Chapter 17

Cosmology

Over one thousand galaxies visible

The Universe on the Largest

Scales

• No evidence of structure on a scale

larger than 200 Mpc

• On very large scales, the universe

appears to be:

• Homogenous - the same everywhere

• Isotropic - the same in all directions

Figure 17.1

Galaxy Survey

Cosmology

• The study of the structure and evolution of the universe

• Cosmological principle - twin assumptions of homogeneity and isotropy

• Generally accepted by astronomers

• No edge (violates homogeneity)

• No center (violates isotropy)

Olbers’s Paradox

• Assume that universe is infinite and

unchanging in time

• When you look at sky at night, your line of

sight will eventually encounter the bright

surface of a star

• Entire sky should be as bright as the sun

• But sky is dark at night - Olbers’s Paradox

• From nineteenth century Heinrich Olbers

Figure 17.2

Olbers’s Paradox

Analogy 17-1

Every sight line intersects a tree

Olbers’s Paradox

• Since sky is dark at night, either

• universe is not infinite and/or

• universe evolves in time

Hubble’s Law

• Recession velocity = H0 X distance

• How long did it take a galaxy to reach

its current distance from us?

• Distance = velocity X time

• time = Distance/velocity

= Distance/(H0 X distance) = 1/H0

• = 14 billion years (for H0 = 70 km/s/Mpc)

Birth of the Universe

• Hubble’s law implies that 14 billion years ago,

all galaxies were at the same location

• Everything in the universe was confined to a

single point then

• The point exploded - this is the Big Bang

• This was the beginning of the universe and

the beginning of time

Big Bang

• Big Bang explains Olbers’s paradox -

even if universe is infinite, we only see a

finite part within 14 billion light-years

• Light from beyond has not yet reached

us

Where was Big Bang?

• Big Bang was not an explosion of matter into space

• Big Bang was an explosion of the universe itself, or of space itself

• Galaxies don’t rush into empty space -instead space itself expands

• Entire universe was a point - the Big Bang happened everywhere at once

Receding galaxies

• Think of galaxies as coins taped to an

expanding balloon

• Surface of balloon represents universe

• Every coin sees every other coin recede

• No coin is at center

Figure 17.3

Receding Galaxies

Cosmological Redshift

• For expanding universe, Doppler

interpretation not technically correct

• Galaxies are not moving apart through

space

• Instead, space itself is expanding

• Redshift represents expansion of

wavelength as universe expands

Figure 17.4

Cosmological Redshift

Fate of the Universe

• Will universe expand forever?

• Similar to escape velocity from a planet

• Will object tossed upward rise forever or

fall back?

• Depends on launch speed and mass of

planet

Figure 17.5

Escape Speed

Critical Density

• Low density universe expands forever

• High density universe collapses in a Big

Crunch

• Critical Density is the dividing line

• For H0 = 70 km/s/Mpc, critical density is

9 X 10-27 kg/m3

• 0.1 Milky Way galaxies per cubic Mpc

Figure 17.6

Model Universes

Geometry of space

• Mass/energy warps space

• The greater the total density, the greater

the curvature

• Density includes mass (visible and dark

matter)

• Also includes all energy

Cosmic density parameter

0 is ratio of actual to critical density

0 > 1.0 is a closed universe

0 < 1.0 is an open universe

0 = 1.0 is a critical universe

Flat space

• Euclidean geometry

• Parallel lines never meet

• Angles in triangle add to 180°

• Circumference of circle is X diameter

0 = 1, critical universe

• Infinite in extent

Positively curved space

• Studied by Georg Riemann

• Like surface of sphere

• “Parallel” lines intersect twice

• Angles in triangle add to more than 180°

• Circumference of circle is < X diameter

0 > 1, closed universe

• Finite in extent

Figure 17.7

Einstein’s Curve Ball - Closed Universe

Negatively curved space

• Studied by Nikolai Lobachevsky

• Imagine a saddle shape

• Infinite number of lines through a point

parallel to another line

• Angles in triangle add to less than 180°

• Circumference of circle is > X diameter

0 < 1, open universe

• Infinite in extent

More Precisely

17.1

Curved Space

Cosmic density parameter

• Counting all luminous matter gives 0 of

several percent

• Adding in estimated dark matter in

galaxies and clusters gives 0 ≈ 0.25

• On a larger scale distribution of dark

matter not well known

• Overall cosmic density less than critical

Cosmic acceleration

• Use Type I supernovae to measure distances

(independent of Hubble’s law)

• If gravity slowing expansion - universe is

decelerating - objects at great distances -

(long ago) - should be receding faster than

Hubble’s law predicts

• Data seems to show expansion is

accelerating

Figure 17.8

Accelerating Universe

Cosmic acceleration

• What causes this acceleration?

• Dark energy - exerts repulsive force

• Dark energy may greatly exceed total

mass (luminous and dark) of universe

Cosmological Constant

• “Vacuum pressure” force associated with empty space

• First suggested by Einstein in 1917 - his equations showed universe evolved in time

• Expansion of universe not known then

• When discovered, he discarded Cosmologial Constant as the biggest mistake of his scientific career

• May be making a comeback as a dark energy explanation

Discovery 17-1

Einstein and the Cosmological

Constant

Cosmic Composition

• Theoretical studies suggest universe is flat

• A variety of measurements lead to 0 = 1.0

• Density is made of both matter (27%) and

dark energy (73%)

• Gravity tends to slow expansion

• Dark energy tends to increase expansion

• Universe will expand forever

Figure 17.9

Geometry of the Universe

Age of universe

• For H0 = 70 km/s/Mpc,

• Age of critical density universe with no

cosmological constant is 9 billion years

• Age of low density universe > 9 billion y

• Age of high density universe < 9 billion y

• Age of accelerating universe is about 14

billion y

Figure 17.10

Cosmic Age

Age of universe

• Globular clusters formed 10 - 12 billion

years ago

• Consistent with 14 billion years age for

universe with 2 billion years for galaxies

to evolve

• Inconsistent with critical density with no

dark energy

Cosmic Microwave

Background• Penzias and Wilson in 1964 discovered a

“hiss” in all directions of space

• Microwave wavelengths - blackbody curve at 2.7 K

• Gamma ray wavelengths in early universe cosmologically redshifted to microwave wavelengths

• Radiation is isotropic (same in all directions)

• Contains far more energy than all of energy emitted by all stars and galaxies

Figure 17.11

Microwave Background Discoverers

Figure 17.12

Cosmic Blackbody Curves

Figure 17.13

Microwave Background Spectrum

Matter and Radiation

• Currently density of matter much

greater than density of radiation

• Matter-dominated universe

• In past, both radiation and matter more

dense

• But radiation cosmologically redshifted

• Early universe radiation-dominated

Figure 17.14

Radiation-Matter Dominance

Formation of nuclei and atoms

• Early universe almost entirely radiation

• In first minute photons had sufficient

energy to transform into electrons,

protons, neutrons and exotic particles

• Primordial nucleosynthesis - formation

of elements heavier than hydrogen

shortly after Big Bang

Deuterium and helium

• Below 900 million K, about two minutes after Big Bang, protons and neutrons fused into deuterium

• After short while, deuterium fused into heavier elements, mostly He-4

• Almost all neutrons consumed

• By 15 minutes, elemental abundance set

Figure 17.15

Helium Formation

Deuterium abundance

• Not all primordial deuterium converted to He

• Present day density of universe indicated by

deuterium remaining

• Gives density of “normal” matter of 3 to 4

percent of critical

• Total matter density is about 1/3 of critical

• Most of matter is “dark” and not composed of

protons and neutrons

Formation of Atoms

• At age of tens of thousands of years, matter began to dominate over radiation

• Cooled enough for nuclei and electrons to form atoms - known as de-coupling

• Before then, free electrons scattered radiation

• Universe went from opaque to transparent

• After about 400,000 years, temperature fell to 3000 K, and microwave background we see now released when universe was 1100X smaller than today

Figure 17.16

Radiation-Matter Decoupling

Horizon Problem

• Observe two regions at opposite

directions in sky

• Microwave background same at both

• Density and temperature same at both

• But not enough time, even at speed of

light, to “connect” them

Figure 17.17

Horizon Problem

Flatness Problem

• Universe is very close to being flat

today

• Universe must have been extremely

close to critical in the past

• Why is universe’s density nearly critical,

out of all possibilities?

Figure 17.18

Flatness Problem

Horizon and Flatness problems

explained

• Grand Unified Theory (GUT) describes

superforce made up of electromagnetism and

strong and weak nuclear forces

• 3 forces unified at very high temperatures

• Predicts that at 10-34 s after Big Bang, at 1028

K, universe greatly expanded by factor of 1050

until 10-32 s

• Epoch of inflation

Figure 17.19

Cosmic Inflation

Cosmic inflation

• Explains horizon problem

• Inflation took parts of universe that had

“communicated”, then dragged them far

apart

• Explains flatness problem

• Curved space, greatly expanded,

“appears” flat

Figure 17.20

Inflation and the Flatness Problem

Formation of large-scale

structure

• Small inhomogeneities in early universe

grew into large scale structures

• Dark matter, unaffected by radiation,

clumped and gravitationally affected

normal matter

Figure 17.21

Structure

Formation

Figure 17.22

Structure Simulated

COBE map

• Dark matter doesn’t emit or absorb

radiation

• Its gravity affects redshift of cosmic

microwave background radiation

• Measured by COBE satellite

• Map shows universe is of critical density

Figure 17.23

Cosmic Microwave Background Map

Figure 17.24

Early Structure - WMAP spacecraft