Modified Gravity

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Modified Gravity

• Takeshi Chiba
• Nihon University

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Why?
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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
• We simply do not know the correct
• gravity theory in the large (and small) scale

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Gravity is Probed at
10-3cm 1AU 1kpc 1Mpc 1000Mpc
large extra dimensions?
MOND?
Modified Gravity?
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Modified Gravity I

• Theory Motivated
• String theory ? Scalar-tensor Gravity
• If dilaton is (almost) massless, then cosmology
  and gravity can be different (time varying G)
• Brans-Dicke parameter ?0 gt 20000 (Cassini
  satellite,2004)

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(No Transcript)
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Scalar-Tensor Cosmology

• Scalar-Tensor Gravity
• Consequence Varying G
• Constraints
• z1010 (BBN) -0.15lt(GBBN-G0)/G0lt0.21
• (Copi-Davis-Krauss,2004)
• z0 (LRR) dG/dt/Glt4x10-13 yr-1
• What else?

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Scalar-Tensor Cosmology

• z1100 (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 factorexp(-?2/?D2) ?)
• Decay of gravitational potential
• (???0, ISW)

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Nagata-TC-Sugiyama(2002)
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Grecom-G0/G0lt0.05 (Nagata-TCSugiyama,2004
)
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Scalar-Tensor Cosmology

• Scalar-Tensor Gravity
• Consequence Varying G
• Constraints
• z1010 (BBN) -0.15lt(GBBN-G0)/G0lt0.21
• (Copi-Davis-Krauss,2004)
• z1100 (CMB) (Grecom-G0)/G0lt0.05
• z0 (LRR) dG/dt/Glt4x10-13 yr-1

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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/a0GM/r2 )

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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

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MOND
Bekensteins Tensor-Scalar-Vector theory for MOND
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MOND

• CMB and LSS by Bekensteins model
• (Skordis et al.,2005)
• consistent with
• obs.(WMAP,SDSS)
• if neutrino is massive
• (??0.17)
• (? first peak location)

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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 ?

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MOND

• trouble with higher (second and third) peaks of
  CMB(Slosar-Melchiorri-Silk,2005)
• (? Silk damping
• for baryons)

WMAP/Boomerang
WMAP
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Modified Gravity III

• Recent acceleration of the Universe (SNIa)
• 1.Dark energy modify RHS of Einstein equation
• 2.Modify LHS instead ? Modified gravity
• modification should be significant only recently
• ? 1/R gravity (Carroll et al., 2003)

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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 ?0
• can be in conflict with solar system experiments
• (?gt20000, Cassini satellite) if Brans-Dicke
  scalar is (almost) massless
• This is the case for 1/R gravity m H0

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Rise and Fall of 1/R Gravity

• 1/R gravity modifies gravity not only at large
  scales but also at local scale

Einstein
??
1/R
scale
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So much ado

• F(R,P,Q) gravity?(Carroll et al.,2004)
• PRabRab,QRabcdRabcd
• ? higher derivative (4th order) theory
• ? Ghosts (Stelle 1977,Nunes,Chiba)
• propagator
• cross coupling
• The situation is much worse!!

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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?)

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Gravity is Probed at
10-3cm 1AU 1kpc 1Mpc 1000Mpc
large extra dimensions?
MOND?
Modified Gravity?
??????!(100???3??)
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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
  specifying the gravitational theory
• solve the motions of planets and light using
• the metric and compare them with the
  observations
• ? - 1lt4.4 x 10-5 (Cassini,2003),
• ? - 1lt 2.3 x 10-4 (LLR,2004)

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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

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??2 ? ?2/?2
nonlinear
?
post Newton
linear
??H
Newton
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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 ? ? -gt second order perturbation

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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)

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Ishak,Upadhye,Spergel(2005) see also
Knox,Song,Tyson(2005)
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Searching for alternatives

• is important
• to reinforce the evidence for
• DM and DE
• to check the internal consistency of cosmological
  data (? understand systematics)