modified gravity
DESCRIPTION
Modified Gravity. Takeshi Chiba Nihon University. Why?. Why?. 1. A theory predicts the modification!: Scalar-Tensor Gravity 2. The Nature of Dark Matter is unkown: MOdified Newtonian Dynamics(MOND) 3. The Nature of Dark Energy is completely unkown: F(R) type gravity - PowerPoint PPT PresentationTRANSCRIPT
Modified Gravity
Takeshi ChibaNihon University
Why?
Why?1. A theory predicts the modification!: Scalar-Tensor Gravity2. The Nature of Dark Matter is unkown: MOdified Newtonian Dynamics(MOND)3. The Nature of Dark Energy is completely unkow
n: F(R) type gravityWe simply do not know the correct gravity theory in the large (and small) scale
Gravity is Probed at …
10-3cm 1AU 1kpc 1Mpc 1000Mpc
large extra dimensions?
MOND?Modified Gravity?
Modified Gravity I
Theory Motivated: String theory → Scalar-tensor Gravity If dilaton is (almost) massless, then cosmolo
gy and gravity can be different (time varying G)
Brans-Dicke parameter: ω0 > 20000 (Cassin
i satellite,2004)
Scalar-Tensor Cosmology Scalar-Tensor Gravity Consequence: Varying G Constraints: z=1010 (BBN) -0.15<(GBBN-G0)/G0<0.21 (Copi-Davis-Krauss,2004) z=0 (LRR) dG/dt/G<4x10-13 yr-1
What else?
Scalar-Tensor Cosmology
z=1100 (CMB) (Nagata-TC-Sugiyama,2004)
Effect of G Projection effect(first acoustic peak, H-1
) Shift of zero point of oscillation(Bh2 ) Diffusion damping(D H-1lmfp ) (damping factor:exp(-2/D
2) ) Decay of gravitational potential (0, ISW)
Nagata-TC-Sugiyama(2002)
Grecom-G0/G0<0.05 (Nagata-TC=Sugiyama,2004)
Scalar-Tensor Cosmology
Scalar-Tensor Gravity Consequence: Varying G Constraints: z=1010 (BBN)
-0.15<(GBBN-G0)/G0<0.21
(Copi-Davis-Krauss,2004)
z=1100 (CMB) (Grecom-G0)/G0<0.05
z=0 (LRR) dG/dt/G<4x10-13 yr-1
Modified Gravity II Observation motivated(Phenomenology?) Flat rotation curve → MOdified Newtonian Dynamics (MOND)(Miligrom,1986): alternative to dark matter
v is constant at large scale ( (v2/r)2/a0=GM/r2 )
MOND
Problems(so far): no relativistic formulation ← ✖ light propagation(gravitational lensing) ✖ large scale structure ✖ cosmology
(only recently) relativistic formulation by Bekenstein(2003):
vector-scalar-tensor gravity
MOND
Bekenstein’s Tensor-Scalar-Vector theory for MOND
MOND CMB and LSS by Bekenstein’s model(Skordis et al.,2005): consistent with obs.(WMAP,SDSS)if neutrino is massive (~0.17)(← first peak location)
MOND CMB peaks: sensitive to baryon and dark matter
B h2 (shift of zero point of oscillation)
→ first peak height second peak height Mh2 (increases the depth of potential well decreases radiation relative to matter(ISW))→ first peak height second peak → third peak height
MOND trouble with higher (second and third)
peaks of CMB(Slosar-Melchiorri-Silk,2005)
(← Silk damping for baryons)WMAP
WMAP/Boomerang
Modified Gravity III Recent acceleration of the Universe (SNIa)1.Dark energy: modify RHS of Einstein
equation2.Modify LHS instead ⇒ Modified gravity
modification should be significant only recently
→ 1/R gravity (Carroll et al., 2003)
Rise and Fall of 1/R Gravity
F(R) gravity is equivalent to Scalar-Tensor Gravity(Higgs,Whitt,Wands,Chiba):
Scalar-tensor with vanishing Brans-Dicke parameter: ω=0
can be in conflict with solar system experiments(ω>20000, Cassini satellite) if Brans-Dicke scalar
is (almost) masslessThis is the case for 1/R gravity :m ~ H0
1/R gravity modifies gravity not only at large scales but also at local scale
Einstein
1/R
ずれ
scale
Rise and Fall of 1/R Gravity
So much ado… F(R,P,Q) gravity?(Carroll et al.,2004) P=RabRab,Q=RabcdRabcd
→ higher derivative (4th order) theory→ Ghosts (Stelle 1977,Nunes,Chiba)propagator:
cross coupling:
The situation is much worse!!
But…
This does not mean all attempts at modifying gravity in the large scale are in trouble
(eg. DGP model) We simply do not know the correct gravity
theory in the large (and small) scale (→ cosmological PPN formalism?)
Gravity is Probed at …
10-3cm 1AU 1kpc 1Mpc 1000Mpc
large extra dimensions?
MOND?Modified Gravity?
ガモフの飛躍!( 100 億年→ 3分間)
PPN(Parameterized Post-Newtonian)
PPN formalism: • expand the metric around the Minkowski up to post-Newtonian order ( (v/c)^4 )• parametrize possible form of the metric without specifyi
ng the gravitational theory
• solve the motions of planets and light using the metric and compare them with the observations• | - 1|<4.4 x 10-5 (Cassini,2003), | - 1|< 2.3 x 10-4 (LLR,2004)
Cosmological PPN(or constructing approximate geometry of the universe)
Newtonian gauge: Cosmological (,x):
Lessons from scalar-tensor gravity: for large and is constant if H-1
~H
~2 ~ 2/2
nonlinear
linear
Newton
post Newton
Cosmological PPN(or constructing approximate geometry of the universe)
Cosmological metric (valid for H-1)
Bad: a() is model dependent (H())
Good: (once H is specified) we only
have to solve the same linear equations
What about ? -> second order perturbation
But…
This does not mean all attempts at modifying gravity in the large scale are in trouble
(eg. DGP model) We simply do not know the correct gravity
theory in the large (and small) scale (→ cosmological PPN formalism?) In this respect, various consistency checks
among cosmological observations are important (eg. growth rate, H via lensing and SNIa)
Ishak,Upadhye,Spergel(2005)see also Knox,Song,Tyson(2005)
Searching for alternatives
is important to reinforce the evidence for DM and DE
to check the internal consistency of cosmological data (→ understand systematics)