Transcript Document

Attempts to explain the nature of dark
energy -- How desperate can we get?
Ed Copeland
University of Sussex
1. Quintessence – tracking solutions.
2. Models (some inspired by particle physics).
3. K-essence v Quintessence
4. Evidence for evolving dark energy (enter WMAP) ?
5. Problems facing models of dark energy.
Cochin, India, Jan 5th, 2004
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Science Magazine -- Breakthrough of the year -Dec 2003
``Disks represent an aging and expanding
universe.
Work this year confirmed a bizarre story of
how the cosmos was born and what it is
made of.
Dark energy is the primary ingredient in a
universe whose expansion rate and age are
now known with unprecedented precision.’’
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Big result in cosmology: still there in 2004
Lum dist to over 170Type 1a SN -- Universe is accelerating from z of order 1.
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New sort of matter driving acceleration.-- Where from?
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The problem with the cosmological constant
Einstein (1917) -- static universe
with dust
Not easy to get rid of it, once universe found to be expanding.
Anything that contributes to energy density of vacuum
acts like a cosmological constant
Lorentz inv
or
Effective cosm const
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Age
Effective vac energy
Flat
Non-vac matter
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Hence:
Problem: expect <> of empty space to be much larger.
Consider summing zero-point energies of all normal modes
of some field of mass m up to wave number cut off >>m:
Planck scale:
But:
Must cancel to better than 118 decimal places.
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Even at QCD scale require 41 decimal places!
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Different approaches to Dark
Energy include amongst many:
A true cosmological constant -- if so, why this
value?
 Many possible cosmological constants (false
vacua)
 A time-dependent cosmological constant.
 Solid –dark energy such as arising from frustrated
network of domain walls.
 Time dependent solutions arising out of evolving
scalar fields -- Quintessence/K-essence.
 Modifications of Einstein gravity leading to
acceleration today.
Over 300 papers on archives since 1998 with
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dark energy in title.

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Key equations :
Friedmann eqn
Fluid eqn.
Acceleration eqn
Note:
where  8G
2
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Coincidence problem – why now?
If:
Universe dom by
Quintessence at:
Univ
accelerates at:
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Wetterich,
Tracker solutions
Peebles and Ratra,
Zlatev, Wang and Steinhardt

2

2
2
2
Scalar field:  :     V() ; p     V()
 2 2
H
(  B )
2

EoM:

 B   3 H  B


dV
  3H  
d

Intro:
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
x
6H
 V
y
3H

+ constraint:
2

H2 
(   B )
3
 1 dV
V d
 1 
d  1 


d   
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2
Eff eqn of state:

 
2
V

2
2x 2
 2
x  y2
 
 2
3H 2
 x 2  y2
Friedmann eqns and fluid eqns become:
x '  3x  


3 2 3
y  x 2x 2   1  x 2  y 2
2
2


3
3
y'   xy  y 2x 2   1  x 2  y 2
2
2
 2 
3H
2
 x 2  y2  1
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where
/


 d / d(ln a)
Note: 0     2 : 0    1
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Generic behaviour
Ng, Nunes and
Rosati
1. PE  KE
2. KE dom scalar
field energy den.
3. Const field.
4. Attractor solution:
almost const ratio
KE/PE.
5. PE dom.
Attractors make initial conditions less important
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Example of late time domination of energy
density -- 20 seconds left!
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Original Quintessence model
4 
M
V  

Find:
Peebles and Ratra;



 a
  i 
a
 i




3(1 w B )
1
 1 

( 2  )
and
Zlatev, Wang and Steinhardt
w 
w B  2
2
6
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Fine Tuning in Quintessence
Need to match energy density in
Quintessence field to current critical
energy density.
4 
M
V  

H
 47
4
 
 10 GeV

V
2 2
Find: y 
 
2
3H
2
2
c
2
0
2
V
2
so: H  2     0  M pl

2
Hence:
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A few models
1. Inverse polynomial – found in SUSY QCD - Binetruy
2. Multiple exponential potentials – SUGR and String
compactification.
V    V1  V2
 V01e
  1
Barreiro, EC,
Nunes
 V02 e
  2 
Enters two scaling regimes depends on lambda, one
tracking radiation and matter, second one dominating at
end. Must ensure do not violate nucleosynthesis
constraints.
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  20;   0.5
Scaling for wide range of i.c.
Fine tuning:
Mass:
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47
3
V0    10 GeV  (10 eV)
4
V0
33
m
 10 eV
2
M pl
4
Fifth
force !
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Quintessential Inflation – Peebles and Vilenkin
Same field provides both initial inflaton
and todays Quintessence – not tracker.
V    (  M )
4
4
M

1  M 
4
for   0
for   0
Reheating at end of inflation from grav particle production
Avoids need for minima in inflaton potential
14
Ford
  10 : 0  0.7    4 ; M  10 GeV,
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Need to be careful do not overproduce grav waves.
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Quintessential Axion -- Kim and Nilles
Linear combination of two axions together through hidden sector supergravity
breaking.
Light CDM axion (solve strong CP problem) with decay const
through hidden sector squark condensation:
Quintaxion (dark energy) with decay const as expected for
model independent axion of string theory:
Model works because of similarities in mass scales:
Scale of susy breaking and scale of QCD axion.
Scale of vacuum energy and mass of QCD axion.
Potential for quintaxion remains very flat, because of smallness
of hidden sector quark masses, ideal for Quintessence.
Quintessence mass protected through existence of global
symmetry associated with pseudo Nambu-Goldstone boson.
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Acceleration from new Gravitational Physics? Starobinski 1980,
Carroll et al 2003
Modify Einstein
Const curv vac
solutions:
de Sitter or Anti
de Sitter
Transform to EH
action:
Scalar field min coupled to gravity and non minimally
coupled to matter fields with potential:
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Cosmological solutions:
Eternal de Sitter -  just reaches Vmax
and stays there. Fine tuned and
unstable.
1.
2.
Power law inflation --  overshoots
Vmax , universe asymptotes with
wDE=-2/3.
3.
Future singularity--  doesn’t reach
Vmax , and evolves back towards =0.
Fine tuning needed so acceleration only recently:
~10-33eV
Also, any modification of Einstein-Hilbert action
needs to be consistent with classic solar system tests
of gravity. Not obvious these models are!
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Quintessence and M-theory -- where are the
realistic models?
`No go’ theorem: forbids cosmic acceleration in cosmological solutions
arising from compactification of pure SUGR models where internal space is timeindependent, non-singular compact manifold without boundary --[Gibbons]
Why? : 1.acceleration requires violation of strong energy condition.
i.e
2. Strong energy condition not violated by either 11D SUGR or any of the 10D
SUGR theories
3. For any compactification described above, if higher dim stress tensor satisfies
SEC then so does the lower dimensional stress tensor.
Must avoid no-go theorem by relaxing conditions of
the theorem.
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1. Drop condition that internal space is compact,
but not so realistic -- Townsend
2. Allow internal space to be time-dependent,
analogue of time-dependent scalar fields -- Lukas
et al, Kaloper et al, Townsend & Wohlfarth, Emparan & Garriga.
Compactified spaces are hyperbolic and lead to
cosmologies with transient accelerating phase. Four
dimensional picture, solutions correspond to bouncing
the radion field off its exponential potential.
Acceleration occurs at the turning point where the
radion stops and potential energy momentarily
dominates.
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Emparan &
Garriga
• Field starts at large positive values, with large kinetic energy.
• At turning point, energy is pot dominated and acceleration.
• Left picture, two positive potentials, right picture, sum of positive
and negative potentials.
Problems:
Difficult to obtain sustained period of inflation.
Current realistic potentials are too steep
These models have kinetic domination, not matter domination before entering
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accelerated phase.
However progress is being made to obtain inflation in
string theory:
Metastable de Sitter string vacua in TypeIIB string
theory, based on stable highly warped IIB
compactifications with NS and RR three-form fluxes.
[Kachru et al 2003]
There remain fine tuning issues in these brane models
concerning the method of volume stabilisation, the
warping of the internal space and the source of the
inflationary energy scale. [Kachru et al 2, 2003]
Still early days for inflation in string/M-theory.
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Dymanical approach to cosmological constant
[Mukohyama and Randall 2003]
with
R~0
and
Pot min at negative value.
As well as std kinetic term, non standard kinetic term-coeff
diverges at zero curvature.
Causes lowest energy state never to be achieved.
Instead cosmological constant stalls at or near zero.
Model stable under radiative corrections, leads to stable dynamics.
Still requires reheating
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Also issues over solar system tests as earlier.
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K-essence v Quintessence
K-essence -- scalar fields with non-canonical kinetic
terms. Advantage over Quintessence through solving the
coincidence model? -- Armendariz-Picon, Mukhanov, Steinhardt
Long period of perfect tracking, followed by
domination of dark energy triggered by transition to
matter domination -- an epoch during which structures
can form.
Eqn of state
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can be <-1
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Fine tuning in K-essence as well: -- Malquarti, EJC, Liddle
Not so clear that K-essence solves the coincidence problem. The basin of
attraction into the regime of tracker solutions is small compared to those
where it immediately goes into K-essence domination.
Shaded region is basin
of attraction for stable
tracker solution at
point R. All other
trajectories go to Kessence dom at point
K.
Based on K-essence
model astroph/0004134,
Armendariz-Picon et
al.
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Evidence for Dark Energy?
Enter CMBR:
0  m  
l peak
Provides clue. 1st angular peak
in power spectrum.
220

0
0.094
0.144
0 1.095
WMAP-Depends
on assumed priors
Tegmark et al 2003
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Concordat between SN1a and
CMBR
SN1a measures
(4 / 3) m  
CMB measures
0   m   
Almost
orthogonal
0  1 ; m  1/ 3 ;   2 / 3
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Consistent with 2df LSS survey and
clusters.
Efstathiou et al, astro-ph/0109152
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Evidence for dynamical dark
energy ?
Ideally look for evidence in evolution of
equation of state as go back in time.
1.
Precision CMB anisotropies – lots of models currently compatible.
2.
Combined LSS , SN1a and CMB data – tend to give wQ<-0.85  difficult to tell
from cosmological constant.
3.
Look for more SN1a – SNAP will find over 2000 – can then start to constrain
eqn of state.
4.
Constraining eqn of state with SZ cluster surveys – compute number of clusters
for given set of cosm parameters.
5.
Probing the Dark Energy with Quasar clustering – redshift distortions constrain
cosm parameters –sensitive to matter-lambda combination.
6.
Reconstruct eqn of state from observation – offers hope of method indep of
potentials – example is Statefinder method.
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Look for evidence in variation of fine structure constant.
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How much dark energy is there?
m    k 1
Tegmark et al.
astro-ph/0310723
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WMAP + SDSS: lots
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How much dark energy is there?
CMB
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Cmbgg OmOl
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How much dark energy is there?
CMB
Cmbgg OmOl
+
LSS
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WMAP + SDSS: lots
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How much dark energy is there?
CMB
Cmbgg OmOl
+
LSS
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How much dark energy is there?
CMB
Cmbgg OmOl
+
LSS
Note
impact of
SN 1a -- if
excluded
parameter
space
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opens up
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Dynamical evolution of w?
Weller and Albrecht; Kujat et al; Maor et al;
Gerke and Efstathiou, Kratochvil et al
SNAP as a
discriminator
Write:
N
w (z)   w i z i
i 0
or:
N
w (z)   w i ln(1  z) i
i 0
Evaluate magnitude difference for each model
and compare with Monte Carlo simulated data
sets.
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Evolution of Fine Structure
Constant Olive and Pospelov
Non-trivial coupling to emg:
Expand about current
value of field:
Lm  
1
B F () F F
4
B F ()  1   F  
1
 F2
2
Eff fine structure const depends on value of field
e 02
 () 
4B F ()
Claim from analysing
quasar absorption
spectra:
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
1
  F   ( F  2 2F ) 2

2

( z  0.5  3.5)  10 5

Webb et al
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EJC, Nunes,
Pospelov,
A way of constraining the eqn of state?
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Model independent approaches
Sahni et al; Gerke&Efstathiou; Bassett et al; Corasiniti & EC
Idea: certain features common to many
models, such as tracker behaviour 
characteristic time scales for most models.
w P (a )  F1f r (a )  F2 f m (a )  F3
1
f r , m (a ) 
1 e
Constants: a c ; 
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
a  a cr ,m
 r ,m
Scale factor at transition and
width of transition to and from
tracker regimes.
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Actual
Corasiniti &EC
Best fit
1. Allows for case where have rapid change
2. Physically motivated
3. Depends on tracker properties – otherwise model
indep.
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Probing Quintessence with the cmb through the ISW
effect-- Corasaniti et al
Use parameterisation of w(z) to test whether we can see difference with Lambda CDM
Rapid
transition
Need late
rapid
transition to
differentiate
Slow
transition
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Probing Quintessence with WMAP and SN1a -- Kunz et al
2D Likelihood shows that
today w very close to - 1,
as expected.
This is not the same
though as saying it
always had to be -1.
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Using
Black dots:
Red dots:
Pointing
towards
lambda if
sigma8 turns
out to be large.
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Nature of the dark energy
CMB
Cmbgg OmOl
+
LSS
Recent claim
that w<-1
preferred with
evolution from
w=0.
Alam et al.
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Tegmark et al.astro-ph/0310723
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Example showing rapid evolution of w(z) for different
matter contributions, assuming no priors on remaining
parameters, in particular allowing w<-1, and allowing
violtaion of weak energy condition. Note claimed best fit
is for w<-1! [Alam et al, 2003]
What does it mean for cosmology to have unstable
phantom energy (w<-1)? How do we then include
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cosmological perturbations ?
Summary
•Observations transforming field, especially CMBR and LSS.
Constraining the cosmological parameters, even before Planck arrives
on the scene.
•Why is the universe inflating today – can particle physics provide an
answer through scaling solutions – see it through time varying
constants?
•Brane inspired cosmology – so much going on in this area. Not
discussed here [i.e. self tuning mechanisms -- Nilles et al].
•New Gravitational Physics [1/R terms in Action -- Carroll et al]. Not
discussed here.
•Lots of models of dark energy but may yet prove too difficult to
separate one from another such as cosmological const – need to try
though!
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•Finally
-- could we all be wrong and we do not need a lambda term? --