1. Relativistic Universe
Our universe

2. The Hubble Law
According to the Hubble Law, the space between the galaxies is constantly increasing, with Velocity = H0 D istance
To determine the age and fate of the universe, all we need to know is H0 and the gravity (i.e., the density) of the universe. This means measuring the distance to a distant galaxy.

3. The Distances to Galaxies
In general, galaxies are too far away to observe RR Lyrae or main sequence stars. You need a brighter standard candle!
Recall the Instability Strip. Pop II (low mass) objects aren’t the only type of star to wander through the strip after igniting helium. High mass (Pop I) stars can also enter the strip. These stars are called Cepheid variables.

4. The Cepheids of the Large Magellanic Cloud
Cepheid variables can be 100 times brighter than RR Lyr stars, but they do not all have same brightness. They are difficult to measure in the Milky Way due to dust, but many Cepheids exist in the Large Magellanic Cloud, our nearest (non-dwarf) galaxy.
The LMC is close enough so that we can identify its RR Lyrae stars. We therefore know its distance.

5. The Cepheid Period-Luminosity Relation
In 1912, Henrietta Leavitt showed that LMC Cepheids had a range of brightness (some extremely luminous, some faint). But the brighter the Cepheid, the longer it took to pulsate. This Period-Luminosity relation makes Cepheids a standard candle.

6. Spectroscopic Parallax Trigonometric Parallax
The Distance Ladder
Cepheids
RR Lyrae Stars
Spectroscopic Parallax
Trigonometric Parallax

7. Cepheid Distances
Using Cepheids as a standard candle, one can obtain the distances to galaxies as far away as 20 Mpc.
But this is not far enough away. Peculiar velocities are still too important. We need a brighter standard candle!

8. The Tully-Fisher Relation
According to Newton, the rotation speed of a galaxy depends on its mass, and the greater the mass, the brighter the galaxy.
If we can translate mass into absolute luminosity we can have a standard candle as bright as a galaxy. And we can do this – by calibrating the relationship using galaxies whose distances are known from Cepheids.

9. Type Ia Supernovae
When an accreting 1.4 M white dwarf goes over the Chandrasekhar limit, it becomes a Type Ia supernova. SN Ia can be seen across the universe.
We can determine exactly how bright SN Ia are by measuring their brightness in galaxies with known Cepheid distances.

10. Spectroscopic Parallax Trigonometric Parallax
The Distance Ladder
Hubble Law
T-F Relation
SN Ia
Cepheids
RR Lyrae Stars
Spectroscopic Parallax
Trigonometric Parallax

11. The Age of the Universe
Our current measurements give a value of the Hubble Constant of H0 = 72 8 km/s/Mpc. This implies an age for the universe of …
13 billion years, if we live in an empty universe
9.0 billion years, if we live in a flat universe.
But the stars in globular clusters are at least 13 billion years old. Did we do something wrong … ?

12. Such a universe obeys the Perfect Cosmological Principle
A Big Bang Alternative
Is it possible that the Big Bang did not occur? For instance, let’s postulate a Steady State Universe where the universe looks the same to everyone no matter where he/she/it is, and no matter when he/she/it lived. In other words, as matter moves beyond our horizon, new matter is created to replace it.
Such a universe obeys the Perfect Cosmological Principle

13. Telescopes as Time Machine
Under the Big Bang hypothesis, the universe was very different in the past. Can we prove this? Yes!
Light travels at a finite speed: the light we see today started out long ago. The farther away the object, the further back in time we observe. (And remember, the greater the distance, the greater the redshift.)
With big telescopes or telescopes in space, we can look for high-redshift galaxies and look back in time.

14. Galaxies at High Redshift
Some of these galaxies date from a time when the universe was only 10% of its present age

15. Galaxies at High Redshift
In the deepest images, the high redshift galaxies appear bluer, and more irregular than galaxies in the nearby universe. Many high redshift galaxies are interacting.

16. The Microwave Background
Suppose we were look further back in time, to when the universe was only 100,000 yr old. At that time …
The universe was very dense and under great pressure.
According to the equation of state, high pressure means high temperature.
According to the blackbody law, high temperature means light was produced.
Since this was a long time ago, if we were to observe it, the light would be redshifted into the microwave region of the spectrum.
Since the entire universe was glowing, this light should come from all over the sky.

17. The History of Light
The light from the Big Bang should now appear as emission from a blackbody at 3 degrees above absolute zero.

18. Prediction vs. Observation
1948: 3 degree blackbody emission from the entire universe predicted by George Gamow
1965: 3 degree blackbody emission found by Arno Penzias and Robert Wilson
1998: Blackbody spectrum measured by the COBE satellite
Prediction of Big Bang confirmed!

19. The Big Bang Universe
The universe was once small; now it is large. The only thing to slow the expansion is gravity – the more gravity, the more deceleration that will occur.

20. The Evolution of the Universe
The Universe has been expanding since the Big Bang. It will either keep expanding (an open or unbound universe), or reverse itself due to gravity (a closed or bound universe). Or it could be on the border line between these two possibilities.
The type of universe we live in depends on the Hubble Constant and how much matter there is.

21. The Shape of the Universe
Because matter bends space, the universe has a shape. A closed universe is like the surface of a sphere; an open universe is like a saddle. In the middle is flat space.
Type
Shape of Universe
Open Universe
Closed Universe
Flat Universe
Note that:
Parallel light rays act differently, depending on the shape of the universe.
Since E = mc2, energy can also warp space.

22. The All-Sky Microwave Background
Because the earth is moving through space, the microwave background should be redshifted in one part of the sky, and blueshifted in another part of the sky.
Blue is cooler (moving away); red is hotter (moving toward)

23. The All-Sky Microwave Background
When the earth’s motion is removed, the distribution of microwaves on the sky becomes more uniform.

24. The All-Sky Microwave Background
When emission from cold gas in the Milky Way is removed, the remaining distribution becomes very (but not perfectly) smooth.
The fluctuations are only a few parts in 10,000!

25. The All-Sky Microwave Background
From the equation of state, slightly higher temperatures means slightly higher densities and pressures. The red areas are over-dense by a factor of
From these primordial density fluctuations come today’s galaxies and clusters.

26. The All-Sky Microwave Background
Over time, the very small density fluctuations of the early universe have been amplified many times by gravity. The galaxies and clusters we see today grew from the slight fluctuations seen in the microwave background.

27. The All-Sky Microwave Background
The hot gas of the early universe cools and, with the aid of gravity, gets turned into galaxies and clusters of galaxies.

28. Formation of Structure
Over time, the very small density fluctuations of the early universe have been amplified many times by gravity.

29. The Shape of the Universe
The microwave background fluctuations also allow us to determine the shape of the universe. (The method is complicated: it has to do with how far apart the positive (and negative) areas appear on the sky. Theory tells us how far they should be, and we can observe how far apart they are.)
We observe that the Universe is Flat!

30. Fate of the universe: big crunch

31. Fate of the universe: continued expansion

32. Fate of the universe: big rip

33. The Deceleration of the Universe
The age of the universe depends on both its expansion rate (the Hubble Constant) and its density. Determining density is hard, since most of the mass is invisible. But over time, gravity has slowed down the expansion rate. By looking into the past, we can see how the universe has decelerated.
HUBBLE DIAGRAM
Closed
Closed
Flat
Flat
Empty
Empty

34. The Deceleration Parameter, q0
The deceleration rate is called q0. If
q0 = 0, the universe is empty (no gravity)
q0 < ½, the universe is open
q0 = ½, the universe if flat
q0 > ½, the universe is closed
Type Ia supernovae can be used as standard candles to look across the universe and measure the deceleration via a Hubble Diagram. This was done in The answer was…

35. The Accelerating Universe!!!
The universe is not slowing down at all. In fact, it’s speeding up!!! We live in an accelerating universe!
It’s as if there’s another force pushing the universe apart – a Cosmological Constant!!!

36. The Accelerating Universe!!!
Whatever this force is, we think that it is growing stronger as the universe evolves. The more empty space in the universe, the greater the acceleration – as if the vacuum of space has energy.

37. The Accelerating Universe!!!
We appear to live in a universe with a flat shape, but which will go on accelerating forever. The universe is 13.7 billion years old, and is now dominated by dark energy. And it will only get worse – the more empty space, the more dark energy.
The Dark Energy even dwarfs dark matter! Regular matter is really insignificant. We really don’t know anything about what’s going on!!

38. What is the Dark Energy?
We’re clueless. There is one “traditional” theory– that particles and anti-particles are constantly being created and annihilated in the empty space (due to the uncertainty principle). For the instant these particles exist, they would act as a repulsive force. But our estimate of this force is off by a factor of

39. Helium in the Universe
If the universe began as a high density soup of protons and neutrons, some of those particles must have undergone fusion.
In the Big Bang, about 1 of every 10 should have been changed to helium. That’s almost exactly the helium abundance we observe for the universe!

40. History of the Universe
The Big Bang occurred 13.7 billion years ago. Since then
seconds: protons, neutrons form
+3 minutes: fusion of hydrogen to helium ends
+100,000 years: release of the microwave background
+400,000,000 years: Milky Way begins to form
+2,000,000,000 years: era of galaxy formation/interaction
+9,000,000,000 years: Birth of the Sun

41. History of the Universe
The Big Bang occurred 13.7 billion years ago. Since then
+9,000,000,000 years: Birth of the Sun
+2,000,000,000 years: era of galaxy formation/interaction
400,000,000 years: Milky Way begins to form
+100,000 years: release of the microwave background
+3 minutes: fusion of hydrogen to helium ends
seconds: protons, neutrons form
seconds: particles form an annihilate
seconds: quarks form; gravity begins to exist
seconds: ???? Grand unification

42. Additional Puzzles about the Universe
Why is the universe flat?
Why does one side of the sky look like the other side of the sky? (They were never in contact with each other.)

43. (the observable universe is in red)
Inflation
A theory which explains these puzzles (and others) is that, very early on (10-34 sec after the beginning), the universe expanded much faster than now (1030 instead of 64). This is called inflation. The universe we see now is just a small region of a “bubble”. It therefore just looks flat.
(the observable universe is in red)

44. (But these other universes can never be observed.)
Multiverses
Inflation allows that our bubble may not be the only bubble. Bubbles may be forming all the time in a multi-universe.
(But these other universes can never be observed.)

45. The Discovery
In 1962, Cambridge University just completed a radio survey of the sky. Maarten Schmidt took their radio positions and looked for optical counterparts. He found a few peculiar “radio” stars.
3C 273 looked like an ordinary, fairly-bright star (with possibly a little fuzz). But ordinary stars do not emit much in the radio part of the spectrum.

46. The Spectrum The spectrum of the star was odd. It had
Emission lines instead of absorption lines
Broad (~10,000 km/s) emission lines, instead of narrow lines
Emission lines at “strange” wavelengths
The solution: the emission lines were those of hydrogen, but at enormous redshift. The object was moving away at 0.1 the speed of light!

47. Quasars Properties of quasi-stellar radio sources (quasars, or QSOs):
Star-like appearance (with possibly some “jets”)
Emission-line spectra with internal motions of ~10,000 km/s
Does not emit as a blackbody (at least, not at a single temperature). The objects emit light in x-rays, ultraviolet, optical, infrared, and sometimes microwave and radio
Irregularly variable on timescales of days/months
Enormous redshifts (up to 90% or more of the speed of light)
Stars in the Milky Way cannot move that fast. The only way to have such a redshift is through the Hubble Law. So, through v = H D, the objects must be incredibly far away. They are therefore incredibly bright – as bright as 1000 supernovae.

48. Size and Variability
Since many quasars vary in brightness we have a crude way to estimate their size.
Imagine that there is some mechanism near the center of the QSO that controls the object’s brightness. It says “get bright”.
That command goes forth no faster than the speed of light.
Within a few months, the object gets bright.
Since no signal can go faster than the speed of light, the object must be no bigger than a few light-months across!

49. The Energy Source
What can outshine ~1000 supernovae for millions of years, and be just slightly larger than our Solar System. Theoretically, not much – only a very, very big black hole.
Start with a 10,000,000,000 M black hole
Have a star come close enough to be tidally disrupted
Have the material form into an accretion disk. Energy is released via the friction in the disk. If you accrete ~ 1 M per year, you get the luminosity of a quasar.

50. Feeding the Monster
If a star comes too close, the enormous gravity of the black hole will cause tides on the star and rip it apart. Some of that material will be trapped in orbit about the hole.

51. Feeding the Monster
If a star comes too close, the enormous gravity of the black hole will cause tides on the star and rip it apart. Some of that material will be trapped in orbit about the hole.

52. Explaining a Quasar’s Properties
Near the event horizon, the gas is moving close to the speed of light. Any emission lines which are produced will be broad.
Because of the high speed of the gas, there is a lot of friction in the disk. A lot of light is produced.
The temperature of disk depends on the speed of the gas. Near the event horizon, the friction produces x-rays. At larger radii, where the gas revolves more slowly, optical and infrared light is made.

53. Black Holes and Jets
As matter accretes onto the black hole, particles can get ejected out the poles of the system at % of the speed of light. How this occurs is almost a complete mystery. But it’s often observed.

54. Where are the Quasars Today?
The nearest quasar is 25% of the way across the universe; most belong to an era when the universe was only 15% of its present age. If supermassive black holes existed then, where they now?
In the centers of galaxies!

55. The Quasar-Galaxy Connection
When a supermassive black hole is accreting, it can be thousands of times brighter than its surrounding galaxy. On the other hand, if the black hole is not accreting, it will be invisible.

56. Active Galactic Nuclei
Many nearby galaxies have some activity in their nucleus: they may have an extremely bright nucleus, or show a jet of emission, or have broad emission lines, or emit at radio wavelengths. These objects (which are probably just accreting a little mass) are said to have an Active Galactic Nucleus.
The energy produced by an AGN is still often many times that of the stars.

57. Galaxies with Active Galactic Nuclei

58. Sleeping Monsters
When a black hole is not accreting matter, then it’s invisible. But it’s gravitational influence on its surroundings can still be detected – the stars surrounding the hole must move fast (due to Kepler’s and Newton’s laws).

59. Sleeping Monsters
There’s even a 2,000,000 M black hole at the center of the Milky Way. We can measure its mass by the motions of stars which pass close to it.

60. AGN and Starbursts
In the present day universe, AGN are rare. However, they are more common in interacting galaxies. This suggests that the orbits of some stars have been perturbed enough to pass close to the black hole. It also suggests that all galaxies possess supermassive black holes.

61. AGN and the Universe
Since quasars can be seen 90% of the way across the universe, they allow us to detect gas throughout the universe. We can therefore examine galaxies (and proto-galaxies) that we can’t even see!
Any time the light from a quasar goes through a galaxy that has hydrogen gas, there will be absorption at the wavelength appropriate to hydrogen. But remember – this hydrogen is moving, due to the Hubble Law. So …

62. AGN and the Universe
Each absorption is due to hydrogen gas at a different redshift (i.e., distance). Quasars allow us to probe structure throughout the universe!