Theoretical Explanations for Cosmic...

transcript

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)

d(!c2r3a3) = !pd(r3a3)

p = wc2! =" ! # 1a3(1+w)

• Newton’s second law:

a(t)r = !G

!43!r3a3"

a= !4!G

d(!c2r3a3) = !pd(r3a3)

p = wc2! =" ! # 1a3(1+w)

• Newton’s second law:Correction due to general relativity

a(t)r = !G

!43!r3a3"

a= !4!G

3!" + 3pc!2

d(!c2r3a3) = !pd(r3a3)

p = wc2! =" ! # 1a3(1+w)

• Newton’s second law:Correction due to general relativity

a(t)r = !G

!43!r3a3"

a= !4!G

3!" + 3pc!2

"• Acceleration if p < !1

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

a3(1+w)+

1 = !M + !! + !R + !k

a2 =8!G

3"a2 ! k, k = 0,±1

• Rewrite as:1

a3(1+w)+

1 = !M + !! + !R + !k

• Cosmic microwave background (standard yardstick)

!R ! 10!4, |!k| " 0.05

a2 =8!G

3"a2 ! k, k = 0,±1

• Rewrite as:1

a3(1+w)+

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.)

No Big Bang

1 2 0 1 2 3

expands forever

closed

recollapses eventually

Supernovae

Clusters

Knop et al. (2003)Spergel et al. (2003)Allen et al. (2002)

Supernova Cosmology Project

Evidence for acceleration (cont.)

–1.5

–0.5

–1.5

–0.5

–1.5

–0.5

0 0.5–2

2dFGRS

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)+

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.

• 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!

d4x!"g

16!G+ Smatter[gµ! ,!matter]

• 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!

d4x!"g

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.

Example:

d4x!"g

16!G+ Smatter[e!(!)gµ" ,!matter]"

!d4x!"g

"12(#")2 " V (")

gµ" $ e!(!)gµ" , " $ f("),

d4x!"g

"A(")R16!G

" 12(#")2 " V (")

#+ Smatter[gµ" ,!matter]

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)

d4x!"g

16!G+ Smatter[e!(!)gµ" ,!matter]"

!d4x!"g

"12(#")2 " V (")

gµ" $ e!(!)gµ" , " $ f("),

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!(!) = !/!

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

Theoretical Explanations for Cosmic...

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