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David F . Mota
Institute of Theoretical Astrophysics University of Oslo 2015
Basic Observational Requirements
- f Modifying Gravity
Dark Energy The Modified Gravity Perspective Part II: Beyond GR - - PowerPoint PPT Presentation
Dark Energy The Modified Gravity Perspective Part II: Beyond GR - - PowerPoint PPT Presentation
Dark Energy The Modified Gravity Perspective Part II: Beyond GR with Screening David F . Mota Institute of Theoretical Astrophysics University of Oslo 2015 Basic Observational Requirements of Modifying Gravity Modified Gravity as
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µν µν µν
πGT R g R 8 2 1 = −
gravity matter
+ ) (
µν
g F ) ( 8 φ π
µν
GT +
Modifying Matter Sector
(dark matter / dark energy)
Modifying Gravity Sector
Modified Gravity as alternative to Dark Energy The need of screening Mechanisms
(assuming homogeneity and isotropy)
Often equivalent via conformal or disformal transformations
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Scalar-Tensor Theories
Extra scalar degree of freedom (fifth force)
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E.g. scalar-tensor theory - new scalar graviton Cassini: Theory is GR on local scales
What do local tests mean?
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ln A(j) j b0 a0 curvature slope j0
ln A(j) = a0 (j–j0) + 1 b0 (j–j0)2 + …
2
j matter j j j j j ...
Geff = G ( 1 + a0
2 )
gPPN– 1 a0
2
bPPN– 1 a0
2 b0
a0 a0 b0 a0 a0
scalar graviton
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- 4
- 2
2 4 6
b0
General Relativity
|a0|
0.025 0.030 0.035 0.010 0.015 0.020 0.005
LLR perihelion shift VLBI LLR
j matter j matter j
Cassini
S = 16 p G Ú -g {R - 2 ( µj)
2 } + Smatter[matter , gµn A2(j) gµn] 1
Tensor-scalar theories
spin 2 spin 0 physical metric
* * *
Vertical axis (b0 = 0) : Jordan–Fierz–Brans–Dicke theory a0 = 2 wBD + 3 Horizontal axis (a0 = 0) : perturbatively equivalent to G.R.
2 1
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10-3cm 1AU 1kpc 1Mpc 1000Mpc
extra dimensions?
GR
MOND? Modified Gravity?
Extremely tight constraints on Modified Gravity from experiments at small scales!
Cassini Probe Lunar Laser Range
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( )
...
3 2 4
+ +
∫
R R + R g x d
✓ f(R) models are simple ✓ easy to produce acceleration (first inflationary model) ✓ high-energy corrections to gravity likely to introduce higher-order terms ✓ particular case of scalar-tensor and extra-dimensional theory
( )
[ ]
matter
L + R f g x d
4
∫
Modified Gravity as Dark Energy
Negative Pressure!
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Supernovae Supernovae + Large Scale Structures Supernovae + Large Scale Structures + CMBR Supernovae + Large Scale Structures + CMBR + Baryon Oscillations
Decelerated Expansion Accelerated Expansion
PLANCK SDSS High-Z Supernovae Search Team
Almost LCDM!
Large Scale Structure Formation: deviations from GR must be small
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Laboratory Bounds (Coupling to ordinary matter) Solar System Bounds (Modified Gravity)
Amendola PRD (1999)
Cosmological Bounds (Coupling to Dark Matter)
How to Modify Gravity and evade constraints?
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Screening Mechanisms!
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Scalar-Tensor Theories
Extra scalar degree of freedom (fifth force)
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Quantum Picture: Yukawa Interaction
an interaction between a scalar field ϕ and a Dirac field ψ of the type ϕ ψ ψ
g g
mass of the scalar boson
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Yukawa Potential
ϕ ψ ψ
g g
Feynman amplitude of the diagram
mass of the scalar boson
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Classical Picture: Fifth Force
Yukawa potential is equivalent to a scalar field profile (think of Photons and Electromagnetic field)
Fφ = rVYukawa
ϕ
Fφ = rφ φ(r) = −g2 e−kmr r
What sources a scalar field profile? How to compute the scale field profile?
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Scalar-Tensor Theories
Gravity experiments should see the total force!? Ftotal = FG + Fφ
/
( ) (1 )
r
GM r e r
λ
α
−
Ψ = − +
coupling range
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Scalar bosons lead to Yukawa correction to Newton potential:
/
( ) (1 )
r
GM r e r
λ
α
−
Ψ = − +
Screening mechanisms key elements
Either coupling becomes very small in Solar System or…
Long et al. Nature (2004)
the range becomes very short in Solar System
coupling range coupling range
scale dependent coupling/range!
α ∼ O(1) ⇒ λ ∼ 0.1mm
If extra scalar for gravity, then:
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Range of Fifth Force on Scalar-Tensor Gravity
/
( ) (1 )
r
GM r e r
λ
α
−
Ψ = − +
range
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Chameleon Screening: range of fifth force depends on local density
} Nonlinear mass/range
Mpc mm
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Mpc Kpc mm
Chameleon mechanism
Range of dark force depends on local environment (Khoury & Weltman 2004)
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coupled! Symmetron Screening: coupling of fifth force depends on local density
} Nonlinear coupling
Φ VeffHΦL Φ VeffHΦL
vev vev
No coupling! coupled!
/
( ) (1 )
r
GM r e r
λ
α
−
Ψ = − +
coupling
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