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:0704.0882, 0707.1086 [astro-ph] TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA

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

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.

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

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

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

We fit supernova data (redshifts and magnitudes) to H(z) using the 192 SNeIa in the compilation of Davis & al., arXiv:astro-ph/ 0701510 which includes the ”passed” set in Wood-Vasey & al. arXiv: astro-ph/ 0701041 and the ”Gold” set in Riess & al., Ap.J. 659 (2007)98. We also use a weak constraint from CMB data: Wm0 = 0.24 +- 0.09 Our best fit has c2 = 195.5 for 190 degrees of freedom, (as successfully as LCDM). The parameter values are The 1s errors correspond to c2best + 3.54.

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)

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

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.

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

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

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

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.