An Introduction to Astronomy

Part XIV: Cosmology

Lambert E. Murray, Ph.D.

Professor of Physics

Cosmology

Cosmology is the study of the structure and evolution of the Universe on its grandest scale. In the study of cosmology we wish to answer question like:– What do our observations tell us, if anything,

about the size and geometry of the Universe?– What do our observations tell us, if anything,

about how the Universe came into existence?– What do our observations tell us, if anything,

about the future of the universe?

What Have we Learned about the Nature of the Universe so far?

There seems to be an infinite number of galaxies (of various types). No matter the direction you look, as we build bigger and bigger telescopes, you see more and more galaxies.

They are Everywhere

Galactic Clusters and Superclusters

There are enormous distances between galaxies, but as we look deeper and deeper into our Universe we find that galaxies are grouped together by gravitational attraction.

If we plot the location of galaxies, we begin to see large-scale structure within the Universe.

We find that although there are small scale fluctuations within the universe – we can think of the universe as rather homogeneous and isotropic on the very largest scale.

Structure Within the Universe

Computer Model

of Universe

What Else Have we Learned about the Nature of the Universe so far?

Hubble’s work indicates that the farther away a galaxy is, the faster it moves away from us. This is true in every direction we look.

The Hubble Law

Are we in a “Special” Place?The Cosmological Principle

Since we see a large number of galaxies in all directions, and these are all moving away from us are we at the center of the universe (a very special place)?

A fundamental assumption in the study of cosmology is that we are not located in a unique region within the universe – this is the “Copernican Principle”.

In addition, we assume that the universe at the largest scale is isotropic and homogeneous, i.e., that the universe “looks the same in all directions” and that this is true no matter where you are. This is the “cosmological principle”.

This principle assumes that our location within the universe is characteristic of any other location within the universe and is the only assumption that will allow us to make any progress in understanding our Universe as a whole.

An Expanding Universe

If we are not located at a special spot in the Universe, and

If we would expect to obtain the same Hubble plot of the recessional speeds of galaxies from any arbitrary location within the Universe,

This means that the distance between any two galaxies (on average) is increasing all over the Universe.

Thus, the Universe is expanding – like a raisin cake or an expanding balloon.

Is the Universe Infinite?Olbers’ Paradox

Olbers’ paradox: If our universe is infinite in time and space, and if we see galaxies wherever we look, why is the sky dark?– Although the light intensity drops off as 1/R2, the

number of stars you can see in an infinite universe increases like R2 so these two effects cancel.

– Likewise, if the universe is filled with dark material which would absorb the light, that material would heat up and eventually glow – especially if there were an infinite number of stars.

Conclusion: The universe must not be infinite in space and time!

The Big Bang Initially many astronomers believed that the

Universe was static and infinite. Olbers’ paradox raised serious questions about this assumption.

Hubble’s observations of an expanding Universe seems to indicate that the Universe had a beginning in time – and perhaps in space.

The “Hubble” Age of The Universe Hubble’s Law can be written as velocity of recession =

(constant) x distance– the “constant” is Hubble’s Constant, H0

– We believe that Hubble’s constant is “constant” over all the universe at any instant of time, but it may actually change over time.

Running the expansion backwards– Since H0 = velocity/distance,

1/H0 = distance/velocity = time– Thus, 1/H0 is a measure of the age of the universe.

Using a value for H0 of 50 km/sec/Mpc (kilometers per second per megaparsec) leads to an age of about 19.7 x 1010 years, or roughly 20 billion years, while using a value of 100 km/sec/Mpc leads to an age of only about 10 billion years.

A Correction to the “Hubble” Age of the Universe

Most astronomers believe that Hubble’s “constant” has changed with time. Gravity should be “slowing” the expansion of the Universe, causing a deceleration.

Thus, the initial expansion should have been faster, leading to a younger universe – one with an age of about 2/3 of the age determined from the present value of Hubble’s constant.

Astronomers are using several different techniques to determine an accurate value of Hubble’s constant so that we can get a handle of the actual age of the Universe.

Measurements of Hubble’s Constant

Hubble’s initial measurements of H0 was 550 km/sec/Mpc, but by the 1990’s the most frequently quoted values were 50 – 70 km/sec/Mpc.– Hubble’s measurements did not take into account

several effects now known to astronomers that would have influenced his measurements.

2/3 of the Hubble age calculated from these values would give 9 – 13 billion years for the approximate age of the Universe.

An Alternate Age Measurement

An alternate method of determining the age of the Universe is to determine the age of objects within the Universe, since the Universe cannot be younger than the oldest objects in the Universe.

We can get an estimate of the age of globular clusters based upon their HR diagrams – observing their turning points.

HR Diagram for M13

Additional Evidence for the Big Bang? Cosmic Microwave Background

– In the 1940’s Russian physicist George Gamov worked out a theory for the creation of elements (a nucleosynthesis) in a big-bang type event.

– He predicted that copious amounts of radiation would be emitted from the hot gas of this Big Bang with a black-body spectrum of about 3000K when the Universe became transparent to photons. (Prior to this the photons were “trapped” by the non-transparent universe.)

– Later it was realized that this radiation would have been red-shifted over time and would look like emissions from a very cool gas.

– In the mid-60’s Robert Dicke at Princeton began building a receiver to detect this radiation.

Penzias’ & Wilson’s Microwave Experiment

1964-65 Bell Labs scientists Arno Penzias & Robert Wilson were working on a microwave horn antenna for satellite communication.

They were troubled by a persistent background noise. After trying everything to eliminate the background:– recalibrated antenna– cooled their detectors– removed nesting pigeons from horn– cleaned antenna– could not eliminate the static

they found that the background persisted.

A Cosmic Background?

The peak in the background radiation from Penzias’ and Wilson’s experiment occurred at 7.35 cm (4080 MHz)

They found that the background was constant regardless of time of day, season of year, direction in the sky, etc.

When they learned of Dicke’s work, they realized that they might be seeing this residual radiation remnant from the Big-Bang now called the Cosmic Microwave Background Radiation.

If a blackbody curve is assumed, the 7.35 cm peak corresponds to a background temperature of roughly 3.5 Kelvin.

1976 Penzias & Wilson received the Nobel Prize for their work.

Experimental Measurements of the Cosmic Background Radiation

Very little of the 3 K background radiation can penetrate the atmosphere:– This made it difficult to measure radiation curve– Early attempts used balloons, rockets, aircraft, etc.

In 1989 NASA launched the Cosmic Background Explorer (COBE) which orbited the Earth.

Within two months it was determined that this background followed (within 1%) a blackbody radiation curve corresponding to a temperature of 2.735 Kelvin (within 0.06K).

Blackbody Spectrum of COBE Satellite and fit to a 2.73 K Curve

Variations in the Background Radiation Pattern

COBE data is accurate enough to measure the motion of the earth relative to the background radiation by analyzing variations in the data to 1 part in 10,000. This is shown in the next image.

A more detailed analysis, with the dipole effect of the Earth’s motion subtracted out, shows small scale variations in the background radiation data.

COBE Dipole: Speeding Through the Universe Credit: NASA, COBE, DMR, Four-Year Sky Map

Astronomy Picture of the Day, February 5, 1996

A map of the brightness of the cosmic microwave background made by the cosmic background explorer (COBE) satellite. Notice the patchiness of the brightness. Each pink patch may represent a "lump" of matter from which groups of galaxies ultimately grew. The patches were approximately one half billion light years across when they emitted the radiation. (NASA GSFC and the COBE Science Working Group.)

Confidence in the Big Bang

There seems little doubt that the Universe as we know it is expanding, and that it was the result of a Big Bang.

Small fluctuations in the cosmic background radiation are consistent with our observations of the grouping of galaxies within the Universe.

Recent Confirmation

The excellent agreement between the current theories of cosmology and the most recent data from Cosmic Background Radiation (WMAP) indicate that:– The age of the Universe is 13.7 billion years to

within 1%.– That the Universe is flat and that the visible

universe makes up only 4% of the Universe.

WMAP Composition of the Universe

Theoretical Models for the Expansion of the Universe

Until recently, precise, unambiguous, experimental measurements of H0 with distance did not exist.

Theory indicates that there are three basic models for our Universe:– Closed Universe M > 1

– Flat Universe (M = 1)

– Open Universe (M < 1)

Diagram of Theoretical Models for the Expansion of the Universe

The Future in Different Models

In a “closed” universe, the recessional speed of galaxies would decrease to zero and that universe would begin to collapse as gravity overcame the initial expansion from the Big Bang. This universe would eventually collapse completely – or perhaps oscillate.

In a “flat” universe, the recessional speed continues to decrease and approach zero only as time approaches infinity.

In an “open” universe, the recessional speed decreases, but never reaches zero.

A Surprise

Recent measurements of large-z Type Ia Supernovae indicate that the recession rate follows none of the previous patterns, but actually are consistent with an “accelerating” universe which would require some sort of “anti-gravity” repulsive force which is now associated with Einstein’s cosmological constant .

Many suggest that the source of this “anti-gravity” is a “vacuum energy” or “dark energy” due to quantum fluctuation.

End of Part XIV