The Hot Big Bang The Big Bang Model Our prior discussion suggests that the universe has been expanding for billions of years. (10-20 Gyr) This implies

The Hot Big Bang

The Big Bang Model• Our prior discussion suggests that the universe has

been expanding for billions of years. (10-20 Gyr)• This implies that in the past all of the matter in the

universe must have been closer together.– MORE DENSE– HOTTER

• The idea is that there was a certain time when all matter/energy and space/time were concentrated in a single point from which it has since expanded rapidly.

• If you can just imagine far enough into the past, you can think of the “point” as being like the center of a black hole.

• Matter at the center of a black hole is crushed to an infinite density.

The Big Bang Model – Not a conventional explosion

• This illustration shows the curvature of the “fabric” of space-time.

The Big Bang Model – Not a conventional explosion• The key point is that at the

center of the black hole time and space become muddled (indistinguishable).

• The phrases “before the Big Bang” and “at the moment of the Big Bang” are meaningless since time did not really exist until after the Big Bang.

• 1D Expansion – Consider a rubber band with dots equally spaced.

The Big Bang Model – The rubber band and balloon comparisons

As the rubber band stretches it is obvious that the center of expansion is not physically inside the band, but rather in the center of the circle.

• 2D Expansion – Consider a balloon with dots equally spaced.

The Big Bang Model – The rubber band and balloon comparisons

Again, as the balloon stretches it is obvious that the center of expansion is not physically on the surface of the balloon, but rather in the center of the balloon.

The Big Bang Model – The rubber band and balloon comparisons• 3D Expansion – It is not possible to find any

point where the BB happened.

• It happened in the 4th dimension, time.

• We can say that the BB did happen, but where is not only unanswerable, but also meaningless.

The Big Bang Model – Details

Before 10-43 seconds after the BB, all four fundamental forces were unified all having equal strength


From 10-43 to10-35 seconds gravity separated. We believe that the total energy in the universe became too low to keep gravity unified.


At 10-10 seconds the strong nuclear force and electromagnetic force separated.


Energy becomes low enough for quarks (sub-elementary particles) to finally stick together and form neutron and protons.


Primordial Helium produced as the “annihilation” of matter reaches a point where enough electrons are left over to bond with protons and form proto-atoms.


Temperature low enough for both Hydrogen and Helium to start forming.Era of Recombination


Temperature low enough for hydrogen and Helium to fuse and form stars, which in turn organize into galaxies, then galactic clusters, and finally galactic superclusters.

The Hertzsprung Russell Diagram

The Early Universe was a “Primordial Fireball”

Everything in the Universe

Mass -- or -- Energy

Stars, planets, galaxies and Dark Matter

Photons

Cosmic background radiation

Dark Matter?• Einstein’s calculations predict that large mass distorts surrounding space

–passing light is bent toward center of cluster–shapes of background galaxies distorted

• Measuring distortions of background galaxies allows cluster mass measurement.

Hubble Space Telescope Image of Abell 2218 Gravitationally Lensed Galaxies

Massive Galaxy Cluster

Distant GalaxyObserver

Direction of light changes.Light bent toward center

of galaxy cluster.

Light from distant galaxy

Apparent position of Distant Galaxy

Apparent position of Distant Galaxy

Einstein Rings in Nature – Indicates presence of Dark Matter• Gravitational rings are rare, because

they require exquisite alignment of observer, lens and source, and they require symmetric lenses

Hubble Space Telescope image of abackground galaxy lensed by

a foreground galaxy

Einstein ring in the radio bandwidth

• MACHO’s “Massive Compact Halo Objects”– Not “visible” because the best candidates are…

• Black Holes (predicted by General Relativity)• Brown Dwarfs (stars that never ignite, predicted by stellar evolution)

– Can gravitationally lens light just like a massive galaxy that is visible.

Dark Matter? MACHO’s and WIMPS

Dark Matter? MACHO’s and WIMPS

Dark Matter? MACHO’s and WIMPS• WIMP’s “Weakly Interacting Massive Particles”

– MACHO experts admit that they cannot account for all of the dark matter required to describe galactic motions

– MACHO’s make up no more that 40% of Dark Matter

• WIMP’s – Non-baryonic particles that have very tiny interactions with baryonic

particles (neutrons and protons) – Believed to be 10 - 10,000 times larger that protons and neutrons.

• Detecting WIMP’s – If a WIMP collides with an atom, there would be a measurable amount of

heat produced.– Crystals can be used– The AMANDA project (Antarctica Muon and Neutrino Detector Array) is

using the Antarctic ice sheet as a large crystal to try to detect WIMP’s


Everything in the Universe

Mass -- or -- Energy

Stars, planets, galaxies and Dark Matter

Photons

Cosmic background radiation

Which is more important?

Combining E=mc2 with Stefan-Boltzman Law for Blackbody Radiation (stay tuned) it can be shown that …

• Mass Density of Radiation = 4.6 x 10 –31 kg/m3

• The Mass Density of Matter can also be determined – (although much more difficult)

• Mass Density of Matter = 2 to 11 x 10 –27 kg/m3

• Dm>>>>Drad matter dominated universe!• However consider the density

– Given mass of Hydrogen atom, this is only 1-6 Hydrogen atoms per m3!!!!

– By contrast, on Earth 1m3 of air has 5 x 10 25 atoms!!!!– On average, Universe has very little matter in it. – The ultimate question is “How much matter is there?”

• Will determine the fate of the universe


• Even though the Mass Density of Radiation is low, the number of photons in a cubic meter is astounding…– Today, there are 500,000,000 photons/m3 of space.

• So why does matter dominate if photons outnumber particles by a billion to one?


• Universe expanding– Photons

redshifted– Become lower in

energy

• But think if we go backward in time …


• Now universe is being compressed

• Dm and Drad both increasing, but…

• Photons are now being blueshifted– Energy increasing (shorter wavelength)


• The rate at which Dm increases lags behind the rate at which Drad increases

• Before 2,500 years after the BB, radiation dominated.

2,500 years after BB

• Lets take a closer look at the CMBR– Today, ~ 1-10 mm (microwave)– 2,500 years after BB, ~ 40nm (ultraviolet)

• 25,000 x shorter then


• When object undergo temperature changes, they also give off different wavelengths of photons.• The cooler the temp, the longer the wavelength

Blackbody Radiation

Infrared Emission from Living Organisms

Infrared image of a cat. Orange is brighter(and warmer) and blue is dimmer (and cooler).Note the warm eyes and cold nose.

Images from IPAC at the Jet Propulsion Laboratory. The cat image comes courtesy of SE-IR corporation.

Infrared image of a man with sunglasses anda burning match. Black is dim (cold) and white it bright (hot).

Infrared Emission from Living Organisms

Cosmic Background Explorer (COBE)• NASA satellite designed to test nature of cosmic background radiation

• Three instruments– FIRAS- Far Infrared Absolute

Spectrophotometer• measure CMB spectrum

– DMR- Differential Microwave Radiometers

• measure variations in temperature on the sky

– DIRBE- Diffuse Infrared Background Experiment

Image courtesy COBE homepage.

Cosmic Microwave Background RadiationEffects of Expansion on Light

• As the universe continued to expand it also cooled

• the photons from the BB should have increased in wavelength.


• It has been calculated that at 300,000 years after the BB, EM radiation (of wavelength in the microwave region) should be spread throughout the universe (Wien’s Law – stay tuned)

• Arno Penzias and Robert Wilson– Bell Labs in New Jersey– Discover background in

1965 when they tried to filter “noise” from telephone signals being transmitted via satellite.

– temperature is 3 Kelvin– The exact temperature

that would give off radiation at the correct wavelength for radiation left over from the BB.

Penzias and Wilson with radio horn


Cosmic Background Spectrum

FIRAS Spectrum of CMB

Theoretical blackbody spectrum

T=2.728+/-0.004 K


COBE DMR Image (measures temperature on the sky)

• The sky temperature with range from 0-4 Kelvin• Microwave background is very uniform at ~3 Kelvin


COBE DMR Image: 1,000X Zoom• The sky temperature with range from 2.724-2.732

Kelvin• blue is 2.724 K and red is 2.732 K

• Dipole pattern in temperature indicates motion• Doppler Effect at level of ~0.005 K• Solar system is traveling at ~400 km/s with respect to CMB


COBE DMR Image: 25,000X Zoom• The sky temperature ranging from 2.7279-2.7281 Kelvin

• blue is 2.7279 K and red is 2.7281 K

• Dipole variation from Solar system motion removed• Red emission along equator is galactic emission• Other fluctuations are likely cosmic in origin


COBE DMR Image: Galaxy and Dipole Removed


Amplitude of temperature fluctuations is 0.000030 K or 30+/-3 K in 10 degree patches.(1 part in 100,000)

• So, today the CMBR has a temp ~ 3K

• What about 2,500 years after the BB when the densities were equal??

• From Wien’s Law (stay tuned)

max = 0.0029/Temp

40 nm = 0.0029/Temp

Temp ~ 75,000 K at 2,500 years after BB


2,500 years after BB

• Recall that temperature is a measure of KE

• Up to about 300,000 years after BB, the temp was high enough to prevent electrons and protons to combine. A condition known as a Plasma

• Plasmas are…– Opaque– Found in the centers of

stars, neon signs, and florescent tubes


“Primordial Fireball”stage of universe

Transparent stage after “recombination”


Hot Plasma Stage before…

“Cooler” Transparent Stage begins after…

The Development and Fate of the Universe• Since we cannot see past 300,000 years after the BB, then…

“What happened at the beginning of the expansion of the universe? Did space-time have an edge at the BB? The answer is that the boundary conditions of the universe are that it has no boundary, time ceases to be well defined in the very early universe, just as the direction north ceases to be well defined at the North Pole of any planet. Asking what happened before the BB is like asking to walk north from the geographic north pole…

If space time is indeed finite but without boundary or edge, this would have important philosophical and religious implications. It would mean that we would be able to describe the universe by a mathematical model that was completely determined by the laws of science alone…

At first sight it might appear that such a theory would enable us to predict everything in the universe, even its future. However, our powers of prediction are severely hampered by 1) the uncertainty principle of quantum mechanics and 2) the fact that the equations would be so complex that the only time they would be solvable would be simple situations.”

Stephen Hawking

• Thought Experiment – Recall the equivalence of free fall to orbital motion.

• If Vball < Vesc then ball falls back to Earth• If Vball = Vesc then ball will just escape and become

static• If Vball > Vesc then ball will escape and continue moving

according to N1L (straight line, constant speed, forever)

• So, what about the expanding universe?– The fate of the universe is very similar to the above thought

experiment, with just a few twists.

The Development and Fate of the Universe

Click here

• The fate of the universe will depend on primarily 3 things– The Average Mass Density of Matter – The Deceleration Rate of the Universe– The Geometry of the Universe

The Development and Fate of the Universe

0 – The Density Parameter

0 D

Dm

crit

M ass D ensity o f M atter

C ritica l D ensity of the U niverse

DH

Gw h ere H

G

crit

3

8

2

= 1 .1 x 10 k g / m

H ubble C onstant o f 75k m / s / M pc

U n iversa l G ravitational C onstant

the density equ ililan t to abou t 6 H ydrogen atom s / cub ic m eter

-26 3

0 – The Density Parameter

Closed Universe

– gravity wins over expansion

– expansion halts, collapse ensues in a Big Crunch

0 D

Dm

crit

> 1

Flat Universe

– expansion just stops and universe becomes static

0 D

Dm

crit

= 1

Open Universe

– gravity loses to expansion

– expansion continues forever

0 D

Dm

crit

< 1

A “Flat” Universe – Why would 0 = 1 cause the Universe to be flat?• Imagine you are standing on a large, expanding balloon

– as the balloon expands, the curvature becomes less apparent– what if the balloon were the size of the Earth… would you perceive the

curvature of the Earth?

• Inflation drives the Universe towards “flatness” • when inflation stops, the universe will be very large and “flat”

t 1

t 2

t 3

t 4

t 5

In this figure, the sphere expands by a factor of four between each timestep.

The Development and Fate of the Universe – Deceleration of the Expanding Universe

Recall Hubble’s Law V D

• Hubble’s Law seems to hold true for this graph

• However, consider the scale for distance.

• We are only looking back in time 1.6 billion years.

• What about distant galaxies/objects?

• Will their velocities approach the speed of light?

Quasars = Quasi-Stellar Radio SourceThey are ultra luminous centers of distant galaxies.

Quasar (10 billion ly away)

Star in our galaxy

Question: How can we tell the difference?

For speeds > 0.1c the equation no longer holds true

Instead, the redshift (z) plots as a curve.

We can however still determine the distance by applying Hubble’s Law after the speed is determined.

Relativistic Red ShiftR ecall the equation

for G alactic R edsh ift

v

c

Importantly most quasars developed in the early universe.

Allows us to look at distant objects and observe recessional velocities.



Quasar Data allows us to define the

Deceleration Parameter (qo)

qo = 0 for a universe that has no gravity and will continue to

expand forever.

Recession Speed (cz)

Dis

tanc

e (d

) Large (accelerating)

Large , Small (decelerating)

Hubble Diagram


Open Universe – will continue to expand forever, but at slower and slower speeds.

The curve will never get quite flat.


Flat Universe – will continue to expand to a point then become static.

The curve will become flat.


Closed Universe – will continue to expand, stop and then collapse in a Big Crunch

The final outcome has yet to be determined. We just do not have enough data yet

If we can observe quasars, plot a graph like this one and determine the equation of the line, then we should be able to predict the value of qo

The values of both qo and are both dependent on the density of the universe. Therefore we can relate one to the other. Figure one out, you can calculate the other.

Very Open<<1

Closed>1 Oscillating?

Time

Dis

tanc

e B

etw

een

Gal

axie

s

~100 Billion Years

Possible Fates of the Universe

Critical/Open=1

The Geometry of the Universe

• Imagine shining two very powerful lasers that are parallel into space and observing them for billions of light years as they travel across the space whose shape we wish to observe.

• There are only 3 possibilities– They stay parallel– They converge– They diverge

• Since we cannot actually do this, we must observe light coming to us.


This is a picture of the CMBR.

The colors represent variations in temperature, red being a HOT SPOT

Note the scale size of the Moon

Parallel lines convergeArea of circle < R2

Sum of angles of triangle > 1800

qo > ½

The Geometry of a Closed Universe (Universe will collapse)

qo = ½

Euclidean - normal geometryParallel lines remain parallelArea of circle = R2

Sum of angles of triangle is 1800

The Geometry of a Flat Universe (Universe will become static)

Parallel lines divergeArea of circle > R2

Sum of angles of triangle < 1800

0 < qo < ½

The Geometry of a Open Universe (Universe will continue to expand)

2-D Examples of Curved Spaces



Documents

The Hot Big Bang The Big Bang Model Our prior discussion suggests that the universe has been expanding for billions of years. (10-20 Gyr) This implies