# Cosmology Lecture 22

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### Motivating Inflation

The Big Bang model of the universe has 3 pillars supporting it:

- It predicts the relative abundances of .
- It explains the Hubble expansion.
- It predicted the CMB.

However, there are 4 problems with the original Big Bang model:

- The Horizon/Homogeneity Problem * Why is the universe so uniform on large scales? * The CMB temperature is uniform to a part in , implying that large areas of the universe should have been in causal contact with one another. * However the “acoustic horizon” at photon decoupling subtends only on the sky. Note that the CMB angular spectrum depends on , but so does the acoustic horizon size. These effects cancel, making the above statement true for all .
- The Flatness Problem * Why is so close to 1? * In PS#1 we showed that . Thus at , when recombination occurred, for a matter-dominated universe:

- Even worse, at Planck time, . Scaling backward through matter-domination to equality time, and then on back through radiation-domination, we get that to get , we need . * Why so close to 1.0, but not 1.0? This is level of extreme fine tuning is a little hard to swallow.
- The Monopole Problem * This is the problem which originally motivated Guth to invent inflation. Most GUTs (Grand Unified Theories) predict the possible creation of monopoles. * The monopole mass where is the symmetry-breaking energy, and is the coupling constant. * The monopole # density, in terms of the correlation length is . Thus, the Energy density of monopoles should be . This means the universe should have collapsed long ago.
- The Structure Formation Problem: Where is and from? What is the origin of these fluctuations?

Inflation solves all of these problems.