Chaplygin gas in decelerating DGP gravity Matts Roos University of Helsinki Department of Physics and and Department of Astronomy 43rd Rencontres de Moriond, Cosmology La Thuile (Val d'Aosta, Italy) March , 2008

Contents I. Introduction II. The DGP model III. The Chaplygin gas model IV. A combined model V. Observational constraints VI. Conclusions Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

I. Introduction The Universe exhibits accelerating expansion since z ~ 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.  or self-accelerating DGP ) of Einstein’s equation (e.g.  or self-accelerating DGP )  or simply by some new energy density on the righthand side in T  (a negative pressure scalar field, Chaplygin gas) in T  (a negative pressure scalar field, Chaplygin gas) (Other viable explanations are not explored here.) (Other viable explanations are not explored here.)   CDM works, but is not understood theoretically.  Less simple models would be  modified self-accelerating DGP (has  CDM as a limit)  modified Chaplygin gas (has  CDM as a limit)  self-decelerating DGP and Chaplygin gas combined Matts Roos at 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 DGP model. The action of gravity can be written  The mass scale on our 4-dim. brane is M Pl, the corresponding scale in the 5-dim. bulk is M 5. the corresponding scale in the 5-dim. bulk is M 5.  Matter fields act on the brane only, gravity through- out the bulk.  Define a cross-over length scale * Dvali-Gabadadze-Porrati Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

► The Friedmann-Lemaître equation (FL) is  G /3) ► On the self-accelerating branch  =+1 gravity leaks out from the brane to the bulk, thus getting weaker on the brane (at late time, brane to the bulk, thus getting weaker on the brane (at late time, i.e. now). This branch has a ghost. i.e. now). This branch has a ghost. ► On the self-decelerating branch  =-1 gravity leaks in from the bulk onto the brane, thus getting stronger on the brane. This branch has onto the brane, thus getting stronger on the brane. This branch has no ghosts. no ghosts.  When H << r c ) the standard FL equation (for flat space k=0)  When H ~ r c the H /r c term causes deceleration or acceleration.  At late times Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

Replace  m  by,   by and r c by and r c by then the FL equation becomes  DGP self-acceleration fits SNeIa data less well than  CDM, it is too simple. less well than  CDM, it is too simple.  Modified DGP requires higher-dimensional bulk space and one parameter more. Not much better! and one parameter more. Not much better! Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

III The Chaplygin gas model III The Chaplygin gas model  A simple addition to T  is Chaplygin gas, a dark energy fluid with density    and pressure p  and an energy fluid with density    and pressure p  and an Equation of State Equation of State  The continuity equation is then which can be integrated to give which can be integrated to give where B is an integration constant. where B is an integration constant.  Thus this model has two parameters, A and B, in addition to  m. It has no ghosts. addition to  m. It has no ghosts. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

III The Chaplygin gas model III The Chaplygin gas model ► At early times this gas behaves like pressureless dust ► at late times the negative pressure causes acceleration: ► Chaplygin gas then has a ”cross-over length scale” This model is too simple, it does not fit data well, unless one This model is too simple, it does not fit data well, unless one modifies it and dilutes it with extra parameters. modifies it and dilutes it with extra parameters. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

IV A combined Chaplygin-DGP model IV A combined Chaplygin-DGP model Since both models have the same asymptotic behavior Since both models have the same asymptotic H/ r c  constant  like  CDM) H/ r c  constant  like  CDM) H/ r c > 1,  1 / r H/ r c > 1,  1 / r 3 we shall study a model combining standard Chaplygin gas acceleration with DGP self-deceleration, in which the two cross-over lengths are assumed proportional with a factor F we shall study a model combining 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. Actually we can choose F = 1 and motivate it later. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

IV A combined model IV A combined model  The effective energy density is then where we have defined where we have defined  The FL equation becomes  For the self-decelerating branch  At the present time (a=1) the parameters are related by At the present time (a=1) the parameters are related by ► This does not reduce to  CDM for any choice of parameters. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

IV A combined model IV A combined model We fit supernova data, redshifts and magnitudes, to H(z) We fit supernova data, redshifts and magnitudes, to H(z) using the 192 SNeIa in the compilation of Davis & al. * using the 192 SNeIa in the compilation of Davis & al. * Magnitudes: Magnitudes: Luminosity distance: Luminosity distance: Additional constraints: Additional constraints:   m 0 = from CMB data  Distance to Last Scattering Surface = 1.70 § 0.03 from CMB data  Lower limit to Universe age > 12 Gyr, from the oldest star HE * arXiv:astro-ph/ which includes the ”passed” set in Wood-Vasey & 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. arXiv: astro-ph/ and the ”Gold” set in Riess & al., Ap.J. 659 (2007)98. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

IV A combined model IV A combined model The best fit has   = for 190 degrees of freedom (  CDM scores   = ). The best fit has   = for 190 degrees of freedom (  CDM scores   = ). The parameter values are The parameter values are The 1  errors correspond to   best The 1  errors correspond to   best Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

Are the two scales identical? Are the two cross-over scales identical?  We already fixed them to be so, by choosing F =1.  Check this by keeping F free. Then we find  m =0.36,  rc =0.93,  A =2.22, F =0.90  m = ,  rc =0.93,  A = , F =   Moreover, the parameters are strongly correlated  F,  This confirms that the data contain no information on F, F F can be chosen constant without loss of generality. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

Banana: best fit to SNeIa data and weak CMB  m constraint (at +), and 1  contour in 3-dim. space. E llipse: best fit to SNeIa data and distance to last scattering. Lines: the relation in (  m,  rc,  A )-space at  A values +1  (1), central (2), and -1  (3).

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

Constraints from SNeIa and the Universe age  U / r chronometry of the age of the oldest star HE yields t * = 13.4 § 0.8 stat § 1.8 U production ratio ) t Univ > 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 effective dynamics by ► Note that  eff can be negative for some z in some part of the parameter space. in some part of the parameter space. Then Then  the Universe undergoes an anti-deSitter evolution  the weak energy condition is violated  w eff is singular at the points  eff = 0. This shows that the definition of w eff is not very useful This shows that the definition of w eff is not very useful Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

w eff (z) for a selection of points along the 1  contour in the  rc,  A  -plane Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

The deceleration parameter q (z) along the 1  contour in the (  rc,  A ) -plane Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

V. Conclusions 1. Standard Chaplygin gas embedded in self-decelerated DGP geometry with the condition of equal cross-over scales DGP geometry with the condition of equal cross-over scales fits supernova data as well as does  CDM. fits supernova data as well as does  CDM. 2. It also fits the distance to LSS, and the age of the oldest star. 3. The model needs only 3 parameters,  m,  rc,  A, while  CDM has 2:  m,   while  CDM has 2:  m,   4. The model has no ghosts. 5. The model cannot be reduced to  CDM, it is unique. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

V. Conclusions V. Conclusions 6. The conflict between the value of  and theoretical calculations of the vacuum energy is absent. 7. w eff changed from super-acceleration to acceleration sometime in the range 0 < z < 1. acceleration sometime in the range 0 < z < 1. In the future it approaches w eff = -1. In the future it approaches w eff = The ”coincidence problem” is a consequence of the time-independent value of r c, a braneworld property. the time-independent value of r c, a braneworld property. Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008