Lecture 26: Cosmological Observations

We have been touching on several issues already that relate to the character of the Universe as a whole -- for example, we have already seen from Hubble's Law that galaxies are moving away from us with velocities proportional to distance which is a consequence of the expansion of the Universe.

1. You know that people and the Solar System exist.
2. You know that the sky is dark at night.

We exist: proves that the Universe is not comprised of equal amounts of matter and anti-matter which are well-mixed { either there is much more matter than anti-matter or something happened to separate matter and anti-matter on at least the size scale of the Local Group}.

The sky is dark at night (Olber's Paradox):

Make the following assumptions:

1. the Universe is infinite
2. the number of stars (or equivalently galaxies) per unit volume is some constant n
3. each star has luminosity L (constant in time)
4. the inverse-square law for the dimming of light with distance holds everywhere

Consider the light received from a shell of thickness t at distance R:

Notice that the flux from a shell is independent of its distance. If the Universe is infinite then there is an infinity of shells and the total flux also goes to infinity (i.e., the sky should be bright at night and hence the paradox discovered by Olbers). If you take into account that stars have a finite size, then the flux does not go to infinity but every line of sight will intercept the surface of a star so the sky should be as bright as a star's surface.

• may be dust absorbs the starlight

but then the dust would get hot and we would see it

• may be the Universe isn't infinite

but then we would see and "end" in some direction

The real solution: the Universe is expanding so the light is shifted towards longer wavelengths and also, with each passing instant, the light from an object has to travel further to reach us. The combination of these effects would reduce the total light by about a factor of 2 -- sky still would be very bright!

The final point is that light travels at finite speed and the Universe has a finite age. Light emitted from portions of the Universe which are more distant than c x ~13 billion yrs cannot reach us. This "unobservable" part of the Universe saves us from Olber's paradox.

The expansion of the Universe is therefore well-established on two bases: Hubble's Law and the darkness of the night sky.

Next question: What caused the expansion of the Universe (we now know that it was the Big Bang, but this was not obvious in the 1930s).

Georges Lemaître, a Belgian who had developed some of the solutions to Einstein's equations for the size of the Universe as a function of time, envisioned playing time backwards and that therefore at some time in the past, all matter was jammed together. He called this the "primeval atom" , and he postulated that some explosion must have split the "primeval atom" apart thus causing the expansion.

Around this same time, nuclear fusion was being identified at the cause of the Sun's luminosity. The combination of "primeval atom" with an explosion and the understanding of nuclear fusion lead George Gamow and others to suggest that perhaps the explosion was the source of all the naturally occurring elements in the Universe (from H to U). However, when he attempted to calculate exactly how the elements were produced, he didn't discover the excited state for the carbon nucleus (see the triple-alpha process discussion in Lecture 16). Gamow concluded that only H and He could arise in the explosion-- a correct conclusion.

At this point (~1950), the notion of an "explosion" causing the expansion of the Universe fell into disrepute:

1. Expansion rate as measured by Hubble indicated a ridiculously low age for the Universe
2. [ this was largely the result of not properly calibrating the Cepheid distance scale]

3. Explosion could not explain the existence of heavy elements.
4. Many astronomers and physicists just did not like the concept of the Universe originating in an explosion.

An Alternative: The Steady State Theory

Fred Hoyle and others proposed the continuous creation of matter (!!!!) to avoid having an explosion. Newly created matter would push the old matter further apart to cause the observed recession of the galaxies. To support this idea, the Steady-State group developed an extensive series of calculations which showed how all of the elements could be created as the result of steps in stellar evolution. This legacy of the Steady State remains today as an outstanding contribution to astrophysics. However, the rest of the theory has been discredited because no new matter has ever been observed, and more importantly, the relic radiation from the Big Bang was discovered.

As a result of trying to understand some interference when experimenting with transmission of telephone conversations over microwave links, Arno Penzias and Robert Wilson discovered that the sky emits blackbody radiation with a peak at microwave wavelengths.

Wilson and Penzias

Characteristics of the CMB:

2. The intensity of the radiation is very nearly isotropic (the same in all directions).

This radiation is the highly redshifted (z~1000) remnant of photons emitted ~500,000 years after the Big Bang. The radiation results from the Universe cooling sufficiently that electrons can be captured by protons to form neutral atoms. Before this time, the Universe was filled with electrically charged particles which prevented the free motion of photons. The Universe was opaque before recombination. The temperature at this time was 3000° K, similar to the outer layers of a cool star. (Note that "recombination" is a bit of a mis-nomer as neutral atoms never existed in the Universe before this point in time!).

The uniformity of the CBR in all directions is impressive -- before the COBE satellite was launched, the variation in T with direction was known to be less than 1 part in 10-4. COBE discovered very small variations at the level of ~10-5 on scales of ~7°.

The raw data returned by the COBE mission shows the red and blue shifts in the background spectrum due to the Sun and the Milky Way's motions through space:

After correcting for emission from stuff in the Milky Way and for the spectral shifts caused by our motion, the residuals are the actual fluctuations in the CMB emission:

What is the significance of these variations? Since the CBR is emitted by electrons going into orbit around protons, it traces the locations of mass in the Universe. If the CBR is uniform, then the distribution of matter at the time of its emission must have been uniform. Because we see matter so clumped now, we would like to know when the clumping of matter began. The COBE discovery of at least small non-uniformities (anisotropies) on scales comparable to filaments and voids begins to give us a glimpse of how superclusters arose. Future missions such as MAP and PLANCK will study these anisotropies on even finer scales and may reveal whether galaxy-sized clumps had formed at z~1000.

More on the Significance of Matter and its Distribution

Recall from Lecture 25 that the fate of the Universe depends on the amount of matter it contains relative to the expansion imparted by the Big Bang:

How can we determine whether the Universe will expand forever or not? How can we determine where our Universe is relative to   ?

Method 1: Measure how much matter there is by counting how many stars, galaxies, etc. are observed. Be careful to make an allowance for the unseen dark matter.

Result: Only about 10% of can be accounted for.

Method 2: Since Ho is a measure of the rate of expansion of the Universe, see whether Ho is increasing or decreasing with time.

Result: Not a practical experiment because only recently using the Hubble Space Telescope have we been able to measure Ho to an accuracy of 10%; much too crude to look for changes over time.

Method 3: Recall that space-time becomes curved near concentrations of matter and that the Universe as a whole must have "curvature" if it contains matter.

What exactly do we mean by curvature of the Universe? We mean the path that a light ray will follow:

 Shape of the Universe Length of light path Light dimming with distance Type of Universe Mass density Age (109 yrs) Negative Curvature Longer than straight line Faster than 1/r2 open < >13 Flat Straight line 1/r2 flat = 13 Positive Curvature Shorter than straight line Slower than 1/r2 closed > <13

The rate at which light dims with distance depends on the curvature of the Universe which in turn depends on the amount of mass. We select some object visible over great distances and which can be used as a "standard candle" whose intrinsic brightness we know. We see whether these objects are getting fainter with distance as 1/r2 (flat Universe) or more slowly (closed) or more rapidly (open).

Test was first conducted with the most luminous galaxies (giant ellipticals): A big problem is that because the galaxies to be measured are so far away, the light we receive from them was emitted several billions of years ago. Therefore we are observing these galaxies as they were at a more youthful stage in their evolution. These galaxies would have more massive and hence brighter stars still on the main sequence that would be the case in nearby galaxies. Hence we cannot assume that the intrinsic brightness of a distant elliptical galaxy would be the same as for a nearby elliptical. We can make corrections for the kinds of stars present, but this complicates this test.

Method 4: By understanding the nuclear reactions that occurred during the Big Bang, we can obtain another estimate of the amount of mass in the Universe -- to be considered in the next lecture.

Most models assume that is 0 and that the expansion of the Universe is slowing down due to the gravitational pull of all the matter in the Universe.

Recent measurements of the brightnesses of Type Ia supernovae (the exploding white dwarf type of supernova) indicate that the expansion rate was SLOWER in the past than now. This is a new version of method 3.

By measuring the apparent brightnesses of these distant supernovae and their redshifts, one can trace whether Hubble's Law (v=Hoxd) applies or not. If the Universe was expanding more rapidly in the past than now, the data should follow the green curve in the plot below. This test compares the dimming of light with distance to the flat Universe expectation of 1/r2 and hence the use of m-M.

These data are not the final word -- if some dust is present in intergalactic space, then distant supernovae would appear dimmer and this may be an alternative explanation. If the Universe actually is expanding faster now, this is a mathematically permitted solution to the equations given in Lecture 39. A constant, (lambda), needs to be added to the solutions -- this is also called the "Cosmological Constant". Einstein had realized that such a constant could appear in the solution to the equations but had set it =0 because it had no physcial interpretation to him. If the Universe is expanding faster now, then > 0 and the Universe has some "repulsive" or "vacuum" force that we do not now understand.

Latest Experiments to Measure the Cosmic Background

Two balloon-borne experiments produced the best Cosmic Background Data so far last year:

The small dot is the size of the full moon -- these fluctuations in the Cosmic Background are still larger than the size that would be associated with "proto-super clusters". This experiment can determine whether the Universe has close to the crital density of matter or not because high density would imply stronger gravitational fields which would "damp" out waves in the matter:

open (low density)               flat (critical den.)                closed (high den.)

So the supernova and CBR data taken together imply a flat Universe with a positive

( the s above are scaled values for the amount of matter in the Universe (m=1 means that the Universe has exactly the critical density while gives in this same style).