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Theoretical Explanations for Cosmic Acceleration Physics Colloquium, University of Guelph, 17 October 2006 Eanna Flanagan, Cornell
Theoretical Explanations for
Cosmic Acceleration
Physics Colloquium, University of Guelph, 17 October 2006
Eanna Flanagan, Cornell
Recent observations show that the expansion of the Universe is accelerating, which according to general relativity implies the existence of a form of matter with negative pressure (dark energy).
• Negative pressure in general relativity
• Acceleration: observational pillars
• Why the new physics required is puzzling
• Survey of (i) frameworks (ii) models (iii) theoretical problems (iv) potential new observational channels
• Can we avoid dark energy by modifying gravity?
Outline
The Hot Big Bang
Image credit: Wayne Hu and Martin White
Constituents of the Universe today
Dark matter: we don’t know what this is, but there are several well-motivated ideas (particles).
Dark energy: we don’t know what this is (not particles), many ideas but few compelling ones.
Observations show that on scales larger than about 10 million light years, the Universe is homogeneous and isotropic
The Large-scale Universe
Image credit: Stephen Landy
Observations show that on scales larger than about 10 million light years, the Universe is homogeneous and isotropic
The Large-scale Universe
Fluctuations in the temperature of the 3K cosmic microwave background, 1 in 100,000
Characterizing sources of gravity
Characterizing sources of gravity (cont)Examples:
Dynamics of the Expanding Universe
• Uniform expansion with scale factor a(t)
• Concentric spherical shells labeled by r, size a(t)r
• First law of thermodynamics:dE = !pdV
d(!c2r3a3) = !pd(r3a3)
p = wc2! =" ! # 1a3(1+w)
Dynamics of the Expanding Universe
• Uniform expansion with scale factor a(t)
• Concentric spherical shells labeled by r, size a(t)r
• First law of thermodynamics:dE = !pdV
d(!c2r3a3) = !pd(r3a3)
p = wc2! =" ! # 1a3(1+w)
• Newton’s second law:
a(t)r = !G
!43!r3a3"
"
[ra]2
a
a= !4!G
3[" ]
Dynamics of the Expanding Universe
• Uniform expansion with scale factor a(t)
• Concentric spherical shells labeled by r, size a(t)r
• First law of thermodynamics:dE = !pdV
d(!c2r3a3) = !pd(r3a3)
p = wc2! =" ! # 1a3(1+w)
• Newton’s second law:Correction due to general relativity
a(t)r = !G
!43!r3a3"
"
[ra]2
a
a= !4!G
3!" + 3pc!2
"
Dynamics of the Expanding Universe
• Uniform expansion with scale factor a(t)
• Concentric spherical shells labeled by r, size a(t)r
• First law of thermodynamics:dE = !pdV
d(!c2r3a3) = !pd(r3a3)
p = wc2! =" ! # 1a3(1+w)
• Newton’s second law:Correction due to general relativity
a(t)r = !G
!43!r3a3"
"
[ra]2
a
a= !4!G
3!" + 3pc!2
"• Acceleration if p < !1
3c2!
Analog of dark energy
Evidence for acceleration • By combining first law of thermodynamics and acceleration equation:
a2 =8!G
3"a2 ! k, k = 0,±1
• Rewrite as:1
H20
a2
a2=
!M
a3+
!!
a3(1+w)+
!R
a4+
!k
a2,
1 = !M + !! + !R + !k
Evidence for acceleration • By combining first law of thermodynamics and acceleration equation:
a2 =8!G
3"a2 ! k, k = 0,±1
• Rewrite as:1
H20
a2
a2=
!M
a3+
!!
a3(1+w)+
!R
a4+
!k
a2,
1 = !M + !! + !R + !k
• Cosmic microwave background (standard yardstick)
!R ! 10!4, |!k| " 0.05
Evidence for acceleration • By combining first law of thermodynamics and acceleration equation:
a2 =8!G
3"a2 ! k, k = 0,±1
• Rewrite as:1
H20
a2
a2=
!M
a3+
!!
a3(1+w)+
!R
a4+
!k
a2,
1 = !M + !! + !R + !k
• Cosmic microwave background (standard yardstick)
!R ! 10!4, |!k| " 0.05
• Infer a(t) from brightness and redshifts of standard candles (Type Ia supernova)
Evidence for acceleration (cont.)
Evidence for acceleration (cont.)
Evidence for acceleration (cont.)
No Big Bang
1 2 0 1 2 3
expands forever
-1
0
1
2
3
2
3
closed
recollapses eventually
Supernovae
CMB
Clusters
open
flat
Knop et al. (2003)Spergel et al. (2003)Allen et al. (2002)
Supernova Cosmology Project
!
!"
M
Evidence for acceleration (cont.)
!M
–1.5
–1
–0.5
0
–1.5
–1
–0.5
0
–1.5
–1
–0.5
0
0 0.5–2
w
2dFGRS
w
w
Combined
With limits from;2dFGRS (Hawkins et al. 2002)and CMB (Bennet et al. 2003,� � Spergel et al. 2003)
Supernova Cosmology ProjectKnop et al. (2003)
Assuming constant w
w = –1.05 (statistical)+0.15–0.20
–0.09 (systematic)+
SNe
CMB
Simplest model: Cosmological constant
• The case , constant energy density • Puzzle: expect quantum loops to generate a much larger
energy density, • Unknown higher energy physics can in principle cancel out this
contribution, but it requires exquisite fine tuning.• String theory predicts a multiverse with huge number of
different vacua, each with its own . Anthropic principle could explain smallness of our
• Problem: life might still evolve if were 1000 times larger.
w = !1 !! ! (10!3 eV)4
!! ! E4cuto"
!!
!!
!!
• Puzzle: The Universe has expanded by 35 orders of magnitude. Why are dark energy and matter comparable right now? Seems to require fine tuning of initial conditions.
Dark energy versus time
Dynamical models of dark energy
• Typically do not address cosmological constant problem• Can address the cosmic coincidence problem• Typically invoke new fundamental or effective fields
S = !!
d4x"!g
"12(#!)2 + V (!)
#
! =12!2 + V (!), p =
12!2 ! V (!)
!2 ! V (!) =" p # $!
• Like inflation models, but at much lower energy scale• Problem: expect loop corrections to spoil flatness of potential
and small mass of scalar field• One solution: scalar field is the size of compact extra
dimensions (radion), protected by diffeomorphism invariance
Quintessence:
Modified Gravity vs. Dark Energy
• Evidence for dark energy presumes validity of general relativity. Perhaps, instead, general relativity is modified on large scales.
Modified Gravity vs. Dark Energy
• Evidence for dark energy presumes validity of general relativity. Perhaps, instead, general relativity is modified on large scales.
• How do we decide if a given a modification of the laws of physics involves a modification of gravity? Perhaps ask which side of the Einstein equation is modified, or which term in action is modified:
Gµ! = 8!GTµ!
S =!
d4x!"g
R
16!G+ Smatter[gµ! ,!matter]
Modified Gravity vs. Dark Energy
• Evidence for dark energy presumes validity of general relativity. Perhaps, instead, general relativity is modified on large scales.
• How do we decide if a given a modification of the laws of physics involves a modification of gravity? Perhaps ask which side of the Einstein equation is modified, or which term in action is modified:
Gµ! = 8!GTµ!
S =!
d4x!"g
R
16!G+ Smatter[gµ! ,!matter]
• This criterion is in fact ambiguous. Instead, we should ask if there are universal, long-range, 5th forces between macroscopic bodies.
Modified Gravity vs. Dark Energy
Example:
S =!
d4x!"g
R
16!G+ Smatter[e!(!)gµ" ,!matter]"
!d4x!"g
"12(#")2 " V (")
#
gµ" $ e!(!)gµ" , " $ f("),
S =!
d4x!"g
"A(")R16!G
" 12(#")2 " V (")
#+ Smatter[gµ" ,!matter]
Modified Gravity vs. Dark Energy
Example:
• In this theory, scalar field both acts like quintessence and mediates 5th forces.
• This mixed character is generic, since loop corrections generate matter couplings.
• Solar system tests of gravity (light bending, perihelion precession) require
• These theories can arise as effective description of extra dimensions• Other possible observational signatures: time evolution of effective
Newton’s constant (fine structure constant for generalized models)
S =!
d4x!"g
R
16!G+ Smatter[e!(!)gµ" ,!matter]"
!d4x!"g
"12(#")2 " V (")
#
gµ" $ e!(!)gµ" , " $ f("),
S =!
d4x!"g
"A(")R16!G
" 12(#")2 " V (")
#+ Smatter[gµ" ,!matter]
|!!(!)| ! 10"2 if V !!(!)! (A.U.)"2
Modifying gravitational action: a catalog
• Are there successful models that are not “mostly quintessence”?
S[gµ! ,!m] =!
d4x!"g
f(R)16!G
+ Sm[gµ! ,!m]
‣ Equivalent to last model with , ruled out by Solar System!(!) = !/!
6
S[gµ! ,!m] =!
d4x!"g
f(R,Rµ!Rµ! , Rµ!"#Rµ!"#)16!G
+ Sm[gµ! ,!m]
‣ Problems with ghosts/acausality
Modifying gravitational action: a catalog
‣ Ruled out; predicts modifications of particle physics at energy scale
S[gµ! ,!µ,!m] =!
d4x"#g
f(R)16!G
+ Sm[gµ! ,!m]
!!
H0Mp ! 10!3 eV
S[gµ! ,!µ,!m] =!
d4x"#g
f(R, R)16!G
+ Sm[gµ! ,!m]
‣ Some successful models. Equivalent to tensor bi-scalar model similar to the mixed models discussed earlier.
• Some interesting models based on extra dimensions do not have a simple effective 4-dimensional description, eg DGP model
• Probes of the expansion history of the Universe
• Probes of the growth of perturbations
• Precision tests of general relativity
• Specific observational windows (i) Supernovae (ii) Measurements of numbers of clusters using CMBR (iii) Weak gravitational lensing (iv) Baryon acoustic oscillations
Observational probes of dark energy
Image credit: Max Tegmark
• The discovery of the acceleration of the Universe requires new fundamental physics
• The dark energy might be a cosmological constant. We may never be able to explain its tiny size.
• The dark energy may be dynamical. Potential observational windows include (i) Probing the expansion history of the Universe (ii) Probing the growth of structure in the Universe (iii) High precision tests of general relativity (iv) Measurements of time evolution in fundamental constants of nature.
Conclusions
