Chapter 26: Cosmology

• Why is the sky dark?

• The expanding universe

• Beginning of the universe: The Big Bang

• Cosmic microwave background

• The early universe

• Shape of the universe

• The accelerating universe

Cosmology

• What is cosmology? It is the study of the nature of the universe.– How large is the universe?– What is the structure of the universe?– How long has the universe existed?– How has the universe changed over time?

Olber’s paradox: Why is the night sky dark?

• Newton imagined the universe was infinite and static.– An infinite number of stars are

scattered randomly throughout an infinitely large universe.

– If it weren’t infinite then over time gravity would cause the universe to collapse.

• If this were really true then everywhere we looked we would see a star and the night sky would be bright…

Einstein’s contributions

• What does general relativity say about the universe as a whole?

• Einstein’s calculations couldn’t produce a static universe.

• He added a term called the cosmological constant to force a prediction of a static universe.

• Einstein later said that was “the greatest blunder of my life.”

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The expanding universe

• Edwin Hubble found the first evidence that the universe was expanding.– Hubble law: v=H0d

– This law states that remote galaxies are moving away from us with speeds proportional to their distance.

• Because remote galaxies are getting farther and farther apart as time goes on, astronomers say that the universe is expanding.

The expanding universe

The expanding universe

Yet another redshift

• Expansion explains why light from distant galaxies is redshifted.

• Space expands as photons travel through it and the photon becomes “stretched.”

• This is called a cosmological redshift.– It is NOT a Doppler shift.

Cosmological redshift

• The cosmological redshift lets us calculate how much the universe has expanded since the light was emitted.

• The factor 1+z indicates the amount of expansion.

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z =λ − λ 0

λ 0

⇒λ

λ 0

=1+ z

Lookback time

• An object’s redshift along with the Hubble law allow us to determine the distance to the object.– This gives us the lookback time to the object.

– The distance measured in light years is equal to the lookback time in years.

• To avoid uncertainties, astronomers typically describe the distance to an object in terms of its measured redshift.

The cosmological principle

• The idea of the expanding universe demonstrates a central idea of cosmology.

• Cosmological principle: The universe is homogenous and isotropic.– Homogeneous: all regions are the same– Isotropic: looks the same in every direction

• Ultimately the cosmological principle means that we do not occupy a special location in the universe - they are all essentially the same.

The Big Bang

• If you imagine time moving backward the Hubble flow will reverse direction.

• If we look far enough into the past there must have been a time when the density of matter was inconceivably high.

• An event, called the Big Bang, marks the “birth” of the universe.

• I know it sounds crazy, but hold on because it turns out there is plenty of convincing evidence.

Can we estimate the age of the universe?

A resolution to Olber’s paradox: Part 1

A resolution to Olber’s paradox: Part 2

• According to the Hubble law, the greater the distance to an object the greater its redshift.

• Light from a galaxy nearly at the cosmic light horizon has a nearly infinite redshift.– This light has nearly no energy at all meaning

the galaxies emitting the light are nearly invisible.

Evidence for the Big Bang

• First, a dilemma: There is too much helium in the universe. Where did it come from and how can we explain it?

• 65 years ago physicists first postulated that the early universe was at least as hot as the center of the Sun.– At this time, the universe was filled with many high-

energy photons which should now have much longer wavelengths thanks to cosmological redshift.

• Can we see them?

Cosmic microwave background

• Wien’s law predicts that this radiation should have its peak in the microwave part of the spectrum.

• The CMB was first detected in the 1960s by scientists working on communications systems.

• Persistent noise in their system turned out to be the CMB.

Observations of the CMB

Observations of the CMB

Building blocks of the universe

• Everything in the universe is either matter or radiation.– Matter: luminous and dark matter– Radiation: photons (majority are CMB photons)

• Which plays a more important role in the universe?– The answer to this question depends on when you ask

it.– We are interested in comparing the relative mass

densities of matter and radiation.

Radiation mass density

• We can combine E=mc2 with the Stefan-Boltzmann law to find the mass density of radiation in the universe:

• For the present day T=2.75 K and rad=4.6x10-31 kg/m3

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rad =4σT 4

c 3

ρ rad = mass density of radiation

T = temperature of radiation

σ = Stefan - Boltzmann constant

c = speed of light

Matter mass density

• To find the average matter mass density we must determine the amount of matter in a large volume of space. m=M/V

• Measurements of rich clusters we estimate that m=2.4x10-27 kg/m3.– Equivalent to about 1.5 H atoms per m3.

– Luminous matter constitutes only about 17% of the total matter mass density of the universe.

Which wins?

• The average density of matter is thousands of times larger than the mass density of radiation.– This is mainly because the CMB photons have such low

energy.

– There are actually 4.1x108 CMB photons per m3.

• As we go back in time the universe gets smaller so both densities increase.– The photons become less redshifted (more energetic) and

the total mass density of radiation increases rapidly.

Evolution of density

• Transition happened about 24,000 years after Big Bang.– z=5200

• Using Wien’s law we can determine the radiation temperature at z=5200 to be 14,000 K.

Recombination

Recombination

• The photons that had been colliding with charged particles could now stream unimpeded through space.– These same photons are today the CMB photons.

• Because the universe was opaque before z=1100 we can’t see further back into the past.– CMB photons are the most ancient photons we can

observe.

Temperature variations in the CMB

Shape of the universe

• We also want to know about the combined mass density of all forms of matter and energy.– We can do this by studying the shape of the universe.

• Einstein tells us that gravity curves space.– Mass and energy are equivalent, so both can curve

space.– Matter and energy scattered across space should give

the universe an overall curvature.• Degree of curvature depends on combined mass density of

energy and matter - called 0.

Density of the universe

• A flat universe is a special case with a specific density.– Call this density the critical density or c.

• Spherical: 0> c, • Flat: 0= c, • Hyperbolic: 0<c,

• Alternatively, we define the curvature of the universe by the ratio of the combined average mass density to the critical density. c

Can we measure the curvature?

• If we could observe the paths of light from a distant source we could in principle measure the curvature of the universe.– We use the CMB photons.– The presence of CMB hot spots allows us to

make the measurement.– Calculations indicate that these hot spots should

have an angular size of about 1°.

Can we measure the curvature?

Results of curvature measurements

• We find that 0=1.0 with an uncertainty of 2%.– This says the universe is flat. (0= c)

• Unfortunately, m is measured to be only about 24% of the critical density.– Radiation density is insignificant.

• Radiation, matter and dark matter acount for 24% of the total density of the universe. What accounts for the rest?– Must be some form of energy we cannot detect

gravitationally or electromagnetically.– Dark energy!

Dark energy

• This is Einstein’s cosmological constant.– It is a form of energy that tends to make the

universe expand.– It turn out that Einstein’s error was not

introducing . The error was not making it big enough.

• This is an extraordinary claim. Do we have any evidence to support it?

Measuring the expansion of the universe

Actual measurements

Actual measurements

The future of the universe

• If dark energy truly is a cosmological constant the universe will continue to expand forever.– In about 30 billion years only 1000 or so of the nearest

galaxies will be visible.

• Several models have been proposed describing a type of dark energy whose density slowly decreases as the universe expands.– This leads to predictions that the universe could either

expand forever or eventually recollapse.– Future observations will help clarify these predictions.