LECTURE 29

Evolution of expanding Universe:  

Universe = space-time + energy (matter & radiation)

the shape of the Universe:

• matter (mass) distorts (curves) space
• three possibilities for geometry of space:

1. if positive curvature (convex) => closed Universe => expansion gradually slows down => will eventually stop => contraction will begin => Universe ends in Big Crunch
   
   
2. if zero curvature (flat) => open Universe => expansion will stop but no contraction
   
   
3. if negative curvature (concave) => open Universe => expansion continues forever => heat death of Universe

which is it?

• initial Big Bang "explosion" generates expansion "pressure"
• gravity (always attractive!) counteracts expansion
• balance between gravity and hot matter pressure determines geometry:

1. if total mass greater than critical => closed Universe
2. if total mass less than critical => open Universe
3. if total mass equal to critical => flat Universe

• critical mass generated at Big Bang => critical density of matter now ~ 3 protons / m³

how to estimate present matter density?

• "measure" total amount of mass (i.e. strength of gravity)

1. measure mass of clusters of galaxies (luminous matter)
2. add mass of Dark Matter needed for clustering, rotation, etc.

open Universe !

• but is there dark matter between clusters of galaxies?

1. mini black holes
2. cosmic strings
3. massive neutrinos
4. magnetic monopoles...
   

• "measure" Hubble constant (i.e. rate of expansion)

1. if deceleration of the expansion small => open Universe
2. if large => closed Universe
   
   

• how to measure H changes? - compare H for nearby and distant galaxies
• but hard to measure H (inaccuracy might be greater than expected change)

present conclusion: open Universe but close to flat