Duke Physics 55 Spring 2007 Inflation; the Concordance Model Lecture #31:
OUTLINE BDSV Chapter 23.3, 23.4 Inflation of the Early Universe: Solving the structure problem Solving the horizon problem Solving the flatness problem The Concordance Model
Review PRS Question Based on our current understanding of physics, it would seem that we can understand pretty well the conditions that prevailed in the early universe as far back as: a. One ten billionth of a second after the Big Bang. b. 380,000 years after the Big Bang. c. 3 minutes after the Big Bang. d. 10 billion years ago. e. We cannot understand the early universe.
Based on our current understanding of physics, it would seem that we can understand pretty well the conditions that prevailed in the early universe as far back as: a. One ten billionth of a second after the Big Bang. b. 380,000 years after the Big Bang. c. 3 minutes after the Big Bang. d. 10 billion years ago. e. We cannot understand the early universe. We can see in photons back to 380,000 years after the Big Bang; earlier than that we understand based on extrapolation & physics knowledge
Last class: eras after the Big Bang Early universe was hot and dense; it has expanded and cooled Forces 'froze out' as the universe cooled
Evidence for the Big Bang from COSMIC MICROWAVE BACKGROUND RADIATION, from era of recombination when the universe went transparent Thermal, T=2.7K Small temperature variations map density fluctuations after recombination
Review PRS Question Why does the Big Bang theory predict that the CMBR should have a near perfect thermal spectrum? a. The background radiation came from the heat of the universe, with a peak corresponding to the temperature of the universe. b. The spectrum of pure hydrogen is a perfect thermal spectrum. c. The spectrum of 75% H and 25% He is a perfect thermal spectrum. d. The light from all the stars and gas in the sky averaged over the entire universe is a perfect thermal spectrum.
Why does the Big Bang theory predict that the CMBR should have a near perfect thermal spectrum? a. The background radiation came from the heat of the universe, with a peak corresponding to the temperature of the universe. b. The spectrum of pure hydrogen is a perfect thermal spectrum. c. The spectrum of 75% H and 25% He is a perfect thermal spectrum. d. The light from all the stars and gas in the sky averaged over the entire universe is a perfect thermal spectrum.
Particle physics is reasonably well understood back to here We will zoom in here this class
Before ~1980, questions with no good answers: Where does the universe's structure (galaxies, clusters, large scale structure) come from? (structure formation problem) Why is the large scale universe so smooth? (isotropy or horizon problem) Why is the density close to critical? (flatness problem)
A theory which solves (or at least gives plausible explanations for) all of these problems: INFLATION Alan Guth, MIT Expansion by a factor of ~10 in ~10 50 32 seconds!!
Aside: quantum mechanics (tested in the lab) HEISENBERG UNCERTAINTY PRINCIPLE Something with a well defined position has a large uncertainty on its momentum Something with a well defined momentum has a large uncertainty on its position p x ℏ /2 (uncertainty in position) x (uncertainty in momentum) ~ Planck's constant
What this means for the early universe: For tiny sizes in the early universe, there are relatively large fluctuations in energy: 'quantum fluctuations' or 'ripples' But these mass energy density fluctuations are not big enough to 'seed' structure formation... so how did the galaxies & clusters form?
Inflation helps to fix this problem by magnifying the density fluctuations Details not completely worked out, but models are improving
Next problem: smoothness of the universe (the ISOTROPY or HORIZON problem) CMBR is very uniform The temperature differences represented by this plot A B are only a few parts in 100,000 Two spots on the sky in opposite directions have almost exactly the same temperature (on average, the sky looks uniform on very large scales)
Why is this a problem? A's horizon spacetime diagram B's horizon Photons from A and B have traveled nearly 14 billion years to get here How can the matter from two distant parts of the sky have communicated with each other (to have the same temperature) in the distant past?
Inflation solves this problem If the universe expanded a lot at early times, regions in equilibrium then were then pushed to great distances (and maintain the same temperature). Photons can cross the gap before inflation, but not after
Note: special relativity is not violated by this rapid expansion. It's all of space that's expanding
Next: the 'flatness problem' FLAT SPHERICAL HYPERBOLIC (saddle shaped) Curvature of spacetime depends on how much matter/energy is present
Density ρ0: mass energy density of the universe Critical density ρc: mass energy density of the universe required to make spacetime flat 0 Density parameter: 0 = c Ω0=1 means flat spacetime All normal and dark matter: 27% of critical m M= =0.27 c This is very close to 1! (it's not 10000 or 0.00001)
A perfectly flat universe will remain perfectly flat as it expands Without inflation, a tiny imbalance at early times would have been magnified into enormous non flatness by now (universe would have ended immediately as Big Crunch, or Big Emptiness)... but now, we're pretty close to balanced! How did that happen? Seems a coincidence...; this is the 'flatness problem'
Inflation solves this problem too! Space flattens as the universe blows up, no matter what the original density
In fact, although matter is only 27% of a flat Ω0, current observations show that the total Ω0 of the universe is actually extremely close to 1 The details of the CMBR temperature map depend on overall curvature of space: look at typical angular distances between lumps
The sizes and separations of the hot/cold spots depend on the curvature of space More closed apparently bigger lumps More open apparently smaller lumps
For a flat universe, expect biggest temperature differences at about 1 deg: this implies 0=1 This is support for the idea of inflation!
All normal and dark matter: m 27% of critical M= =0.27 c What is the missing mass energy density required to make the universe flat? It's the dark energy: 0= m =1 This is the contribution of DARK ENERGY to the total: 73%
The current CONCORDANCE MODEL ΩΛ of cosmology Different data WD supernovae CMBR matter surveys all agree at one point Ωm
The Cosmic Pie Chart (latest best measurements) Cosmological parameters known to % level Precision cosmology! Still a lot that's 'dark'...
One more point about cosmology: Olbers' Paradox If the universe is infinitely large and old, the sky should be bright.. no matter where you look, there will be a star In an infinite forest of trees, you'll see a tree in every direction
But the night sky is dark... Therefore, either the universe is finite, or it must not be static... it could be infinite, but changing in a way that prevents us from seeing very distant stars So, the Big Bang solves this apparent paradox
WUN2K INFLATION of the early universe (end of GUT era) Expansion by a factor of ~1050 32 in ~10 seconds!!
WUN2K Helps with structure formation problem Quantum fluctuations magnified to seed structure formation Helps with horizon problem Parts of the universe were able to communicate before inflation Helps with flatness problem Expansion flattens the universe
WUN2K Angular sizes and separations of patches depend on curvature Evidence for inflation from CMBR 0 0= =1 c
WUN2K 'Corcordance Model': different methods together agree on amounts of dark matter and dark energy ΩΛ Ωm 'Precision cosmology'
WUN2K If the universe is infinitely large and static, the sky should be bright.. no matter where you look, there will be a star The Big Bang resolves this apparent paradox: the universe may or may not be infinitely large, but it's not infinitely old and static