5.2 Quantum Fluctuations Review

summary

It turns out that the early universe was not exactly uniform.

- Had it been completely uniform, it would have stayed that way forever, and all matter would have been a bland, homogeneous “soup.”
- Instead, there were small variations in mass density. This led to the clumping or “clustering” of matter.
- Bits of matter began to attract each other, forming bigger bits, which in turn could pull in even more matter with their gravitational forces.
- Slowly, structure started to appear in the universe. We see this today in the form of galaxies and the clustering of galaxies.

This led cosmologists to wonder where these variations in mass density originated from.

- The inflationary picture explains this using the idea of
*quantum fluctuations*. - Heisenberg’s uncertainty principle allows energy and time to be related. $$\Delta E \Delta t \approx \frac{h}{2\pi}$$ where $E=$ energy, $t=$ time, and $h=$ Planck’s constant.
- This means that energy conservation can appear to be violatedâ€”but only for very small instances of time.
- Quantum fluctuations appear as temporary changes in the amount of energy at a specific point.
- The mass density of the early universe fluctuated on the quantum scale, having a recurring effect that produced all the clumping of matter we see today.

Inflation predicts these quantum fluctuations extremely accurately.

- These ripples can be analyzed like any other wave, with inflation making generic predictions for their spectrum.
- We can calculate how the intensity of the ripples varies with their wavelength.
- The fluctuations we measure in the cosmic background radiation agree very well with those predicted by inflation.