Cosmology and Dark Matter II: The inflationary Universe

Jerry Sellwood

Matter-radiation equality

• Next milestone

• Very little happens

• Expansion rate changes

Formation of the CMB• For the first 300,000 years, the intense

radiation kept hydrogen ionizedH+ + e H +

• Constant scattering of photons – maintains thermal equilibrium with matter – makes the universe opaque

• But as photons are redshifted, atoms are quite suddenly able to survive

• The universe quickly becomes neutral and transparent

Re-ionization

• Diffuse gas in the universe did not stay neutral for long

• First stars and/or quasars emitted enough UV radiation to ionize all the diffuse gas

• Density is far too low by that time for the ionized gas to be opaque

Density of Matter

• BBN tells us that normal (baryonic) matter b = b / crit = 8G b / 3H0

2 0.04

– In stars in galaxies, gas in galaxies, gas between galaxies in clusters of galaxies

– yet most remains undetected – it is believed to fill the universe as very low density ionized gas

• But galaxies and clusters of galaxies contain much more mass that emits no light

Galaxy rotation curves• Measure speed of gas using Doppler shift• Constant circular speed observed, whereas prediction from

visible matter decreases• Large mass discrepancy → “dark matter halo”• Mass in dark matter (at 30kpc) 4 mass in stars & gas

Coma cluster of galaxies• Originally studied

by Zwicky in 1930s

• Galaxies moving much faster than expected

• More than 50 times as much mass as we would have guessed from the brightness of the galaxies

Gravitational light deflections

Hot gas in galaxy clusters

• Chandra data (Grego et al)

• 0.3 – 10 keV from hot gas (+ 3 point sources)

• Coincident with a distant galaxy cluster

• Hot gas is gravitationally confined

Dark Matter• Some 80% – 90% of the matter in the

universe is “dark”. What could it be? – Not regular protons, neutrons & electrons– Does not emit any detectable radiation– Does not feel electromagnetic forces– Does not feel the strong nuclear force– Exerts gravitational forces

• Most popular guess is that it is made of WIMPs – fundamental particles that we have not yet detected in any other manner

An open universe?

• Our best estimate: DM 0.250.05

• BBN gave us b 0.04• Total matter density is

therefore M 0.3crit • No other matter known• Seems to imply that we

live in an open universe, that will expand forever

The Hot Big Bang

• Successfully accounts for:– Uniform expansion – Hubble’s law– Relic radiation

• now cosmic microwave background• fills all space• almost perfectly isotropic

– 76% hydrogen + 24% helium• set up in the first 3 minutes

• But 4 serious problems with this beautiful picture were apparent by the late 1970s

Horizon Problem

Horizon Problem

• Uniform temperature of CMB• At the time the radiation was emitted, the

past light cone of matter in region A did not overlap with that from region B

• Why are the temperatures the same to 1 part in 105?

• Why are they chemically homogeneous• Apparently violates causality

Flatness problem

• Recall Friedmann’s equation above– 1st term on RHS decreases as a-, where =3

for dust, =4 for radiation– 2nd term on RHS decreases as a-2

• a has increased by 1010 since BBN• Why is first term not negligible now?

1– was no more than 10-20, but not zero!

• How did it start out so finely balanced?

Structure problem• What caused galaxies

and clusters of galaxies to form?

• Surveys reveal a clustering hierarchy– on scales that were

larger than the horizon at much earlier times

• How were the seeds of this frothy structure sowed?

Monopole problem

• Unified gauge theories may predict the existence of one or more stable, superheavy relic particles – e.g. magnetic monopoles

• They should have been formed in abundance and survived

• Why is the universe today not dominated by such heavy relics?

Solution is InflationInflation

• If the term dominates, then the scale factor a(t) grows exponentially (recall aH = da/dt)

• A non-zero implies a constant energy density = c2/8G, generally interpreted as “false vacuum” or a scalar field

• Postulate a large for a short period in the early universe

• Long enough for a to increase by e100

Solves all 4 problemsHorizon: Regions of the

universe that were close enough to have become homogeneous are now far apart

causality is not violated

Note that this does not imply superluminal motion

Solves all 4 problems

Flatness: radius of curvature increases by e100, making the universe flat to a very good approximation

Monopole: If inflation occurs after the heavy relics have formed, their density is diluted by e300

Structure Problem• Quantum fluctuations during inflation cause

tiny variations in the energy density

• Normally they are short-lived

• But during inflation, fluctuations on scales close to that of the local horizon get carried outside the horizon and become “frozen in”

• Random variations about the mean energy density of a flat universe

• Therefore known as “curvature fluctuations”

• Re-enter the horizon later