Key Results from last lecture Friedman Eq. Boundary Condition G.R. Eq. II Robertson-Walker Metric.

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Presentation transcript:

Key Results from last lecture Friedman Eq. Boundary Condition G.R. Eq. II Robertson-Walker Metric

Equation of State of Normal Matter

Model Content of Universe by theEquation of Model Content of Universe by the Equation of State of the different forms of Matter/Energy e.g., w  for normal matter w  for photons w  for Cosmological Constant demo

Figuring Out the Equation of State How does M/E goes as the scale factor?

Flat Universe –Matter Dominated 1

Only way to reconcile these our substitution with our equation is for Fr. Eq from last page

Flat Universe – Radiation Dominated

Flat Universe –Cosmological Constant Dominated

Domination of the Universe As Universe Expands –Photon density decays as a 4 –Matter density decays as a 3 –Cosmological Constant density decays as a 0 Note that exactly flat Universe remains flat – i.e.  i =1 Cosmological Constant Models tend towards flatness overtime Other models tend away from flatness over time.

Log(a) Log(t) radiation matter Cosmological Constant