Teaching the Big Bang Pat Hall, York University Department of Physics and Astronomy pt Evidence for the Big Bang and Inflation The Observable Universe Structure Formation

Summary Hubble’s Law: all galaxies are moving away from each other: space is expanding Our 3-D universe is expanding into a 4 th dimension [time] like the 2-D surface of a balloon expands into a 3 rd dimension

Summary Hubble’s Law: all galaxies are moving away from each other: space is expanding Our 3-D universe is expanding into a 4 th dimension [time] like the 2-D surface of a balloon expands into a 3 rd dimension The Big Bang was a point in time, not in space. It happened 13.7 billion years ago.

Summary Hubble’s Law: all galaxies are moving away from each other: space is expanding Our 3-D universe is expanding into a 4 th dimension [time] like the 2-D surface of a balloon expands into a 3 rd dimension The Big Bang was a point in time, not in space. It happened 13.7 billion years ago. Our Observable Universe: a sphere centered on us, 13.7 billion light-years in radius Physical Universe: effectively infinite in size

Steps to the Big Bang From our viewpoint in the Milky Way Galaxy, we see almost all galaxies moving away from us (Edwin Hubble and others, 1920s-1930s)

By measuring distances to galaxies, Hubble found that redshift and distance are related in a special way

Steps to the Big Bang From the Milky Way, we see almost all other galaxies moving away from us (Edwin Hubble) Either we’re at the center of the Universe…

Either we’re at the center of the universe, or...

Steps to the Big Bang Here in the Milky Way, we see almost all galaxies moving away from us (Edwin Hubble) Either we’re at the center of the Universe… …or galaxies are ALL moving away from each other, and the Milky Way is just another one of those galaxies.

Galaxies are all moving away from each other. Rewind the movie; galaxies must have been closer together in the past.

Galaxies are all moving away from each other. Rewind the movie; galaxies must have been closer together in the past. Universe was denser in the past. The Big Bang was when the density was “infinite”.

Steps to the Big Bang Here in the Milky Way, we see almost all galaxies moving away from us (Edwin Hubble) Space is expanding, carrying all galaxies away from each other, and the Milky Way is just another one of those galaxies. The universe has no center.The universe has no center.

Steps to the Big Bang Here in the Milky Way, we see almost all galaxies moving away from us (Edwin Hubble) Space is expanding, carrying all galaxies away from each other, and the Milky Way is just another one of those galaxies. The universe has no center.The universe has no center. Think of rewinding the movie of the universe: The Big Bang was a point in time, not in space.

Surface of a balloon expands but has no center or edge

Steps to the Big Bang Here in the Milky Way, we see almost all galaxies moving away from us (Edwin Hubble) The 3-D universe has no center, just like the 2-D surface of a balloon has no center.Galaxies are all moving away from each other, and the Milky Way is just another one of those galaxies. The 3-D universe has no center, just like the 2-D surface of a balloon has no center. Our 3-D universe is expanding into a 4 th dimension [time] like the 2-D surface of a balloon expands into a 3 rd dimension. The Big Bang was a point in time, not in space.

Aside: Hubble’s Law and Vectors Galaxies moving away from each other (save for some of each galaxy’s closest neighbors).

Aside: Hubble’s Law and Vectors Galaxies moving away from each other (save for some of each galaxy’s closest neighbors). Vector formula: V=Hd where H is Hubble’s constant and V & d are the velocity & distance vectors of a distant galaxy relative to our own.

Aside: Hubble’s Law and Vectors Galaxies moving away from each other (save for some of each galaxy’s closest neighbors). Vector formula: V=Hd where H is Hubble’s constant and V & d are the velocity & distance vectors of a distant galaxy relative to our own. Change your location to a distant Coma cluster galaxy which has distance vector c relative to Milky Way. You can show that for aliens in that galaxy, Hubble’s law is V c =Hd c where d c =d-c is the distance from their galaxy to a galaxy with distance vector d relative to the Milky Way.

Evidence for the Big Bang and Inflation Here in the Milky Way, we see almost all galaxies moving away from us (Edwin Hubble) Galaxies are all moving away from each other, and the Milky Way is just another one of those galaxies. (Exceptions: galaxies very near to each other can orbit each other or crash into each other due to gravity.) Galaxies all moving away from each other, so…

…the universe must have been much denser (and hotter) early in its history.

At very early times, only the elements helium and hydrogen existed. (Other elements were made later, inside stars.)

What is everything made of? Water (H 2 O) is made up of molecules, as are many other everyday substances. A water molecule is made up of atoms: 2 hydrogen atoms (H) and 1 oxygen atom (O).

What is everything made of? Water (H 2 O) is made up of molecules, as are many other everyday substances. A water molecule is made up of atoms: 2 hydrogen atoms (H) and 1 oxygen atom (O). Every atom consists of two parts:Every atom consists of two parts –One or more electrons surrounding... –the nucleus: ≈ 100,000 times smaller than the electron cloud, but 10,000 to 100,000 times heavier.

What is everything made of? Water (H 2 O) is made up of molecules, as are many other everyday substances. A water molecule is made up of atoms: 2 hydrogen atoms (H) and 1 oxygen atom (O). Every atom consists of two parts:Every atom consists of two parts –One or more electrons surrounding... –the nucleus: ≈ 100,000 times smaller than the electron cloud, but 10,000 to 100,000 times more massive. If you increase the density and temperature enough, you can break apart molecules into atoms, and even atoms into electrons and nuclei. Hydrogen & helium are transparent as atoms, but are opaque when split into nuclei and electrons.

Aside: hydrogen nuclei (protons) and neutrons combined into stable helium nuclei when universe was ~3 minutes old. Leftover neutrons became protons. (Before the protons & neutrons, there were quarks. Before that, we’re not sure!)

Not long after the Big Bang, the universe was very hot. Hydrogen and helium were in the form of nuclei plus electrons, so the universe was opaque.

When the universe cooled to a temperature of about 3000 degrees, hydrogen and helium formed into atoms, and the universe became transparent.

The infrared light from when the universe was 3000 degrees hot has traveled through the universe ever since it became transparent: cosmic microwave background.

Expansion of universe stretches wavelengths of light, causing a cosmological redshift similar to the Doppler effect.

The expansion of the universe has redshifted infrared light from when the universe became transparent to ~1000 times longer wavelength now: microwaves Cosmic background has a nearly uniform temperature 2.73 degrees above absolute zero (2.73 Kelvin = -270 degrees Celsius)

The cosmic microwave background – the radiation left over from the Big Bang – was detected by Penzias & Wilson in 1965, for which they later won the Nobel Prize.

Cosmic microwave background has a nearly uniform temperature, but not quite uniform... Cosmic background has a nearly uniform temperature 2.73 degrees above absolute zero (2.73 Kelvin = -270 degrees Celsius)

Wilkinson Microwave Anisotropy Probe (WMAP) The WMAP satellite has shown that when our universe became transparent (when it was about 380,000 years old), it was uniform in temperature to within a maximum difference of plus or minus 1 part in 5,000.

Wilkinson Microwave Anisotropy Probe (WMAP) The WMAP satellite has shown that when our universe became transparent (when it was about 380,000 years old), it was uniform in temperature to within a maximum difference of plus or minus 1 part in 5,000 If everyone on Earth were the same height to within plus or minus 1 part in 5000, the tallest person on Earth would be only 1 mm taller than the shortest person on Earth.

Remember that every point on this map of the microwave sky represents light that traveled 13.7 billion light years to reach us…

How can temperature be nearly identical on opposite sides of the sky, which didn’t know about each other?

Inflation: regions now on opposite side of the sky were close together before inflation pushed them far apart

Inflation (Alan Guth, Stanford, 1980s) When the universe was almost unimaginably young, the forces between particles got out of balance... we call this symmetry breaking. Analogy: you can balance a pencil on end if you provide a force to balance gravity. Take that force away, and the force of gravity is converted into energy of motion in the pencil.

Inflation When the universe was almost unimaginably young, the forces between particles got out of balance... we call this symmetry breaking. Analogy: you can balance a pencil on end if you provide a force to balance gravity. Take that force away, and the force of gravity is converted into kinetic energy in the pencil. At symmetry breaking, the unbalanced force was converted into kinetic energy that made the universe expand by a mind-boggling amount Analogy: microwave a potato in its skin!

Inflation can make all the structure in the microwave background by stretching sub- atomic “ripples” to enormous size. These ripples in density then become the seeds for all structures in today’s universe

Inflation flattened the overall geometry of the universe like the inflation of a balloon flattens the balloon’s surface – however the universe started out, it ended up almost exactly flat. (Could there be island universes in a long, thin balloon?)

Observable Universe versus Physical Universe Observable Universe has a finite size. Physical Universe is either infinite or has a finite size so large it’s effectively infinite.

Structure Formation Structure means: Galaxies and Satellite Galaxies Groups, Clusters, Superclusters of Galaxies

WMAP gives us detailed baby pictures of structure in the universe

Observed patterns of structure in universe – from WMAP etc. - agree (so far) with what inflation should produce

Gravity pulls mass into denser regions – universe grows lumpier with time. But there’s not enough normal matter to explain the lumpiness. So we think there’s dark matter... matter that exerts gravity but hardly any other force. Time in billions of years Size of expanding box in millions of lt-yrs

Dark Matter and Dark Energy: Will the universe continue expanding forever?

Does the universe have enough energy of motion (kinetic energy) to escape its own gravitational pull?

Fate of universe depends on amount of dark matter Lots of dark matter Not enough dark matter

Critical density of matter Not enough dark matter Fate of universe depends on amount of dark matter Lots of dark matter

Amount of dark matter is ~25% of the critical density suggesting fate is eternal expansion Not enough dark matter

But expansion appears to be speeding up! Not enough dark matter Dark Energy?

Estimated age depends on dark matter and dark energy old older oldest

The Big Bang and our Universe The Big Bang was a point in time, not in space The physical universe has no center or edge

The Big Bang and our Universe The Big Bang was a point in time, not in space The physical universe has no center or edge The observable universe is centered on us. We observe light from everything that was within 13.7 billion light years of our current location when the universe became transparent. Next year, we’ll see 1 light-year farther away.

The Big Bang and our Universe The Big Bang was a point in time, not in space The physical universe has no center or edge The observable universe is centered on us: we observe light from everything that was within 13.7 billion light years of our current location when the universe became transparent. Next year, we’ll see 1 light-year farther away. Energy conservation: the universe’s positive mass-energy & kinetic energy plus its negative potential energy (three kinds: gravitational, electroweak, strong-force) can sum to zero.

Olbers’ Paradox: The night sky tells us that the observable universe isn’t infinitely old and unchanging

Olbers’ Paradox If universe were 1) infinitely old, and infinite in all directions in space 2) unchanging 3) everywhere the same Then stars would cover the night sky

Olbers’ Paradox If universe were 1) infinite in space and time 2) unchanging 3) everywhere the same Then, stars would cover the night sky

Night sky is dark because the universe changes with time, and because the observable universe is neither infinitely big nor infinitely old

Cosmological Horizon Universe’s age of 13.7 billion years limits how far we can see, and 13.7 billion years ago there weren’t any stars around yet.

Thinking about a simpler universe Our universe has 3 (large) dimensions of space: up/down, left/right, forward/backward.

Thinking about a simpler universe Our universe has 3 (large) dimensions of space: up/down, left/right, forward/backward. Our universe has 1 dimension of time (past/future, but we move only forward in time).

Thinking about a simpler universe Our universe has 3 (large) dimensions of space: up/down, left/right, forward/backward. Our universe has 1 dimension of time (past/future, but we move only forward in time). It’s easier to discuss a simpler universe -- one with 2 dimensions of space and 1 of time – and then extend that picture to 3 dimensions. Flatland by Edwin Abbott

Thinking about a simpler universe A universe with 1 dimension of time but only 2 dimensions of space might have left/right and front/back, but no up/down (like a board game). Or it might have left/right and up/down, but no front/back (like some video games [Asteroids]). This two-dimensional universe could be: Flat & infinite (infinite piece of paper) Positively curved & finite (surface of a balloon) Negatively curved & infinite (infinite Pringle)

Thinking about a ‘simpler’ universe A universe with 1 dimension of time but only 2 dimensions of space might have left/right and front/back, but no up/down (like a board game). Or it might have left/right and up/down, but no front/back (like some video games [Asteroids]). This two-dimensional universe could be: Flat & infinite (infinite piece of paper) Flat & semi-finite (infinitely long cylinder) Flat & finite (surface of a donut [a torus]) Positively curved & finite (surface of a balloon) Negatively curved & infinite (infinite Pringle) Negatively curved & finite (can’t be drawn!)

Inflation of universe flattens overall geometry like the inflation of a balloon – however the universe started out, it will end up almost exactly flat. (Could there be island universes in a long, thin balloon?)

Thinking about our universe Our three-dimensional universe appears very close to flat (<=1 part in 50 at the moment), as well as infinite (infinite in all spatial directions) Inflation predicts our universe is very close to flat (probably at the level of 1 part in 100,000) If the universe is that flat, for all intents and purposes it is exactly flat, and we may never know whether our universe started out exactly flat or curved (positively or negatively) (2-dimensional analogies: zero curvature = infinite piece of paper; positive curvature = like a balloon; negative curvature = like a Pringle)

Aside: Spherical Geometry Flat geometry means angles of a triangle in that space add up to 180 degrees (this is the normal ‘Euclidean’ geometry taught in school) Positively curved geometry means angles of a triangle add up to more than 180 degrees (From the north pole, draw two lines to the equator: one through 0 degrees longitude and another through 90 degrees longitude. Connect them along the equator to make a triangle with three 90-degree angles.) Negatively curved: angles of a triangle add up to less than 180 degrees

Overall geometry of the universe is closely related to total density of matter & energy Density = Critical Density > Critical Density < Critical