Download McGill String Cosmology Workshop April 2005

Topics of Branes Interaction
Lev Kofman, CITA
Workshop on String Gas Cosmology
McGill 04/30/05
ESP
Basic Idea
is closely related to the theory of preheating after inflation
Consider two interacting moduli with potential
It can be represented by two intersecting
valleys.
Suppose the field c moves to the right with
velocity
. Can it create particles c
?
Nonadiabaticity condition:
Resonant Preheating in Chaotic Inflation
How does this process occur?
Uncertainty relations imply that during this time one can have particle
production with momenta
Number density of produced particles
Each of these particles has energy g|φ| (for large φ), so the energy
density is
When the field φ passes the (red) nonadiabaticity region near the point of
enhanced symmetry, it created particles χ with energy density proportional to φ.
Therefore the rolling field slows down and stops at the point when
Then the field falls down and reaches the nonadiabaticity region again…
V
φ
When the field passes the nonadiabaticity region again, the number of
particles χ (approximately) doubles, and the potential becomes two times
more steep. As a result, the field becomes trapped at distance that is two
times smaller than before.
V
φ
Each time the field passes the point of extended symmetry, the trapping
distance decreases twice, so the field exponentially rapidly falls to φ = 0. At
this point both fields φ and
χ
become massless.
V
3
4
2
1
φ
Trapping of a real scalar field
Trapping of a complex scalar field
In an expanding universe, momentum decreases, the size of the orbit
rapidly shrinks to zero, and the field falls to the enhanced symmetry
point.
String Theory Landscape
Finding the way in the landscape
•
Anthropic Principle: Love it or hate it but use it
•
Vacua counting:
Know where you can go
•
Moduli trapping:
Live in the most beautiful valleys
Beauty is Attractive
hep-th/0403001
• Quantum effects lead to particle production which
result in moduli trapping near enhanced symmetry
points
• These effects are stronger near the points with
greater symmetry, where many particles become
massless
• This may explain why we live in a state with a large
number of light particles and (spontaneously broken)
symmetries
Interesting features of moduli trapping:
• ESP with greater symmetry (with larger number of
fields becoming massless at these points) are more
attractive
• Symmetry may grow step by step
Example:
Anthropic principle says that we
can live only in those parts of
the universe where we can
survive
Moduli trapping is a dynamical
mechanism which may help us
to find places where we can
live well
Tachyonic Preheating in Hybrid Inflation
l
movie
Tachyonic Preheating
Rolling Tachyon