Density determines the expansion Expansion changes the density Using the EOS We need to put these into the Fluid equation: 0 3 2 = ! " # $ % + + c P a a Fluid Equation 7 0 = P 3 2 c P = 2 c P " = 1 2 3 1 0 3 = + a a ( ) 0 1 3 3 = ! ! " a t a # 4 3 ! " # a $ 2 0 4 = + a a ( ) 0 1 4 4 = ! ! " a t a 4 ! " # a 5 3 0 = const " 6 How does the matter/energy density change as the universe expands? Start with the 3 cases we just described: We get: Evolution of the Density • Matter dominated ( w = 0): ~ R
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Ay21_Lec03_models - Ay 21 Lecture 3 An Overview...

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