Cosmology
The Big Bang and the Fate of the Universe

posted May 2, 2001, jeb
revised May 3, 2001, jeb

Outline

Cosmology


The Expanding Universe


The Big Bang


Space-Time Geometry


Future of the Universe


Einstein's General Theory of Relativity


Age of the Universe


Discovery of Cosmic Microwave Background


Recent Results on the Cosmic Microwave Background


Recent Discovery


Conclusion

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Cosmology

Cosmology is the study of the nature (structure) and evolution of the universe.

The universe shows structure at many scales
• subatomic particles
• atoms
• stars and planets
• star clusters and galaxies
• galactic cluster and superclusters
• voids and sheets

Does this structure ever end?
• While the data is not totally conclusive, it appears that on the scale of greater than 200 Mpc the structure does ends


Cosmological Assumptions
• Universality of Physical Laws
  • The same physical laws apply everywhere in the universe
• Cosmological Principle
  • on a large scale, the universe is:
    • Homogeneous - uniformity
    • Isotropic - direction
  • The universe has no center

The Expanding Universe

Olbers's Paradox
• The observation that the sky is dark at night contrasted with a simple argument that shows that the sky should be uniformly bright.
• This haunted Kepler as long ago as 1610.
• 1823 - Heinrich Olbers proposed paradox
• Argument
  • Assume universe is infinite and stars are randomly scattered.
    • [Isaac Newton (the great physicist) argued that no other assumption made sense]
  • Then - in every direction you will eventually come to a star and the sky will be glowing
• Resolution of the paradox
  1. Stars are moving away so light is red-shift and not as bright.
  2. The universe is not infinitely old - so some light hasn't had time to reach us.

The Big Bang

Explains the features of the universe

Present data favors this model of cosmology

• Follows Einstein's General Theory of Relativity

Early on the universe was compressed to infinite density and it has been expanding ever since.
• Was it compressed to a point?
  • could it be infinite in size still?

Hubble's Law tells us this happened about 15 billion years ago.

Supporting Data for the Big Bang Theory
1. Hubble's Law
   • As the universe expands, galaxies move apart
2. Quasars (i.e. the universe appears to have an early history)
3. Cosmic microwave background (see below)
   • We can reinterpret the cosmological redshift
     • As the universe expands, the wavelength of radiation is stretched
4. Helium abundance (cosmic microwave background)

Steady-State Theory
• An alternative to the Big-Bang, but now out of favor
• Bondi, Gold, and Hoyle - 1940's
• Consistent with Hubble's Law
• Assumption -
  • universe is homogeneous, isotropic, and unchanging in time
  • New matter is continuously created as universe expands to keep universe unchanged
• How much matter must be created?
  • 1 hydrogen atom/cubic cm every 10¹⁵ years
    (1,000,000,000,000,000 years)
  • or 1,000 atoms per year in the Astrodome (cannot be detected)
  • not much
• However, this theory is not in favor since Big Bang explains so much
  • and Steady State Theory cannot explain the cosmic microwave background

Space-Time Geometry

Einstein's General Theory of Relativity (1915) says space is curved by matter
• bending of starlight
• gravitational lens - quasars
• *perihelional advance of Mercury (for the experts)

Einstein found that he couldn't allow universe to be static in his theory
• it either expands or contracts
  • Einstein was unhappy with these two and invented a fudge factor (the cosmological constant) to force a static universe
    • we will see this again later
• Hubble later tells us it's expanding

3 Possibilities in Einstein's General Theory of Relativity:
1. infinite and unbounded - open
2. infinite and unbounded - flat
3. finite - closed (need not be bounded)

Future of the Universe

Major Question - Will it continue to expand or will it collapse to big crunch?
• Open, closed, or flat?

Same Question -
• Is there enough gravity (or matter) to bend universe back in on itself
  • to "close" the universe
• the amount of mass needed to close the universe is call the critical density
  • critical density is about 5 hydrogen atoms per cubic meter, averaged over the entire universe,
    or 10^-26 kg/m³
    not much!


Need to Determine Average Mass in a Given Volume (Density)
• (Remember - Finding all mass is tricky because of the Dark Matter)

Measures of the Density:
• Clusters of galaxies - Bound by mass
  • Virgo cluster - only 2% of mass visible
  • Closed?
  
  
• Deuterium abundance - (created early)
  • Not much - open?
  • Heavy hydrogen
  
  
• Recent Hubble's Law studies
  • galaxies motion - open?
  
  
• Neutrino Mass - very many neutrinos in universe so very small mass for each would add up to a lot open or closed??

Conflicting Indicators
• not clear what density is, but more than 10 percent of the critical density
• we will look more into current thinking about this later


What actually causes the universe to close on itself?
• This is explained by Einstein's General Theory of Relativity

review

Einstein's General Theory of Relativity

Matter warps space
• starlight is bent by matter
• gravitational lenses



density of matter	geometry of space
less matter	open
critical density of matter	flat
more matter	closed




₀("Omega nought")
• Astronomers define a ratio of densities, ₀("Omega nought")
  • ₀("Omega nought") = actual density / critical density
    • A technical point (which we will come back to later) is that this density includes both matter and energy
  • The Geometry of the Universe (open, flat, closed) is determined by value of ₀("Omega nought")
  
  

  0("Omega nought")	geometry
  0	empty universe
  0 - 1	open universe
  1	flat universe
  greater than (>) 1	closed universe

  
  
• Our present data says ₀("Omega nought") is close to 1, maybe bigger, maybe smaller.


Density of the Universe
• From galaxies, luminous matter is 10^-28 kg/m³ (₀("Omega nought") = a few percent)
• perhaps 95% of the matter in the galactic clusters is dark (₀("Omega nought") = 0.2 - 0.3 or more)
• Are voids filled with dark matter and visible galaxies "islands" of brightness? (₀("Omega nought") = 1 or more)

Summary of matter and energy in the universe

Age of the Universe

If expansion speeds are constant,
Hubble's constant tells us the age of the universe


H₀ = 65 km/s/Mpc or 20 km/s/ million light years
---------> 15 billion years

But gravity will slow the expansion (cosmic deceleration)

------> Age of the universe is less than (<) 15 billion years

perhaps < 10 billion years


NOTE: Stars in globular clusters are 12-15 billion years old

WARNING: We now have evidence that instead of slowing down, the expansion of the universe has actually been speeding up (see below)

How can we understand this?

Discovery of Cosmic Microwave Background

1965 - Penzias and Wilson
• Bell Labs, New Jersey
• radio telescope and receiver (7 cm wavelength receiver)

Tried to eliminate all static
• fixed loose joints
• repaired faulty connections
• removed nesting pigeons and "sticky white deposits"

Still there remained an annoying low level static
• coming from all directions
• all times of day
• through all the seasons

WHAT WAS IT?
• Blackbody Radiation
  • All objects emit radiation with the wavelengths characteristic of their temperature
    

    Temperature	peak wavelength
    3 K	about 1mm (radio waves)
    300 K (room temperature)	about 10 microns (infrared)
    6000K (surface of sun)	about 0.5 micron (visible light)
    3,000,000 K	about 1 nanometer (x-rays, gamma-rays)

    
    
  • The 100,000 year old universe was a 3,000 K blackbody.
    • peak wavelength = 1 micrometer = 10^-6m
    
    
  • As we look across space we see it glowing
    • we see 1 millimeter = 10^-3 meters
    • The shift of the spectrum of the cosmic microwave background from 3,000K to 3K is an enormous red-shift (cosmological red shift)
    
    
  • This "light", which we detect on earth now comes from the very early days of the universe
    • (Age~100,000 years or about 15 billion years ago)

WHAT WAS IT? The Cosmic Microwave Background


• Penzias and Wilson soon learned that this was predicted by Big-Bang.
  
  

  Time since start of Big Bang	Condition of universe
  0	Big-Bang
  .	matter in plasma - light cannot pass through Plasma-protons and electrons separated
  <~100,000 years	Era of Recombination (protons and electrons combine)
  .	Protons and electrons form atoms so light can pass through Initial temperature distribution of about 3,000K Light traveling in all directions As universe expands, the wavelength of primordial light also increases
  15 billion years (Today)	Through expansion of space temperature distribution of light is now 2.7 K



1978 - Nobel Prize to Penzias and Wilson

Details of Background Radiation
• In 1989 the Cosmic Background Explorer (COBE) satellite measured the intensity of the microwave background radiation around the peak
  • The curve follows a blackbody curve nearly perfectly (Temperature = 2.735 K)
  • It is very nearly the same in all directions, but slight asymmetry. (0.1%)
    • (local Doppler shift due to our motion)
  • This tells us:
    • sun moves at 382 km/s
    • Milky Way at 540 km/s
  • Milky Way Galaxy moving toward Hydra-Centaurus Supercluster
  • Great Attractor
    • Many clusters are moving in this direction - enormous pull.

Recent Results on the Cosmic Microwave Background

Boomerang
• An airborne detector, carried by a balloon launched gondola, has provided the recent precise data on the cosmic microwave background
• BOOMERANG flew around Antarctica at an altitude of 120,000 feet, above most of the atmosphere
• The flight (December 29, 1998 - January 9, 1999) was 10.5 days long
• Detectors in the instrument are cryogenically cooled to 0.28K
Results:
• Boomerang measures fluctuations in the cosmic microwave background
• from the size and distribution of these fluctuations, the astrophysicists can estimate the the value of ₀("Omega nought")
• they conclude that ₀ is consistent with 1 to within better than 10%
• in other words, the universe is FLAT

Recent Discovery

The expansion of the universe appear to be speeding up


Can this be? Does Einstein's Theory of General Relativity allow it?


Yes, the expansion of the universe depends on the value of the cosmological constant


Measurements by two different groups on the apparent brightness of supernovae with redshifts near z = 1 have generated new interest in the old idea of a cosmological constant.
• The groups look for supernovae in galaxies at a very large distance, that is with large redshifts
  • Astronomy 122 notes on Supernovae
• Data from one of these groups
  • the higher the point, the fainter the supernova

The conclusions from this data:
• The supernovae are farther away than they should be with these redshifts
  • that is, they are fainter
• The expansion of the universe is speeding up
• The cosmological constant is not zero
  • the vacuum energy of the universe is accelerating the expansion

Where does the cosmological constant come from?
We will discuss this in the next chapter

Conclusion

The study of the universe as a whole, including its origin, structure, and evolution.

Why is the universe made of matter, rather than anti-matter?

Is the universe infinite? or finite?

Is there a boundary to the universe?

Is there a center of the universe?

How old in the universe? -or has it always been?

Will the universe end? How?

Modern Science confronts the mysteries of our existence.