Cosmology
The Big Bang and the Fate of the Universe

May 9, 2017, jeb

Outline The Universe on the Largest Scales The Expanding Universe Age of the Universe The Big Bang Discovery of Cosmic Microwave Background Space-Time Geometry Einstein's General Theory of Relativity Future of the Universe Will the Universe Expand Forever? Recent Results on the Cosmic Microwave Background Dark Energy and Cosmology Conclusion

The Universe on the Largest Scales

Cosmology is the study of the structure and evolution of the entire 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?
• Data shows structure does end on the scale of greater than 200-300 Mpc
  • Galaxy Survey
    • largest structure (Sloan Great Wall) nearly 300 Mpc across,
      but no evidence of any larger structures
  • Pencil-Beam Survey
    • voids and sheets on scales of 100-200 Mpc,
      but no indication of any larger structures

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 and isotropic
    • Homogeneous - (uniformity - the same everywhere)
    • Isotropic - (the same in all directions)
  • Consequences of the cosmological principle The universe has no edge, as this would violate the assumption of homogeneity
  • The universe has no center, as this would violate the assumption of isotropy
    • The universe would not be the same in all directions from a non-central point

The Expanding Universe

Olbers's Paradox
• The night sky should be uniformly bright, but it is dark at night
• 1823 - Heinrich Olbers proposed paradox
  • 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 redshifted and not as bright.
  2. The universe is not infinitely old - so some light hasn't had time to reach us.

Age of the Universe

Hubble's law is based on the redshift observations
that show all the galaxies in the universe are rushing away from us:

recessional velocity = H0 × distance

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


H₀ = 70 km/s/Mpc or 21.5 km/s/ million light years
---------> 14 billion years

But gravity slows the expansion (cosmic deceleration)

------> Age of the universe would be about, but not exactly, 14 billion years


NOTE: Stars in globular clusters are 10-12 billion years old
so we know the universe is at least this old

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

The Big Bang

The Big Bang explains the observed features of the universe

Present data strongly supports this (the Big Bang) model of cosmology

• Follows from Einstein's General Theory of Relativity

Early on the universe was compressed to nearly 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 14 billion years ago
• We know from precise measurements that the time since the Big Bang is close to 13.8 billion years.

Supporting Data for the Big Bang
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 reinterpret the cosmological redshift
     • Doppler shift is not technically the correct interpretation of cosmological redshift
     • As the universe expands, the wavelength of radiation is stretched
4. Helium abundance (about 25% of the universe by mass is Helium,
                   or about 10% by number density)
   • also, abundances of deuterium (heavy hydrogen), lithium, and beryllium support Big Bang

IMPORTANT CONCEPT - Redshifts of galaxies result from expansion of space with time, which stretches light.

Discovery of Cosmic Microwave Background

1965 - Arno Penzias and Robert Wilson
• Bell Labs, New Jersey
• radio telescope and 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 400,000 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 redshift (cosmological red shift)
    
    
  • This "light" which is detected on Earth now originated in the very early universe
    • Age then about 400,000 years or nearly 14 billion years ago

WHAT WAS IT? The Cosmic Microwave Background


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

  Time since start of the Big Bang	Condition of universe
  0	Big-Bang
  .	matter in plasma - light cannot pass through Plasma-protons and electrons separated
  <~400,000 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
  13.8 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 slightly asymmetric (~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.
• WMAP
  • launched on June 30, 2001
  • followed COBE with better precision
• Planck
  • launched on May 14, 2009
  • most recent measurements with best precision

Space-Time Geometry

Einstein's General of Relativity (1915) says space is curved by matter
• orbits are determined by curvature of space
• 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 possibilities, preferring to think the universe should be static (neither expanding nor contracting) and invented a fudge factor (the cosmological constant) to force a static universe
    • we will see this again later
• Hubble later discovered the universe is expanding
  • This distressed Einstein, who had guessed wrong
  • He referred to this as his greatest blunder


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

Einstein's General Theory of Relativity

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



Density of matter	Geometry of space
less matter than critical density	open
critical density of matter	flat
more matter than critical density	closed



A two-dimensional version of a closed universe is the surface of a sphere.

• The close universe is finite in size, but there is no boundary in a closed universe.
A two-dimensional version of an open universe is like the surface of a saddle, curving up in one direction and "down" in another.
• Such a low-density, open universe is infinite in extent.

Critical density = 9 × 10^-27 kg / m³
• Equivalent to about 5 hydrogen atoms per cubic meter
• But remember, the density of the universe is not dominated by hydrogen, but includes dark matter and dark energy

Ω₀("Omega nought")
• Astronomers define a ratio of densities, Ω₀("Omega nought")
  • Ω₀("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 - for now we consider just matter
  • The Geometry of the universe (open, flat, closed) is determined by value of Ω₀("Omega nought")
  
  

  Ω0("Omega nought")	geometry
  0	empty universe
  0 - 1	open universe
  1	flat universe
  greater than (>) 1	closed universe

  
  
• Data says Ω₀("Omega nought") is close to 1


Density of the Universe
• From galaxies, luminous matter is about 10^-28 kg/m³
  • Ω₀("Omega nought") = a few percent
• perhaps 95% of the matter in the galactic clusters is dark
  • Ω₀("Omega nought") ≈ 0.25

Future of the Universe

Big Question - Will it continue to expand or will it collapse to big crunch?
• Consider analogy - rocket escaping from a planet
  • With enough speed, the rocket will escape a low mass planet,
    but may not escape a higher mass planet
  • The strength of the gravitational attraction depends on the amount of mass contained by the planet
• Now consider the expanding universe, and the separation of galaxies being pulled by the gravity generated by the whole universe
  • Low density expands forever, high density collapses

Same Question -
• Is there enough gravity (or matter) to bend universe back in on itself
  • to "close" the universe
• or will is expand forever?
• the amount of mass needed to close the universe is called the critical density
  • critical density is equivalent to about 5 hydrogen atoms per cubic meter, averaged over the entire universe,
    or about 10^-26 kg/m³ (9 × 10^-27 kg / m³)
    not much!

Average density of the universe - the mass within a large volume divided by the size of the volume
• Clusters of galaxies - Bound by their mass
  • Virgo cluster - visible mass is about 2% of the critical density
  • Other clusters - visible mass also a few % of the critical density
  • Adding dark matter brings these measures up to about 25% of the critical density
  • Considering the mass of the Great Attractor increases the estimate to about 30%
  
  
  Therefore, from matter alone (dark or visible) the universe would not be closed

Will the Universe Expand Forever?

The universe will expand forever if it is open or flat
• Matter will slow its rate of expansion
• But if Ω₀ is less than or equal to 1, it will continue expanding

However, the expansion of the universe appears to be speeding up (accelerating)


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


Dark Energy

Late in the 1990's, measurements by two different groups on the apparent brightness of supernovae with redshifts near z = 1 generated new interest in the old idea of a cosmological constant.
• The groups looked for supernovae (Type I) in galaxies at a very large distance, that is with large redshifts
  • Type I supernovae are standard candles
  • Astronomy 122 notes on Supernovae
• Images of distant supernovae
• Measurement of change in rate of expansion of the universe
  • redshifts of distant objects are greater than predicted from Hubble's Law

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
  • Most likely explanation - the vacuum energy of the universe is accelerating the expansion
  • This vacuum energy is called Dark Energy

Recent Results on the Composition of the Universe

Planck
• A European Space Agency Explorer mission that launched May 2009 has provided the recent precise data on the cosmic microwave background
  • Planck's objective is to analyze, with the highest accuracy ever achieved, the remnants of the radiation that filled the Universe immediately after the Big Bang - this we observe today as the Cosmic Microwave Background.
  • This microwave radiation was released approximately 400,000 years after the birth of the universe
  • Planck creates a very detailed picture of the microwave radiation
  • The content of this image tells us much about the fundamental structure of the universe
    • Age of the universe
    • Total energy-mass density (Ω₀)
    • Fractions of ordinary matter, dark matter, and dark energy
  
  
• Planck results on the structure of the universe as of 2015:
  • Age of the universe = 13.8 billion years (with less than 0.1% (1/1000) uncertainty)
  • Ω₀("Omega nought")
    • they conclude that Ω₀ is very close to 1.00 (less than 1% uncertainty)
    • in other words, the universe is flat
  • Ordinary matter makes up about 4.9% of the universe
    • contributes 0.049 to Ω₀
  • Dark matter makes up about 27%
    • contributes 0.27 to Ω₀
  • Dark energy makes up about 68%
    • contributes 0.68 to Ω₀

Dark Energy and Cosmology

• Dark Energy speeds up the expansion of the universe

• The universe is flat

• The determination of the age of the universe depends on the measurement of present-day density and the dark energy
  • Gravity slows the expansion
  • Dark Energy accelerates it, reducing the measured age to 13.8 billion years.
  • The competition between these two forces determines the rate of expansion, and therefore extrapolation into the past

Conclusion

Cosmology is 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.