Cosmology

CosmologyThe Study of the Creation and Evolution of

the Universe as an entity

• Did the Universe have a beginning?– If so, how did it begin?– When did it begin?

• Has the Universe changed over time?– Is it changing/evolving now?

• What will the Universe become?– If there is a final state, what will it be like?– How much time will it take?

CosmologyLet's begin by considering an old

and very simple question:

Why is the sky dark at night?

Olbers' ParadoxIt is this seemingly stupid question

that leads us to Olbers' Paradox.

Obviously, at night the Sun is illuminating the opposite hemisphere of the Earth, but what about the stars?

Olbers' ParadoxSuppose that we consider a shell about the Earth at some distance

away. Confined within the bounds of this shell are a number of stars:

Let's say that on the average there are N stars in this shellR

Olbers' ParadoxIf we add additional shells, the total light from a shell decreases as 1/r2

But the number of stars in a shell increases as the area of the shells (we assume they are thin enough that we don't have to worry about the thickness of any shell, therefore the number of stars increases by r2

Total Light per Shell = Light/star X Number of Stars in the shell

r2

Olbers' Paradox

Total Light per Shell = Light/star X Number of Stars in the shell

= Light/star x N x r2 = Light/Star x N r2

Total Light is the sum of the light/shell times the total number of shells

This sums to INFINITY

The dimming of the light by distance is balanced by the increasing number of stars

Olbers' ParadoxAn infinite amount of light is not as bright as daylight --- It

would incinerate the Earth!

The paradox?We are not incinerated; the night sky is dark.What's wrong? Well, the stars are not that close together

--- But the galaxies are!

Hubble Deep Sky North

Olbers' ParadoxPerhaps there are clouds of gas and dust

blocking the starlight? So what, the gas and dust would eventually heat up and re-radiate the starlight.

For a static, infinite Universe, we've got a problem, not only should the sky be as bright as the sun at night, but much, much brighter. And, of course, it isn't.

This problem remained unsolved for over 100 years

The Cosmological Constant

• In 1915, Einstein produced his General Theory of Relativity which amongst many other thing predicted that the Universe was either collapsing or expanding. As this was contrary to 'known fact', Einstein reluctantly introduced a constant into his equations, , which forced the universe to remain static.

• He later referred to this as 'the greatest blunder of his career' for reasons we shall see in a moment.

Hubble's Law• In the 1920's, Edwin Hubble began to measure the spectra of

the galaxies – remember, at this time it still wasn't completely clear just what the galaxies were. He found that the spectra was, in general redshifted, and there was a relationship between the distance and the radial recessional speed. Leading to the realization that the Universe is not static but expanding.

• The dominant motion in the universe is the smooth expansion known as Hubble's Law.• Recessional Velocity = Hubble's constant times distance

V = Ho Dwhere, V is the observed velocity of the galaxy away from us, usually in km/sec; H is Hubble's "constant", in km/sec/Mpc and D is the distance to the galaxy in Mpc

• In 1929, Hubble estimated the value of the expansion factor, now called the Hubble constant, to be about 500 km/sec/Mpc. Today the value is still rather uncertain, but is generally believed to be in the range of 45-90 km/sec/Mpc.

Hubble’s LawThis diagram shows a typical plot of distance versus recessional velocity, with each point showing the relationship for an individual galaxy.

• While in general galaxies follow the smooth expansion, the more distant ones moving faster away from us, other motions cause slight deviations from the line predicted by Hubble's Law.

• Few of the points fall exactly on the line. This is because all galaxies have some additional residual motion in addition to the pure expansion. – This is referred to as the

"cosmic velocity dispersion" or "cosmic scatter" and is probably due to the fact that the gas clouds that formed the galaxies all had some small additional motion of their own.

• The recessional velocity of a galaxy at a particular distance inferred from Hubble's law is called the "Hubble velocity".

Models of the Universe• While Hubble discovered the Expanding Universe,

unfortunately his data was flawed. He mistook – largely due to the available equipment of his time – H II regions for galaxies, and used a different type of Cepheid variable (only one type was known then) in determining distances. This resulted in a Hubble Constant of about 500 km/sec/Mpc. Since H0 can be inverted to give the age of the universe, this results in the universe being created about 2 billion years ago.

• This is a bit of a problem, the geological records here on Earth are older that 2 billion years. Hmmmm

• One solution to this quandary is to devise a model of the Universe which, while expanding, doesn't depend on a starting time.–

This was proposed by Bondi, Gold and Hoyle in the 1950’s

Choices• The Cosmological Principle

– The Universe looks the same from any location in any direction• Applies to large scale• Homogeneous and Isotropic• embodies the “there is no preferred

place”

• The Perfect Cosmological Principle– The Universe looks the same from

any location in any direction and any time

The Steady State ModelThis model of the Universe states that it has neither a beginning

or an end. The Universe is the same now as it always was and always will be.

This, of course, evades the question of the geological record since the expansion rate is independent of a beginning point in time.

We still have to account for the expansion. This is done by the idea of "continuous creation of matter." If matter is allowed to be spontaneously created "out of nothing" then the additional matter will cause the universe to expand appropriately.

How much matter? What about conservation of mass and energy?

The creation rate is about 1 hydrogen atom/cubic meter/10 billion years

This is much to small for us to test the conservation law – we don't know if it holds at this level.

The Big Bang Model• Somewhat later, Hubble's Constant was

revised (using new data) and reduced to a value of between 55 and 75 km/sec/Mpc. Leading to an age of between 10 and 15 billion years.

• George Gamow proposed a model in which there was a definite beginning point. At a given point in the past, the primordial universe exploded. The expansion is a result of this cosmic explosion. This was termed the "Big Bang"

The Big BangThe term, Big Bang, is somewhat

unfortunate because it gives the impression that the stars and galaxies are flying apart like the shards from an exploding bomb.

This is not what is happening! What is expanding is space-time itself –

the galaxies are simply embedded in an ever-enlarging framework.

Big Bang Expansion

The galaxies (raisins) are not expanding, the space-time framework (bread dough) supporting them is.

Olbers' Paradox Revisited

Now we finally have an answer to Olbers' Paradox.

• The universe is not infinitely old nor infinitely large

• The light is redshifted, losing energy, due to the expansion of the universe

• There is a point where the rate of expansion nears the speed of light beyond which the light cannot get reach us in the amount of time since the big bang.

Models• The debate raged until 1964, when Arno Penzias and Robert

Wilson of Bell Labs constructed a new type of microwave radio antenna.

• They kept getting a static signal, no matter how they tuned and oriented the antenna. At one point they even constructed a pigeon trap thinking that the guano being deposited in the horn of the antenna by the nesting pigeons was the source of the static.

• Finally someone mentioned to them to talk to Robert Dicke at Princeton --- It seems that Dicke had predicted that the cooling of the expanding universe from its original hot, dense state would be detectable as a 3º K blackbody background radiation.

CMB• Penzias and Wilson then

looked at the signal and fitted it to the blackbody curve -- It was a match at 2.7 º K

• The remnants of the Big Bang had been found.

Models• Finding the 2.7 º K Cosmic

Microwave Background radiation was the first nail in the coffin for the Steady State theory.

• Other nails were added with quasars, distribution of peculiar galaxies and other things found at distances corresponding to high-redshift values.

Cosmic Microwave Background

Here is a map of the CMB corrected for our motion through the Universe and removing the noise generated by our galaxy. The difference between the red and blue levels (the fluctuations) is 1 in 100,000 or about ±30 micro-Kelvin

Geometry Anyone?Before we continue, let’s take a brief look at something you all learned long ago.

Remember that the circumference of a circle is 2∏ times the radius?

How about the sum of the interior angles of a triangle add up to 180 degrees?

How about the statement that parallel lines never meet?

These rules provide what we call “Flat” space

Flat Space

Positively-curved Space

Negatively-curved Space

Parallel lines diverge

Geometries

How does this relate to the Universe?

Wait and See…

What Next?• If the Universe had a beginning, will it have an end?• This will be determined by the total amount of mass in the

Universe– If there is enough mass, then the force of gravity will

slowly stop the expansion and pull it back together again– If there is not enough then it will keep expanding– The boundary between these two extremes is the critical

mass

• Since we don’t know the exact values, it’s more useful to talk in terms of the ratio of the total mass of the Universe to this critical mass.

– It is given the symbol = (actual mass)/(critical mass)

The Nature of the Universe• There are 4 possibilities

– An ever-expanding universe expanding faster and faster

• The Open Universe ( < 1)

– A universe expanding at the same rate as it is now

• The Critical Universe ( = 1)

– A universe that will eventually slow, and then collapse in a ‘Big Crunch’

• The Closed Universe ( > 1)

– A (theoretical) universe with no matter (and no gravity)

• The 'Coasting' Universe ( = 0)

• Only useful to theorists – the real universe has matter

Ω0 = 1In a Ωo = 1 Universe, the two factors are perfectly balanced. The Universe will expand forever, but at a slower and slower rate.After an infinite amount of time, the Universe will stop expanding and “coast to a halt.”

Ω0 > 1If Ωo > 1, there is more mass than necessary, andgravity wins. The expanding Universe eventually slows,stops, and then contracts faster and faster until the BigCrunch.

Ω0 = 0If Ωo = 0, there is no matter in the Universe and no gravityto slow down the contraction. The Universe expands ata constant rate forever. Of course, this Coasting Universe is purely theoretical – since we know there is mass and gravity!

Ω0 ≤ 1 and Λ > 0If Ω0 ≤ 1 (not enough mass) and we add a cosmologicalconstant Λ > 0 creating a repulsive force, the Universewill continue to expand, but an accelerated rate.

Which is correct?

The recent observations from WMAP suggest we are living in the perfectly balanced Ωo = 1 Universe. The Universe will continue to expand forever.

Evidence, from Type Ia Supernovas, is also suggesting we are living in an accelerating Λ > 0 Universe being driven apart by strange “dark energy.”

The Shape of the Universe

Problems?The Big Bang model (now the

standard) has some problems which are difficult to resolve:

– The Horizon Problem– The Flatness Problem– The Structure Problem– The Relic Problem

The Horizon Problem• Why is the CMB so uniform?

– Looking at one part of the sky and looking in the opposite direction, radio telescopes measuring the CMB see the temperature to 1 part in 10,000.

• Suppose the universe is 14 billion years old, then the two directions are separated by 28 billion lightyears.– Thus they should not be "causally connected"

• That is, they should not know about each other• The two regions should not have the same temperature

– In the past the situation was even worse • 100,000 years after the Big Bang, the separation would be 10 million

lightyears

The Universe is nearly flat today, this implies that it had to be nearly flat in the beginning.

However both the average density and the critical density change with time

In the past, right after the Big Bang, if the average density were slightly larger or smaller we have and open or closed universe.

At the beginning the density would have to be very close to the critical value (1 part in 1015); Otherwise a Big Crunch or Big Chill would have occurred long ago.

The Flatness ProblemWhy are we so close to a flat universe?

• The Structure Problem– What formed the perturbations we see around us. Why is the

Universe structurally the same everywhere if it was not in causal contact in the beginning.

• The Relic Problem– The GUTs (Grand Unification Theories) predict massive particles

that are not observed in reality. What happened to these particles?

Other Problems?

The Inflationary UniverseThese problems are resolved in the Inflationary

model of the Big Bang. This states that what we call the Observable

Universe was really only a small region of the initial universe. This region was small enough to be in causal contact. The region then underwent exponential expansion. The exponential growth caused the flattening out of any curvature; diluted the massive GUTs particles and small quantum fluctuations were preserved and ‘blown up’ providing the seeds for structure formation.

Inflation• Modern particle theories predict that, at very high

energies, there exists a form of matter that creates a gravitational repulsion!

• Inflation proposes that a patch of this form of matter existed in the early universe– it was probably more than a billion times smaller

than a single proton! • The gravitational repulsion created by this material

was the driving force behind the big bang. • The repulsion drove it into exponential expansion,

doubling in size every 10-37seconds or so! • The density of the repulsive gravity material was

not lowered as it expanded!

Inflation• Although more and more mass/energy appeared as the

repulsive-gravity material expanded, total energy was conserved!

• The energy of a gravitational field is negative! • The positive energy of the material was compensated by the

negative energy of gravity. • The repulsive-gravity material is unstable, so it decayed like

a radioactive substance, ending inflation. • The decay released energy which produced ordinary

particles, forming a hot, dense “primordial soup.” • Inflation lasted maybe 10-35 seconds. At the end, the region

destined to become the presently observed universe was about the size of a marble.

• The “primordial soup” matches the assumed starting point of the standard big bang— the standard big bang description takes over. The region continues to expand and cool to the present day.

Evidence for Inflation• Large scale uniformity. The cosmic background radiation is uniform in

temperature to one part in 100,000. It was released when the universe was about 300,000 years old. In standard cosmology without inflation, a mechanism to establish this uniformity would need to transmit energy and information at about 100 times the speed of light.

• “Flatness problem:” Why was the mass density of the early universe so close to the critical density?

,where the “critical density” is that density which gives a geometrically flat universe. At one second after the big bang, must have been equal to one to 15 decimal places! Extrapolating back to the Planck time, 10-43 seconds, must have been one to 58 decimal places! Inflation explains why.

• Since the mechanism by which inflation explains the flatness of the early universe almost always overshoots, it predicts that even today the universe should have a critical density.

• Small scale non-uniformity of the cosmic background radiation. Although only at the level of 1 part in 100,000, these non-uniformities can now be measured!

• The properties measured so far agree beautifully with inflation.

Evidence for Inflation

ΩΛ = 0.7 ΩCDM = 0.257

Inflation!• About 10-35 seconds after the Big Bang, the Universe

cooled to 1027 K• This caused a "phase transition" (Like water changing into

ice)• This phase transition released a lot of energy• The strong force split from the other forces releasing

tremendous amounts of energy• The universe expanded by a factor of 1050 in 10-33 seconds!• Inflation solves the Horizon and Flatness problems The

parts of the Universe we see now were causally connected before inflation Thus the CMB will be the same in all directions afterward

• The Universe becomes flat because of the stretching of space

Experimental Evidence!Inflation predicts that the quantization of the gravitational field coupled to exponential expansion produces a unique pattern in the CMB.

BICEP2 (Background Imaging of Cosmic Extragalactic Polarization) released its results in March 2014

BICEP2 Detector

South Pole Telescope

This pattern, basically a curling in the polarization, or orientation, of the light, can be created only by gravitational waves produced by inflation.

Epochs of the Universe• From the Big Bang until now, the universe can be viewed as

proceeding through different "epochs" (time periods). • Distinguishing characteristics:

– Each succeeding epoch is cooler and thinner. – Different "forces" and/or "particles" may dominate!

Dark Matter

• There is not enough visible mass in the universe to have > 1

• Even if we add estimates of the unseen dark matter – it isn’t enough

Dark Energy• Recently it has been suggested that

Einstein’s blunder was in fact more insight than most of us possess.

• His Cosmological Constant, , is being associated with a ‘Dark Energy’ which is repulsive at large distances.

Accelerating Universe?• Today there is strong evidence coming from the

observation of distant Type Ia Supernova, by two different teams of astronomers, indicating that the cosmic expansion is not slowing down, but is speeding up!

• This observation strongly supports inflationary theory:– It confirms the theoretical conclusion that gravity can act

repulsively. – Acceleration requires “dark energy” permeating space, the

amount needed is just right (about ±10%) to bring the total mass density up to the critical density predicted by inflation. (The makeup is about 1% visible matter, 29% dark matter, and 70% “dark energy”.)

A Newer View

In March 2013, the Planck spacecraft’sfirst 15.5 months of data revealed that the Universe was older than previouslythought, 13.8 Billion years

Planck Full-Sky MapThis full-sky map from the Planck mission shows matter between Earth and the edge of the observable universe. Regions with less mass show up as lighter areas while regions with more mass are darker. The grayed-out areas are where light from our own galaxy was too bright, blocking Planck's ability to map the more distant matter.

Normal matter, which is made up of atoms, is only a small percent of the total mass in our universe. Most of the matter in the universe is dark -- that is, it does not emit or absorb any light -- so creating a map of its distribution is challenging. To make the full-sky map, the Planck team took advantage of the fact that all matter, even dark matter, has gravity that will affect light traveling to us from near the very edge of the observable universe. Planck mapped this light, called the cosmic microwave background, with exquisite precision over the whole sky, enabling scientists to create this matter map.

Curiouser and CuriouserThe Planck mission has imaged the oldest light in our universe. The results fit well with what we know about the universe and its basic traits, but some unexplained features are observed.

One of the anomalies observed by Planck is an asymmetry in the temperature fluctuations of the ancient light across two halves of our sky.

Temperature variations are represented by the different colors, with red being warmer and blue, cooler. The extent of these variations is greater on the hemisphere shown at right than the one at left.

This goes against the accepted simple model of our universe, which holds that the sky is the same in all directions.

Preliminary Planck ResultsThis relic radiation provides scientists with a snapshot of the universe 370,000 years after the Big Bang. Light existed before this time, but it was locked in a hot plasma similar to a candle flame, which later cooled and set the light free. The cosmic microwave background is remarkably uniform over the entire sky, but tiny variations reveal the imprints of sound waves triggered by quantum fluctuations in the universe just moments after it was born. These imprints, appearing as splotches in the Planck map, are the seeds from which matter grew, forming stars and galaxies. The newly estimated expansion rate of the universe, known as Hubble's constant, is 67.15 ± 1.2 Km/Sec/Mpc.

The new estimate of dark matter content in the universe is 26.8 percent, up from 24 percent, while dark energy falls to 68.3 percent, down from 71.4 percent.

Normal matter now is 4.9 percent, up from 4.6 percent.

Current ModelsModels using = mass + energy are now being researched. One such model, predicts the CMB to look like:

Where mass = 0.3 and energy = 0.7

The Fate of the Universe

The past history of the Universe is one of an early, energetic time. As the Universe expanded and cooled, phenomenon became less violent and more stable.

This ruling law of Nature during the evolution of the Universe has been entropy, the fact that objects go from order to disorder. There are local regions of high order, such as our planet, but only at the cost of greater disorder somewhere nearby.

If the Universe is open or flat (as our current measurements and theories suggest) then the march of entropy will continue and the fate of our Universe is confined to

The Fate of the Universe

the principle of heat death, the flow of energy from high regions to low regions.With this principle in mind, we predict the future of the Universe will pass through four stages as it continues to expand.

Stellar Era

The Stellar Era is the time we currently live in, where most of the energy of the Universe comes from thermonuclear fusion in the cores of stars.

The lifetime of the era is set by the time it takes for the smallest, lowest mass stars to use up their hydrogen fuel.

The lower mass a star is, the cooler its core and the slower it burns its hydrogen fuel (also the dimmer the star is). The slower it burns its fuel, the longer it lives (where `live' is defined as still shining).

The longest lifetime of stars less than 1/10 a solar mass (the mass of our Sun) is

1014 years.

Stellar Era

New stars are produced from gas clouds in galaxies. However, 1014 years is more than a sufficiently long enough time for all the gas to be used up in the Universe.

Once the gas clouds are gone, all the matter in the Universe is within stars.

Stellar Era

Degenerate Era• Once all the matter has been converted into

stars, and the hydrogen fuel in the center of those stars has been exhausted, the Universe enters its second era, the Degenerate Era.

• The use of the word degenerate here is not a comment on the moral values of the Universe, rather degenerate is a physical word to describe the state of matter that has cooled to densities where all the electron shell orbits are filled and in their lowest states.

During this phase all stars are in the form of white or brown dwarfs, or neutron stars and black holes from previous explosions.

White and brown dwarfs are degenerate in their matter, slowly cooling and turning into black dwarfs.

Degenerate Era

During this era, galaxies dissolve as stars go through two-body relaxation. Two-body relaxation is when two stars pass close to one another, one is kicked to high velocity and leaves the galaxy, the other is slowed down and merges with the Galactic black hole in the center of the galaxy's core. In the end, the Universe becomes filled with free stars and giant black holes, leftover from the galaxy cores.

Degenerate Era

The Universe would evolve towards a vast soup of black dwarf stars except for process known as proton decay.

The proton is one of the most stable elementary particles, yet even the proton decays into a positron and a meson on the order of once per 1032 years.

Thus, the very protons that make up black dwarf stars and planets will decay and the stars and planets will dissolve into free leptons. This all takes about 1037 years.

Degenerate Era

Black Hole Era

Once all the protons in the Universe have decayed into leptons, the only organized units are black holes.

From Hawking radiation, we know that even black holes are unstable and evaporate into electrons and positrons.

• This process is extremely slow, varying inversely as the mass of the black hole.

• For Galactic mass black holes, the time to dissolve can last up to 10100 years.

• The result is a bunch of photons, slowly cooling in the expanding Universe.

Black Hole Era

Dark Era

After all the black holes have evaporated, the Universe consists of an expanding sea of very long wavelength photons and neutrinos.

This is a system of maximum disorder, no coherent structures or objects. No sources of energy, and no sinks as well.

The rest of time is simply a continual lowering of energy until the state of quantum vacuum is reached.

Finally

In about a 100 trillion years, its going to be a cold, dark empty universe

Unless ....

The Superstring Theory

Each fundamental particle (quark, electron, neutrino) is a different vibration mode of a tiny, elongated, one-dimensional energy packet called a “string”

“Strings” are so small (10-33 cm), they are almost point-like

Universe is 11-dimensional, but 7 of the dimensions are too small to see

Leads to M-Brane theory where two M-branes collide causing a Universe to be born – giving rise to a Multi-verse.