Transcript ppt

Dark Energy, the Electroweak Vacua,
and Collider Phenomenology
Eric Greenwood, Evan Halstead, Robert Poltis, and
Dejan Stojkovic
arXiv:0810.5343 [hep-ph]
Buffalo-Case-Cornell-Syracuse Workshop
On Cosmology and Astro-particle Physics
December 8-9, 2008
Motivation
•
95% of the energy content of
universe is still a mystery to us
•
The majority of the universe is
in the form of dark energy
•
Most proposals to address this
problem involve the
introduction of a new scalar
field
•
We expect new physics to kick
in around the TeV scale
Introduction
•
The current accelerated expansion of the
universe may be driven by an already
“known” field-the Standard Model Higgs
field.
•
We do not address the cosmological
constant problem, but instead propose a
mechanism that might explain the
accelerated expansion of the universe.
•
We will modify the Standard Model Higgs potential
by adding dimension 6 and 8 (non-renormalizable)
operators.
Description of Model
FRetain the standard 2nd order electroweak phase
transition
FAllow the formation of two new symmetric vacua
after the 2nd order electroweak phase transition is
completed
FThe newer vacua eventually become the true
vacua (global minima) of the potential
FTunneling probability from the false (old) vacua to
the true (new) vacua must be sufficiently suppressed
Our potential is written as
V ( ) 
3
16
 
8
2
8
 
6
1
4
 
4

2
2
  Vo
2
This potential may be rewritten as
V ( ) 
3


16
2
 
2 2
1

2

2 2
2

      Vo '
3 3
o 1 2
2
FWe allow non-renormalizable operators to be included,
as the Standard Model is generally accepted as an effective
low-energy theory.
FThe εo term introduces a controlled fine tuning of V(),
similar to Stojkovic, Starkman, and Matsuo (PRD, 2008).
V ( ) 
3


16
2
 
2 2
1

2

2 2
2

      Vo '
3 3
o 1 2
2
•
To account for finite temperature effects, we add
a thermal mass to the potential.
•
We choose to have all temperature effects be
contained in our fine tuning parameter ε, so that
cT 2
 (T )   o  3 3
1 2
•
2
Tcrit

 o1323
At a critical temperature,
c , the
temperature-dependant parameter ε(Tcrit) = 0.
the vacua at ±1 and ±2 are degenerate.
Temperature Evolution of V()
V
0.04
T>>Tcrit
T>>Tcrit
0.03
0.02
T=Tcrit
0.01
T=0
TeV
0.2
0.4
0.6
0.8
Tunneling Rate
•
If the temperature of the universe today is below the
critical temperature, then we live in a false (local, but not
global) vacuum.
•
Because a lower energy state exists, every point in the
universe will eventually tunnel to the lower energy state.
F What is the lifetime of such
a meta-stable state?
•
The semi-classical transition
probability per unit space-time
volume is given by
V
0.014
0.012
0.01
0.008
0.006
  Ae
 SE
You are
here
0.004
0.002
TeV
0.2
0.4
0.6
0.8
Tunneling Rate
 our universe has a four volume ~ tHubble4
 Therefore, we require
Γ tHubble4 1
 Using tHubble~1010 years, we find that the above
requirement is satisfied if εo ≤ 0.012 TeV-4.
FNotice that because today we reside in the
=1 vacuum, we set V(1) = (10-3 eV)4. This
is the only fine tuned value in our model.
Tunneling Rate
The transition rate is small in the current (cold)
universe. But how does the transition rate behave
in the high temperature limit?
The temperature dependence of the Euclidean
action affects the transition probability as

const . 

 ~ exp 
2
 T T  
Therefore in the high temperature limit, the
transition rate to the 1 vacuum state is large.
Tunneling Rate
This high temperature
expression is valid until
just below the critical
temperature, which
places a stronger
constraint on the fine
tuning-parameter.
εo ~ 0.005 TeV-4
Experimental Signatures
Because the Higgs couples to other
Standard Model particles, it is possible
to test this model in colliders.
Vachaspati (PRD, 2004)
showed that given a set of
eigenvalues, it is possible to
use the inverse scattering
method to reconstruct the
original potential.
Field Excitations
V
Exciting the field locally only
probes the local structure of
the potential.
0.014
0.012
0.01
0.008
0.006
0.004
But if we excite the field that
extrapolates between the
vacua, it is possible to learn
about the overall shape of the
potential.
0.002
TeV
0.2
0.4
0.6
Physically, these kink solutions correspond to
closed domain walls…bubbles of true vacuum!
0.8
Reconstruction Of the Field Using
the Inverse Scattering Method
Theory written in standard
form
Schrödinger equation
determines the excitation
spectrum
Zero mode is related to the
shape of the potential
2
1
L      V  
2
 d2



V
''

x
 o   n  n n
 dx 2


where o(x) is the kink solution
do
o 
  2V o 
dx
(Bogomol’nyi equation)
Reconstruction Of the Field Using
the Inverse Scattering Method
Assume we know the spectrum of energy eigenvalues {ωn2}:
 z  U n1zn   z
''
n
2
n n
o 
V o  
2
2 z N2
x  o 
With the proper eigenvalues
(ωn’s), it is possible to
reconstruct an order 8 potential
and obtain the constant terms of
our model (εo, λ’s, etc…).
2
'
 z 
 z 
U n           n2
 zn 
 zn 
'
n

zN
'
n
Bubble Nucleation At the LHC
At the LHC, bubbles of true vacuum
may be created. Each Bubble has
two competing terms:
a volume term which tends to
make the bubble expand
surface tension term which tends
to make the bubble collapse.
FA critical bubble (volume term balances the
surface tension term) requires many individual
excitations coherently supposed.
Nquanta > 109(1/εo)3
Bubble Nucleation At the LHC
•
The creation of a critical bubble is
enormously suppressed.
•
We may still produce smaller
excitations, or sub-critical bubbles.
These sub-critical bubbles will
collapse under their own surface
tension.
Nquanta > 109(1/εo)3
•
These bubbles will most likely be produced in a highly
excited state (not in a spherically symmetric ground state).
•
The decay of these bubbles will give us the energy
eigenvalues of the potential.
Future of the Universe I: V  0
If the difference between the two vacua is
small (V  0, or equivalently, εo  0), the
bubble nucleation rate will be very small.
V
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0.2
0.4
V
TeV
0.6
Because bubbles nucleate slowly, the expansion of the
universe tends to dilute regions of true vacuum, and the
majority of space remains in the false vacuum.
End Result: A few regions of true vacuum in
an inflating sea of false vacuum.
0.8
Future of the Universe II: V Is “Large”
If the difference between the two vacua
is not fine tuned, the phase transition
may be completed faster than the
expansion can dilute regions of true
vacuum.
Bubbles of true vacuum percolate
throughout the entire universe.
Outside the bubbles the Higgs field has a vev of 1, while on
the inside the Higgs field has a vev of 2.
End Result: The entire universe ends up in the
true vacuum state. Standard Model particles have
a different mass than they have today. N
Future of the Universe III:
Phase Transition To Happen Soon
 If the difference between the two vacua
takes on (perhaps) the most generic
value of εo ~ 0.01 TeV-4, then the phase
transition will happen soon.
 Because the characteristic energy scale is of the order
100 GeV, and by our requirement that V(1) ~ 10-3 eV4
implies that the true vacuum at  = 2 is deeply AdS.
 Any initial perturbations grow rapidly in the shrinking
space-time.
End Result: We end up in a black hole in
a collapsing universe.
Conclusions
 A nice feature of this model is that we do not need to
introduce a new field decoupled from the rest of the
universe.
 Unlike many other theories, we can probe the global
structure of the potential, opposed to only the local
structure of the potential.
 We expect new physics to kick in close to the TeV
scale. Our model does not solve the cosmological
constant problem, but addresses the dark energy
problem.
note an interesting numerology:
(TeV/MPL)TeV≈10-3 eV hints towards a possible
gravitational origin of this small number.
Thank You
Photo credits
Wally Pacholka
Chandra.harvard.edu
Apod-NASA
New Scientist
Extra Slides
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