Astronomy 101 Lecture 26, Apr. 30 2003 Cosmology: the Expanding Universe – (Chapter 26.1 – 26.4 in text) Our exploration of astronomy from the small scale.

Astronomy 101 Lecture 26, Apr. 30 2003

Cosmology: the Expanding Universe – (Chapter 26.1 – 26.4 in text)

Our exploration of astronomy from the small scale solar system to the vast reaches occupied by galaxies and quasars has revealed a tremendous range of structures – clumping of matter into planets,

stars, gas clouds, galaxies, galactic clusters and superclusters.

What if we look on even larger scales of the entire observable universe?

What is the structure of the universe at the largest distance scales?

How did the universe begin? What laws governed it?

How will it evolve with time?

This is the branch of astronomy and physics called Cosmology. In the past decade, there has been enormous progress in understanding the universe as a whole.

Galactic maps out to 750 Mpc - about 10% of the way to the most distant quasars show clumpings corresponding superclusters out to about 500 Mpc.

The amount of structure diminishes beyond 500 Mpc and universe becomes ‘smoother. (Though we now think the universe had small variations in density even at the beginning).

But on the largest distance scales beyond 500 Mpc, the universe looks the pretty much the same everywhere.

We are here

north

south

distance

Cosmology Assumptions:

On the largest scale, we see no qualitative differences when we look out in different directions. The number of galaxies within a given area on the sky, and the types and clustering of galaxies we see are essentially the same in all directions. The universe appears to be isotropic.

Similarly, the number of galaxies we see in any given large volume of space is the same as in any other similar volume at a fixed time – providing we take a big enough region, larger than the size of superclusters. The universe appears to be homogeneous at a given time (but not unchanging in time).

The Cosmological Principle is the assumption that the universe on the large scale is homogeneous and isotropic – so it is as good to study one large region as any other.

The cosmological principle then implies that there is no edge to the universe. And that there is no center to it either!

What we know of the universe is based solely on the radiation – light, radio waves, X-rays, gamma rays etc. that come to us from a distance. We interpret what these signals mean using the laws of physics, deduced from earthly labs. We assume that the Laws of Physics are the same everywhere in the universe.

Olbers Paradox:

IF the universe were infinite in size and unchanging with time then:

The night sky would be as bright as the sun, everywhere !

The reason is that any line outward from earth would ultimately intersect a star; thus that ray and all others would report the brightness of a star.

Since the night sky is not bright, the assumptions are wrong – and indeed both are wrong. The visible universe is limited in extent by the time available for light to reach us. There are parts we cannot see.

The universe is changing with time due to the Hubble expansion, so we can’t see infinitely far back in time. Also, distant objects are not as bright, due to the cosmological red shift. (And there is extinction of light due to intervening dust and gas.)

(Think of being in a huge forest – no matter where you look, your line of sight ends on a tree.)

We see more of the universe as time goes on.

distance

time

now

Slope of line fixed by speed of light – distance over time. Range of universe we can receive light from at an earlier time is less than now. Now we can see Galaxy A and galaxy B, but earlier we could not.

earlier

Galaxy A Galaxy B

distance

time

Us now

Galaxy A Galaxy B

At the earlier time, galaxy A cannot see galaxy B and vice versa. And they could not see us either.

Speed of light c = 300,000 km/s is a constant; we can only see things that were close enough for light to reach us. (See objects within the ‘light cone’)

Us earlier

z=0.05 z=0.1 z=0.2 z=0.3 z=0.4 z=0.5

This sequence of galaxy photographs from the Sloan Digital Sky Survey at increasing red shift show the increasingly red appearance of more distant (and fainter) objects.

The cosmological red shift is key to our observation of distant objects. Distant objects are viewed as they were when the light started on its journey – so looking at highly red-shifted objects is like time travel back to the earliest days of the universe.

z = is the red shift and tells us the velocity of the object at time of emission (Doppler effect). Through the Hubble Law, v = H0

d, we get its distance. And since the time taken by light to reach us is t = d/c (c=speed of light=3x105 km/s), the red shift can be thought of as a cosmic clock, ticking as the universe ages.

z (red shift) v (velocity) d (distance) t (lookback time)

Doppler Hubble speed of light

The Big Bang:

We see distant galaxies receding with v = H0 d , and the Hubble constant H0 is presently about 71 (km/sec)/Mpc (the best recent determination). We can estimate where they were in the past:

If the galaxies moved in past with the same velocity we observe now, and continued along the same line, we can project them back to calculate their distance from us at an earlier time.

earthgalaxy

velocity vdistance d

The time T when this galaxy was on top of us is given by d = v T (distance = rate x time), so T = d/v.

But the Hubble Law says v = H0 d, based on observation.

Then the time T when the galaxy was on top of us is (substitute v from Hubble Law into T=d/v)

T = d/v = d/(H0 d) = 1/H0 = around 13 billion years ago

Notice that the calculation does NOT depend on the distance of the galaxy now – all galaxies were apparently on top of each other 15 x 109 years ago.

the BIG BANG -- beginning of the observable universe

Are we special because we see all galaxies rushing away from us?If there is just one place from which all things expand and where the Big Bang occurred, it would violate the cosmological principle, since that place would be special. In fact residents of every galaxy would see all the others receding in proportion to their distance:

Top row of the figure shows speeds of 5 galaxies separated by 100 Mpc, seen to obey Hubble’s law by observer in galaxy 3. We can compute what would be seen for observer in galaxy 2 (middle row) or galaxy 1 (bottom row). All see Hubble’s Law with all galaxies receding from them !

If observers everywhere see Hubble expansion, it would seem that there is no true center of the universe. And indeed since all matter was at the same point at the Big Bang, we can say that the center now is everywhere !

The proper way to view the Hubble expansion and the cosmological principle is to say that the universe itself is expanding – the space in which stars and galaxies and light reside is getting larger with time.

Analogy with a spotted balloon; as the balloon [the universe] is blown up, the distances between the spots [the galaxies] all increase and the velocity with which any particular spot recedes from another grows withthe separation distance of the spots.

The whole universe, like the balloon, is expanding, carrying the galaxies apart with it.

In this analogy, the balloon is 2 dimensional, but the universe is 3 dimensional.

(Galaxies don’t grow with time – they are gravitationally bound)

Interpretation of the cosmological red shift:

When we described Hubble’s Law based on the increasing red shift with distance, we interpreted this as a Doppler shift due to the velocity of distant galaxies.

A better interpretation now is to say that the universe as a whole – including the space coordinates describing up/down, left/right, in/out – are stretching with the expanding universe. Then a wave of light with a certain wavelength in the past is transformed into a wave with longer wavelength with the expanding universe. A wave emitted early in the history of the universe as blue light is stretched to a longer red wave now.

The future of the universe.

We see the universe is expanding (more properly, we see that in the past, galaxies were receding from each other). Will this expansion go on forever?

We need general relativity to really work this out. General relativity says that the presence of matter warps space (and time), and matter follows curved trajectories in the warped space.

But Newton’s mechanics works pretty well to give us the picture, so lets use that.

In Newton’s mechanics, the motion of a rocket shot upwards can be predicted. consider a rocket shot with the same speed from two planets of different masses:

On the larger planet, the rocket rises to a maximum and falls back

On the smaller planet, the rocket slows down but is able to escape the planet altogether

We can plot the distance from the planet versus time in the two cases.

For the more massive planet, the rocket rises to a maximum height and returns. The d vs. t plot is an inverted parabola.

For the less massive planet, the rocket continues to rise forever, but it slows down, so the d vs. t curve still bends downward with time.

For the universe as a whole, the same principle applies. The matter in the universe attracts the expanding galaxies and would tend to slow the expansion down. (Providing that there is only gravity,due to the matter, is operating – not necessarily a good assumption!! See later! )

There is a critical density of matter (kg/m3) above which gravity will ultimately win and the galaxies will someday stop expanding and fall back toward each other. If the density is less than the critical value, the expansion of the universe will continue forever.

The critical density (in the present epoch) is very small – about 8 x 10-27 kg/m3 . That corresponds to on average just 5 hydrogen atoms per cubic meter.

Fate of universe if greater than critical density – recollapse to ‘Big Crunch’

Universe expands forever with finite velocity if less than critical density

Or expands with velocity that ultimately goes to zero if equal to critical density

Not only does the future fate of the universe depend on the density being greater or less than the critical density, so also does the past history.

At present, we know that a galaxy at 1 Mpc is receding at v = 71 km/s (Hubble’s Law). If the matter density is large, there is more slowing down than if density is small, and lookback time to the Big Bang is shorter. So our estimate of the age of the universe also depends on the matter density.

Define the ratio of density to the critical density as

1means a bound or CLOSED universe.

1means an unbound or OPEN universe

Actual age of universe is less in bound than unbound case

Measuring the mass density of the universe is hard to do experimentally. The visible matter in stars and galaxies however seems to contribute less than 1% of the critical density. Adding in the matter in the great interstellar clouds of gas & dust and burned out stars brings the density up to about 4% of critical.

But remember the dark matter! We see something like 5 times as much dark matter influencing the rotatation of stars around galaxies, and galaxies around galaxies as there is matter associated with atoms. If that is true, then we are up to about 27% of the critical density. But we are pretty ignorant of the amount of dark matter, and really don’t know much about it in the furthest reaches of the universe.

We would like a more direct measure of what the deceleration/ acceleration of the universe is, and of the density.

Recently, studies of Type Ia supernovae have given us a direct measurement of the deceleration.

Supernova Project

Special telescopes scan the sky at new moon and 3 weeks later. A supernova is found if, in that time, a new bright star has appeared. The big telescopes like Hubble are then trained on the supernova to measure its spectrum and time dependence to determine its type, and if Type Ia, its peak luminosity.

Type Ia supernovae are standard candles – we know their absolute peak luminosity. Measuring the apparent brightness tells us their distance, independent of the Hubble Law

From the spectral lines red shift, we can get the velocity. Thus for such a supernovae, we have distance and velocity (without using the Hubble Law), so we can check whether the expansion velocity is really just what Hubble predicts. If the velocity is smaller in the past than expected from the Hubble Law, then v is increasing and the universe is accelerating. If velocity was larger in past, then universe is decelerating (as we would expect from the gravitational attraction slowing things down.

SN

dis

tance

SN velocity

If universe is decelerating (velocity is greater at some fixed distance)we see distant SN’s on the red curve

If universe is accelerating we see distant SN’s on the blue curve

velocity

dis

tance The data show a smaller velocity

than predicted from v = H0 x d for the most distant galaxies (around red shift 1).

Apparently the universe is actually accelerating.

Contrary to expectations!

Call it Dark Energy!

Dark energy exerts an outward force on the universe, counteracting the effect of gravity due to the mass, and tending to accelerate the universe.

About 73% of the stuff in the universe is Dark Energy!

We have no clue what it is!

Even if the matter density is less than critical, it would still tend to slow the expansion of matter, so acceleration is a real puzzle !

It looks like there is another ingredient besides matter with gravitational attraction to the universe – one that is counteracting the effect of gravity from the matter and is trying to push the universe apart.