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3rd Kosmologietag at IBZ, Bielefeld, May 8-9, 2008. Cosmological Expansion from Nonlocal Gravity Correction. Tomi Koivisto, ITP Heidelberg. e-Print: arXiv:0803.3399, to appear in PRD. 1. Outline Introduction 2. Nonlocalities in physics 3. The gravity model 4. Scalar-tensor formulation
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Tomi Koivisto, ITP Heidelberg
e-Print: arXiv:0803.3399, to appear in PRD
2. Nonlocalities in physics 3. The gravity model
4. Scalar-tensor formulation
5. Radiation domination 6. Matter domination
7. Acceleration 8. Singularity 9. Summary
10. Solar system 11. Perturbations
-BH information paradox requires nonlocal physics?
t’ Hooft & Veltman: Annales Poincare Phys.Theor.A20:69-94,1974
- Thus, consider the class of simple modications:
- Like a variable G
- When f(x)=cx, could stabilize the Euclidean action
C. Wetterich: Gen.Rel.Grav.30:159-172,1998
- Recent suggestion: could provide dark energy
S. Deser & R.P. Woodard: Phys.Rev.Lett.99:111301,2007.
...then f should be about ~-1. It’s argument is dimensionless
-> fine tuning alleviated ?
Introduce a field and a Lagrange multiplier:
- Equivalent to a local model with two extra d.o.f !
- Massless fields with a nonlinear sigma -type (kinetic) interaction
In the very early universe the correction vanishes:
As matter becomes non-relativistic:
- BBN constrains the corrections during RD
- The possible effects are a consequence of the onset MD
Assume f(x) = Nx^n :
- If n>0, the coupling grows
- If N(-1)^n<0, the nonlocal contribution to energy grows
One may reconstruct f(x) which gives the assumed expansion!
But, assuming power-law f(x)=Nx^n, the expansion goes like:
- For larger |n| the evolution is steeper (here n=3,n=6)
- N is roughly of the order (0.1)^(n+1) in Planck units
Power-law and exponential f(x) which result in acceleration lead to a sudden future singularity at t=t_s>t_0:
Barrow, Class.Quant.Grav. 21 (2004) L79-L82
- Density (and expansion rate) remain finite at t_s
- Pressure (and acceleration rate) diverge at t_s
1) Simply reconstruct different f(x) resulting in finite w
2) Regularize the inverse d’Alembertian!
3) Consider higher curvature terms
Slows down expansion
- If the fields are constant:
- Where the corrections to the Schwarzschild metric are
- Exact Schwarzschild solution: R=0, fields vanish
- They are second order in GM/r < 10^(-6)
- Seems they escape the constraints on
|G_*/G|, |γ-1| ~ 10^(-5)
- In the cosmological Newtonian gauge:
- Effective anisotropic stress appears:
(relevant for weak lensing?)
- Poisson equation is different too:
(detectable in the ISW?)
- Matter growth is given by the G_*:
(constraints from LSS !)
Langlois & Renaux-Petel: JCAP 0804:017,2008
- Thus if L>0 & (1+ψ)>0 ,no ghosts, instabilities or acausalities.
- Coincidence: (Delayed) response to the universe
- Fine tuning: Only Planck scale involved
- Simplest models feature a sudden future singularity
- Seems to have reasonable LSS, could avoid ghosts and
Solar system constraints...
Whereas f(R) gravity does not help with the fine tunings in the first place and
in addition is ruled out (or severely constrained) by ghosts, LSS and Solar system.