I The Curvature of Space

Euclid of Alexandria

Born: about 325 BC
Died: about 265 BC in Alexandria, Egypt

Flat Space (Shortest Distance is a straight Line) 1 parallel Line

August Ferdinand Möbius

Born: 17 Nov 1790 in Schulpforta, Saxony (now Germany)
Died: 26 Sept 1868 in Leipzig, Germany

Johann Carl Friedrich Gauss
Born: 30 April 1777 in Brunswick, Duchy of Brunswick (now Germany)
Died: 23 Feb 1855 in Göttingen, Hanover (now Germany)

Nikolai Ivanovich Lobachevsky

Born: 1 Dec 1792 in Nizhny Novgorod (was Gorky from 1932-1990), Russia
Died: 24 Feb 1856 in Kazan, Russia

1829 Negative Curved Space

Georg Friedrich Bernhard Riemann

Born: 17 Sept 1826 in Breselenz, Hanover (now Germany)
Died: 20 July 1866 in Selasca, Italy

1854 Positive Curved Space

Albert Einstein

Born: 14 March 1879 in Ulm, Württemberg, Germany
Died: 18 April 1955 in Princeton, New Jersey, USA

Field Equation
Geometry = Forces
= (Pressure/density + Velocity/motion of Particles) + k (Constant)

The Curvature of Space

	k = +1 (Positive)	k = 0	k = - 1 (Negative)
	Riemann - Sphere	Euclid - Flat	Lobachevski - Hyperbolic Saddle Back
Sum of angles of Triangles	Gauss measured Mountains Peaks > 180º	= 180º	< 180º
Circumference / R	Orange - Surface of Earth C < 2πR	C = 2πR	Potato Chip C > 2πR
Area / R	< 4πR²	= 4πR²	> 4πR²
Volume / R	< 4/3 π R³	= 4/3 π R³	> 4/3 π R³
Boundaries	Finite, Closed (Bounded)	Infinite, Open (no Boundaries)	Infinite, Open, No Boundaries,

II Space-Time

http://www.damtp.cam.ac.uk/user/gr/public/bb_history.html

A Brief History of the Universe

The history of the Universe divides roughly into three regimes which reflect the status of our current understanding:

The standard cosmology is the most reliably elucidated epoch spanning the epoch from about one hundredth of a second after the Big Bang through to the present day. The standard model for the evolution of the Universe in this epoch have faced many stringent observational tests.

Particle cosmology builds a picture of the universe prior to this at temperature regimes which still lie within known physics. For example, high energy particle acclerators at CERN and Fermilab allow us to test physical models for processes which would occur only 0.00000000001 seconds after the Big Bang. This area of cosmology is more speculative, as it involves at least some extrapolation, and often faces intractable calculational difficulties. Many cosmologists argue that reasonable extrapolations can be made to times as early as a grand unification phase transition.

Quantum cosmology considers questions about the origin of the Universe itself. This endeavours to describe quantum processes at the earliest times that we can conceive of a classical space-time, that is, the Planck epoch at 0.0000000000000000000000000000000000000000001 seconds. Given that we as yet do not have a fully self-consistent theory of quantum gravity, this area of cosmology is more speculative.

Photon

Photon is the name given to a quantum of light or other electromagnetic radiation.
The photon energy is given in the Planck relationship.
The photon is the exchange particle responsible for the electromagnetic force.
The infinite range of the electromagnetic force is owed to the zero rest mass of the photon.
While the photon has zero rest mass, it has finite momentum,
is capable of deflection by a gravity field, and can exert a force.

Gluons

Gluons are the exchange particles for the color force between quarks,
analogous to the exchange of photons in the electromagnetic force between two charged particles.
The gluons carry color and are massive and therefore limited in range.
These properties contrast them with photons, which are massless and of infinite range.
The photon does not carry electric charge with it, while the gluons do carry the "color charge".

Graviton

The graviton is the exchange particle for the gravity force.
Although it has not been directly observed, a number of its properties can be implied from the nature of the force.
Since gravity is an inverse square force of apparently infinite range, it can be implied that the rest mass of the graviton is zero.

Quarks and Leptons are the building blocks which build up matter, i.e., they are seen as the "elementary particles". In the present scheme, there are six "flavors" of quarks. They can successfully account for all known mesons and baryons (over 200).

Quarks

Up
Down
Charm
Strange
Top
Bottom

Leptons
There are six leptons, the electron, muon, and tau particles and their associated neutrinos.
The different varieties of the elementary particles are commonly called "flavors", and the neutrinos here are considered to have distinctly different flavor.

Mesons

Mesons are intermediate mass particles which are made up of a quark-antiquark pair.
Three quark combinations are called baryons.
Mesons are bosons, while the baryons are fermions.

Baryons

Baryons are massive particles which are made up of three quarks in the standard model.
This class of particles includes the proton and neutron.
Other baryons are the lambda, sigma, xi, and omega particles.
Baryons are distinct from mesons in that mesons are composed of only two quarks.
Baryons and mesons are included in the overall class known as hadrons, the particles which interact by the strong force.
Baryons are fermions, while the mesons are bosons.

Hadrons

Particles that interact by the strong interaction are called hadrons. This general classification includes mesons and baryons but specifically excludes leptons, which do not interact by the strong force. The weak interaction acts on both hadrons and leptons.

Hadrons are viewed as being composed of quarks,
either as quark-antiquark pairs (mesons)
or as three quarks (baryons).
There is much more to the picture than this, however, because the constituent quarks are surrounded
by a cloud of gluons, the exchange particles for the color force.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parcon.html

http://www.pbs.org/deepspace/timeline/

Three outstanding problems with the Big Bang cosmological model:
1. The flatness problem
2. The horizon problem
3. The magnetic monopole problem

Flatness problem

    The Universe as observed today seems to have enough energy density in the form of matter
to provide critical density and hence zero spatial curvature.
The Einstein equation predicts that any deviation from flatness in an expanding Universe
filled with matter or radiation only gets bigger as the Universe expands.
So any tiny deviation from flatness at a much earlier time would have grown very large by now.
If the deviation from flatness is very small now, it must have been immeasurably
small at the start of the part of Big Bang.
So why did the Big Bang start off with the deviations from flat spatial geometry being immeasurably small?
This is called the flatness problem of Big Bang cosmology.
Whatever physics preceded the Big Bang left the Universe in this state.
So the physics description of whatever happened before the Big Bang has to address the flatness problem.

Horizon problem

    The cosmic microwave background is the cooled remains of the radiation density from the radiation-dominated phase of the Big Bang.
Observations of the cosmic microwave background show that it is smooth in all directions, in other words, it is highly isotropic thermal radiation.
The temperature of this thermal radiation is 2.73° Kelvin.
The variations observed in this temperature across the night sky are very tiny.
Radiation can only be uniform if the photons have been mixed around a lot,
or thermalized, through particle collisions. This is a problem for the Big Bang model.
Particle collisions cannot move information faster than the speed of light.
But in the expanding Universe that we appear to live in, photons moving at the speed of light
cannot get from one side of the Universe to the other in time to account for this observed isotropy
in the thermal radiation.
The horizon size represents the distance a photon can travel as the Universe expands.
The size of rhe horizon of our Universe today is too small for the isotropy in the cosmic microwave background to have evolved naturally by thermalization.

Magnetic monopole problem

   Normally, magnets only come with two poles, North and South.
If one cuts a magnet in half, the result will not be one magnet with a North pole and one magnet with a South pole.
The result is two magnets, each of with its own North and South poles.
A magnetic monopole would be a magnet with only one magnetic pole.
But magnetic monopoles have never been seen? Why not?
This is different from electric charge, where we can separate an arrangement
of positive and negative electric charges so that only positive charge are in one collection and only negative charge in another.
    Particle theories like Grand Unified Theories and superstring
theory predict magnetic monopoles should exist, and relativity tells us that the Big Bang should have produced a lot of them, enough to make one hundred billion times the observed energy density of our Universe.
   But so far, physicists have been unable to find one.
We may have to go beyond the Big Bang model to look for an explanation of what might have happened when the Universe was very hot and very small.

The Missing Mass "Light" Problem

Possibilities
1) Low Mass Stars, Brown Dwarfs, Jupiter sized planets

2.) Rocks, Planets, Oort Junk

3.) Glumpy Gas

4.) Black Holes

5,) Massive Neutrinos
                a.) Low mass
                b). High Mass

6.) Monopoles

7.) ???

http://superstringtheory.com/

A Trip Through the Big Bang
From the beginning to the end

http://superstringtheory.com/cosmo/bang0.html