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Brane World
Cosmological ideas from string theory
Cosmology
String (M) theory
Particle physics
Branes and brane world
Problems in quantum gravity
Holography
Cosmological Questions
• What are space and time?
• Why are there 3 spatial directions and 1 time?
• How did the Universe begin?
• How will the Universe end?
• Why does it contain the sorts of matter it does?
• How does that matter interact and produce galaxies etc?
Very ambitious! – Physics has been very
successful though so can begin to address
these issues
The Big Bang
In General Relativity space and
time are dynamic – we believe we
live in an expanding Universe
• Explosion! - galaxies are moving apart
• Flash – universe is full of remnant radiation
• Smoke and Ash – correctly predict the abundances of
H, He, Be…
Singular
At very early times the whole Universe and
contents squeezed into a tiny volume…
Beginning
Describe as a hot, dense soup of the
fundamental building blocks of nature
Critical
Ending
Observing the expansion we find it is
slowing due to the gravitational
attraction of matter
It seems to be balanced between expanding
forever and eventual collapse…. But then
95% of matter must be new DARK
MATTER, and DARK ENERGY
We need to know some particle physics!
The Particle World
Forces
• Electromagnetism
• Strong nuclear
• Weak nuclear
• Gravity
Particles
6 quarks
3 electrons
3 neutrinos
Quarks and Leptons
Quarks and electrons
aren’t dark
Neutrinos are too
light (for their
abundance) to be
dark matter
We have not yet
found a dark
matter particle
Quantum Rules of Motion
Energy comes in lumps
E=hf
Fields can look like particles
The photon is the quantum of the electromagnetic field/ light
Quantum Dynamics
The quantum in
some sense travels
by both paths….
There is an uncertainty in the position and momentum of the quantum
Heisenberg’s Uncertainty Principle
Or equally
x
t
p >h
E >h
The Quantum Vacuum
E
t >h
The vacuum can borrow energy for short periods
E = mc 2
The borrowed energy can be used to create particles
(You can’t just create an electron because of charge
conservation - but can create electron positron pair)
The quantum vacuum is a seething mass of particles appearing and
disappearing constantly….
How Can You Tell?
The “virtual” particle
pairs interfere in
electron scattering
processes.
The effective charge
seen in two electron
scattering depends on
the separation of the
electrons.
The Higgs Boson
In the “Standard Model” the origin of mass is
addressed using a mechanism named after the
British physicist Peter Higgs.
This predicts a spinless particle: Higgs boson
According to Higgs,
space is filled with a
new type of field
analagous to
magnetic or electric
fields…
LHC – Higgs Hunting
Observed exclusion mass
range: 127-600 GeV
Mh = 124-126 GeV ??
Quantum Gravity
If the vacuum is full of all this stuff (dark energy) shouldn’t
we be pulled gravitationally by it?
Since it is uniformily distributed there is no net pull (equal
space to all sides)
But General Relativity says the energy should uniformily
curve space-time… the Universe should be the size of a
grapefruit!!
There’s something big we don’t
understand about quantum gravity
Gravity is so weak that we’ve never measured
it’s effects between individual particles or on
distance scales smaller than 0.1mm!
Gravity is different to the other forces – it’s only attractive…
In General Relativity this shows up in that gravitational
waves have different polarizations to electromagnetic waves
What fundamental theory can encompass both types of fields?
String Theory
String theory unifies gravity and other forces
String theory is A quantum theory of gravity.. Is it THE quantum
theory of gravity? - entering realm of speculation!
Extra Dimensions
Surprisingly the mathematics of string theory only makes
sense in 9 spatial dimensions and 1 time dimension!
A prediction…. But wrong!!
Compactification
We can imagine a space where
directions are curled up
We study A string in this space
not ALL the strings that make
the space…. Why are 6
dimensions compact… by what
mechanism? UNKNOWN!
Shrinking Dimensions Away
Remember particles are really quanta of
fields… only very special field
configurations make sense on a compact
dimension
Energy = E, 2E, 3E, 4E, 5E,….
As we shrink the circumference away E grows – eventually
you can’t make the extra states… it’s gone!
19
Standard string lore – E is 10 proton mass
Wrapping Strings
Closed strings can do something new in a compact space
Wrapping modes have energies
E’, 2E’, 3E’, 4E’, 5E’…
As we shrink the circumference away
these states are very low energy
Dual Spatial
Directions
If we “confuse” winding modes and
kinetic modes we can see a new
dimension appear as another disappears!
Membranes
Only closed strings see the new direction… not open strings…
Electromagnetic
particles live on a
sub-space or
“brane”
Gravitons live in a higher
dimension “bulk”
“Existence proof” for
such a world
Could Our Universe Be A Brane?
S
U
2p R
The strength of gravity is
determined by the number of
spatial dimensions (gravitons
spread out around mass)
F=GMm
r2
D=3+1
But…. we don’t know anything about gravity on length scales
below 0.1mm… R could = 0.1mm… and we wouldn’t know it!
If so we’ve miscalculated the strength of gravity (G) – it could
become strong in our particle accelerators at any new energy!!
Matter Loss To The Bulk
Our Universe will slowly lose matter into the bulk…
In particle physics
gravity is too weak to
ever see these events
In fact the energy loss
from the centre of stars
is too low to see too!
Other Branes
Why should there be only one brane in the higher dimension
spacetime?
There could be entire Universes only mm away!
W
E US
N
The matter on the other
brane will only interact
with our world
gravitationally – it’s
dark matter….
Until we can produce high energy gravitons that are strongly
interacting there’s little way to directly probe this idea though
Brane Collisions
There’s no reason branes should be static in the extra
dimensions…. So they could collide!
This would be catastrophic!
Huge amounts of energy
would be dumped into our
Universe….
Could that have triggered the currently observed expansion of the
Universe??!!
Which is all good fun…. BUT
String theory does not solve the cosmological constant
problem… the vacuum is now full of quantum strings… and
ought to roll up into a ball…
Roughly 120 orders of magnitude wrong!!!!
The Landscape
There are billions and billions of
ways to compactify six dimensions
Each choice gives a different
Universe… and all are possible
in string theory.
Inflation &/or many worlds QM means they can all exist at once!
The Anthropic Principle
When the vacuum energy is computed in each Universe there are
many contributions that can cancel each other…
To get
is very unlikely but in an infinite set of Universes there will be a
few….
Only these large, open Universes can support life… so any life will
naturally see a small Cosmological Constant!
Holography
General Relativity predicts there should be objects whose
gravitational attraction is enough to stop even light escaping
– BLACK HOLES
‘tHooft argued that any
information dropped into a
black hole must be
• lost to our Universe
• spread over the surface
If the surface can contain all the information of the contents
the real theory of the Universe must be 2 + 1 dimensional!
Strong Nuclear Force is Holographic
String theory grew out of
attempt to describe confined
quarks
The resulting string theory has recently been discovered to
describe gravity in 4+1 dimensions!
Is the real world holographic??
If there is only as much information in Universe as on surface
problem of over density of vacuum material may be solved…??
Overview
• The large scale structure of Universe was determined by
particle interactions just after the Big Bang
• Our theories of particles don’t fit with theories of gravity
• String Theory is an attempt to construct a sensible theory
of both
• We are realizing it predicts wild possibilities
• Extra dimensions and other Universes
• Or are we a hologram in fewer dimensions?
• Many exciting possibilities but very hard to
experimentally test because gravity is very very weak….
M Theory
If you study strings at scales where they look like particles you
get a theory of particles… can construct these independently
10 dimensional theories
naturally map on to strings
There is an 11d theory that we
now realize naturally maps onto
membranes
Compactifying gives string theory – fundamentally 11d?