1. Cosmo 2007, Brighton, Sussex, August 21-25, 2007
A model of accelerating dark energy in decelerating gravity
Matts Roos
University of Helsinki
Department of Physical Sciences
and
Department of Astronomy
Cosmo 2007, Brighton, Sussex, August 21-25, 2007
arXiv: , [astro-ph]
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2. The accelerated expansion may be explained by changes to the spacetime geometry on the lefthand side of Einstein’s equation
or by the introduction of some new energy density on the righthand side, in the energy-momentum tensor Tmn

3. A model of modified gravity is the braneworld
DGP model (Dvali-Gabadadze-Porrati), where
the action of gravity on the 4-dimensional brane is / MPl2 ,
whereas in the 5-dimensional bulk it is / M53
The cross-over length scale is
the Friedmann-Lemaître (FL) equation takes the form
where e=+1 corresponds to self-acceleration,
e=-1 to self-deceleration.
rm is the baryonic and DM energy density,
rj is any other energy density component, and k=8pG /3. ..
We shall only consider flat spacetime, k = 0.

4. The continuity equation can then be integrated to give
Chaplygin gas is a dark energy fluid with the EOS
The continuity equation
can then be integrated to give
At early times this gas behaves like pressureless dust
at late times like LCDM, causing acceleration:
Chaplygin gas has a cross-over length

5. A combined Chaplygin-DGP model
Both the Chaplygin gas model and the DGP model are characterized by a scale rc,
both have the same asymptotic behavior:
for a / rc -> 0 , r -> constant (like LCDM)
for a / rc >> 1 , r -> 1 / a3
Both models have some problems explaining dark energy.
Consider then a combined model in which the cross-over lengths are assumed identical

6. Let’s solve the quadratic FL equation for H(a)
with the 3 parameters
At present when a=1 (z=0), one can solve for Wm0
which is the flat-space condition, that corresponds in the LCDM model to Wm0 + WL =1.
The self-accelerating branch with e = +1
is not viable, it causes too much acceleration.
We shall now concentrate on the self-decelerating branch with e = -1

7. We fit supernova data (redshifts and magnitudes) to H(z)
using the 192 SNeIa in the compilation of Davis & al., arXiv:astro-ph/ which includes the ”passed” set in Wood-Vasey & al. arXiv: astro-ph/ and the ”Gold” set in Riess & al., Ap.J. 659 (2007)98.
We also use a weak constraint from CMB data: Wm0 =
Our best fit has c2 = for 190 degrees of freedom,
(as successfully as LCDM).
The parameter values are
The 1s errors correspond to c2best

8. Best fit (at +) and 1s contour in 3-dim. space
Best fit (at +) and 1s contour in 3-dim. space. The lines correspond to the flat-space condition at WA values +1s (1), central (2), and -1s (3)

9. Best fit (at +) and 1s contour in 3-dim. space.

10. The customary definition of an
effective dynamics is
reff = rj - H / k rc
weff = -1 – (d reff / dt ) / 3 H reff
Note, however, that reff has zeros, so weff can be singular. This only shows that this definition of reff and weff is artificial.
The region of singularities in the parameter space is indicated by a straight line in the previous figure.

11. The full expression of weff (notation: W=Wrc, A=WA , M=Wm)

12. weff (z) for a selection of points along the 1s
contour in the (Wrc , WA) -plane

13. The deceleration parameter q (z) for a selection
of points along the 1s contour in the (Wrc , WA) -plane

14. Conclusions Chaplygin gas in self-decelerated DGP geometry
with the condition of equal cross-over scales
fits supernova data as well as does LCDM.
2. The model has only 3 parameters.
3. The ”coincidence problem” is a consequence of the time-independent value of rc , a braneworld property.
weff changed from super-acceleration to acceleration sometime in the range 0 < z < 1. In the future it approaches weff = -1.
weff develops a singularity at z ~ 1.1 in the parameter range where Chaplygin gas dominates over DGP.