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## Chaplygin gas in decelerating DGP gravity

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**Chaplygin gas in decelerating DGP gravity**Matts Roos University of Helsinki Department of Physics and Department of Astronomy 43rd Rencontres de Moriond, Cosmology La Thuile (Val d'Aosta, Italy) March 15 - 22, 2008**Contents**• Introduction • The DGP model • The Chaplygin gas model • A combined model • Observational constraints • Conclusions Matts Roos at 43rd Rencontres de Moriond, 2008**I.Introduction**The Universe exhibits accelerating expansion sincez ~ 0.5 . One has tried to explain it by • simple changes to the spacetime geometry on the lefthand side of Einstein’s equation (e.g. L or self-accelerating DGP) • or simplyby some new energy density on the righthand side in Tmn (a negative pressure scalar field, Chaplygin gas) (Other viable explanations are not explored here.) • LCDM works, but is not understood theoretically. • Less simple modelswould be • modified self-accelerating DGP (has LCDM as a limit) • modified Chaplygin gas (has LCDM as a limit) • self-decelerating DGP and Chaplygin gas combined Matts Roos at 43rd Rencontres de Moriond, 2008**II The DGP* model**• A simple modification of gravity is the braneworld DGP model.The action of gravity can be written • The mass scale on our 4-dim. brane isMPl, the corresponding scale in the 5-dim. bulk isM5 . • Matter fields act on the brane only, gravity through- out the bulk. • Define a cross-over length scale * Dvali-Gabadadze-Porrati Matts Roos at 43rd Rencontres de Moriond, 2008**The Friedmann-Lemaître equation (FL) is (k=8pG/3)**On the self-accelerating branch e =+1gravity leaks out from the brane to the bulk, thus getting weaker on the brane (at late time, i.e. now). This branch has a ghost. On the self-decelerating branch e =-1gravity leaks in from the bulk onto the brane, thus getting stronger on the brane. This branch has no ghosts. WhenH << rc )the standard FL equation (for flat space k=0) When H ~ rc the H /rc term causes deceleration or acceleration. At late times Matts Roos at 43rd Rencontres de Moriond, 2008**Replace rmby , rj by**and rc by then the FL equation becomes DGP self-acceleration fits SNeIa data less well than LCDM, it is too simple. Modified DGP requires higher-dimensional bulk space and one parameter more. Not much better! Matts Roos at 43rd Rencontres de Moriond, 2008**III The Chaplygin gas model**• A simple addition toTmnis Chaplygin gas, a dark energy fluid with density rj and pressure pj and an Equation of State • The continuity equation is then which can be integrated to give where B is an integration constant. • Thus this model has two parameters, Aand B, in addition to Wm . It has no ghosts. Matts Roos at 43rd Rencontres de Moriond, 2008**III The Chaplygin gas model**• At early times this gas behaves like pressureless dust • at late times the negative pressurecauses acceleration: • Chaplygin gas then has a ”cross-over length scale” • This model is too simple, it does not fit data well, unless one modifies it and dilutes it with extra parameters. Matts Roos at 43rd Rencontres de Moriond, 2008**IV A combined Chaplygin-DGP model**Since both models have the same asymptotic behavior @ H/ rc-> 0 , r -> constant (like LCDM) ; @ H/ rc > 1 , r -> 1 / r3 we shall study a modelcombining standard Chaplygin gas acceleration with DGP self-deceleration,in which the two cross-over lengths are assumed proportional with a factor F Actually we can choose F= 1 and motivate it later. Matts Roos at 43rd Rencontres de Moriond, 2008**Are the two cross-over scales identical?**• We already fixed them to be so, by choosing F=1. • Check this by keeping Ffree. Then we find Wm=0.36+0.12-0.14 , Wrc=0.93 , WA=2.22+0.94-1.20 , F=0.90+0.61-0.71 • Moreover, the parameters are strongly correlated • This confirms that the data contain no information on F , Fcan be chosen constant without loss of generality. Matts Roos at 43rd Rencontres de Moriond, 2008**Banana: best fit to SNeIa data and weak CMB Wm constraint**(at +), and 1s contour in 3-dim. space. Ellipse: best fit to SNeIa data and distance to last scattering.Lines: the relation in (Wm, Wrc,WA)-spaceat WA values +1s (1), central (2), and -1s (3).**Constraints from SNeIaand the Universe age**• U / r chronometry of the age of the oldest star HE 1523-0901 yields t * = 13.4 § 0.8stat§ 1.8 U production ratio ) tUniv > 12 Gyr (68%C.L.). • The blue range is forbidden Matts Roos at 43rd Rencontres de Moriond, 2008**One may define an**effective dynamics by Note thatreffcan be negative for some z in some part of the parameter space. Then the Universe undergoes an anti-deSitter evolution the weak energy condition is violated weffis singular at the pointsreff = 0. This shows that the definition of weff is not very useful Matts Roos at 43rd Rencontres de Moriond, 2008**weff (z)for a selection of points along the 1scontour in the**(Wrc , WA) -plane Matts Roos at 43rd Rencontres de Moriond, 2008**The deceleration parameter q (z) along the 1s contour in the**(Wrc , WA) -plane Matts Roos at 43rd Rencontres de Moriond, 2008**V. Conclusions**• StandardChaplygin gas embedded in self-decelerated DGP geometry with the condition of equal cross-over scales fits supernova data as well as does LCDM. 2. It also fits the distance to LSS, and the age of the oldest star. 3. The model needs only 3 parameters, Wm, Wrc, W A , while LCDM has 2: Wm, WL 4. The model has no ghosts. 5. The model cannot be reduced to LCDM, it is unique. Matts Roos at 43rd Rencontres de Moriond, 2008**V. Conclusions**6. The conflict between the value of L and theoretical calculations of the vacuum energy is absent. 7. weffchanged from super-acceleration to acceleration sometime in the range 0 < z < 1. In the future it approaches weff = -1. 8. The ”coincidence problem” is a consequence of the time-independent value of rc , a braneworld property. Matts Roos at 43rd Rencontres de Moriond, 2008