Chaplygin gas in decelerating DGP gravity Matts Roos

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Chaplygin gas in decelerating DGP gravity Matts Roos University of Helsinki Department of Physics

Chaplygin gas in decelerating DGP gravity Matts Roos University of Helsinki Department of Physics and Department of Astronomy 43 rd Rencontres de Moriond, Cosmology La Thuile (Val d'Aosta, Italy) March 15 - 22, 2008

Contents Introduction II. The DGP model III. The Chaplygin gas model IV. A combined

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

I. Introduction The Universe exhibits accelerating expansion since z ~ 0. 5. One has

I. Introduction The Universe exhibits accelerating expansion since z ~ 0. 5. One has tried to explain it by Ø simple changes to the spacetime geometry on the lefthand side of Einstein’s equation (e. g. L or self-accelerating DGP) Ø or simply by some new energy density on the righthand side in Tmn (a negative pressure scalar field, Chaplygin gas) (Other viable explanations are not explored here. ) Ø LCDM works, but is not understood theoretically. Ø Ø Less simple models would 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 43 rd Rencontres de Moriond, 2008

II The DGP* model § A simple modification of gravity is the braneworld DGP

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 is MPl , the corresponding scale in the 5 -dim. bulk is M 5. § Matter fields act on the brane only, gravity throughout the bulk. § Define a cross-over length scale * Dvali-Gabadadze-Porrati Matts Roos at 43 rd Rencontres de Moriond, 2008

► The Friedmann-Lemaître equation (FL) is (k=8 p. G/3) ► On the self-accelerating branch

► The Friedmann-Lemaître equation (FL) is (k=8 p. G/3) ► On the self-accelerating branch e =+1 gravity 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 =-1 gravity leaks in from the bulk onto the brane, thus getting stronger on the brane. This branch has no ghosts. § § § When H << 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 43 rd Rencontres de Moriond, 2008

Replace rm by , rj by and rc by then the FL equation becomes

Replace rm by , rj by and rc by then the FL equation becomes Ø DGP self-acceleration fits SNe. Ia data less well than LCDM, it is too simple. Ø Modified DGP requires higher-dimensional bulk space and one parameter more. Not much better! Matts Roos at 43 rd Rencontres de Moriond, 2008

III The Chaplygin gas model § A simple addition to Tmn is Chaplygin gas,

III The Chaplygin gas model § A simple addition to Tmn is 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, A and B, in addition to Wm. It has no ghosts. Matts Roos at 43 rd Rencontres de Moriond, 2008

III The Chaplygin gas model ► At early times this gas behaves like pressureless

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 modifies it and dilutes it with extra parameters. Matts Roos at 43 rd Rencontres de Moriond, 2008

IV A combined Chaplygin-DGP model Since both models have the same asymptotic behavior @

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 / 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 Actually we can choose F = 1 and motivate it later. Matts Roos at 43 rd Rencontres de Moriond, 2008

IV A combined model The effective energy density is then § where we have

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

IV A combined model We fit supernova data, redshifts and magnitudes, to H(z) using

IV A combined model We fit supernova data, redshifts and magnitudes, to H(z) using the 192 SNe. Ia in the compilation of Davis & al. * Magnitudes: Luminosity distance: Additional constraints: § § § Wm 0 = 0. 24 +- 0. 09 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 1523 -0901 *ar. Xiv: astro-ph/ 0701510 which includes the ”passed” set in Wood-Vasey & al. , ar. Xiv: astro-ph/ 0701041 and the ”Gold” set in Riess & al. , Ap. J. 659 (2007)98. Matts Roos at 43 rd Rencontres de Moriond, 2008

IV A combined model The best fit has c 2 = 195. 5 for

IV A combined model The best fit has c 2 = 195. 5 for 190 degrees of freedom (LCDM scores c 2 = 195. 6 ). The parameter values are The 1 s errors correspond to c 2 best + 3. 54. Matts Roos at 43 rd Rencontres de Moriond, 2008

Are the two cross-over scales identical? § § We already fixed them to be

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 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 , F can be chosen constant without loss of generality. Matts Roos at 43 rd Rencontres de Moriond, 2008

Banana: best fit to SNe. Ia data and weak CMB Wm constraint (at +),

Banana: best fit to SNe. Ia data and weak CMB Wm constraint (at +), and 1 s contour in 3 -dim. space. Ellipse: best fit to SNe. Ia data and distance to last scattering. Lines: the relation in (Wm, Wrc, WA)-space at WA values +1 s (1), central (2), and -1 s (3).

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

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

Constraints from SNe. Ia and the Universe age § U / r chronometry of

Constraints from SNe. Ia and the Universe age § U / r chronometry of the age of the oldest star HE 1523 -0901 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 43 rd Rencontres de Moriond, 2008

► One may define an effective dynamics by ► Note that reff can be

► One may define an effective dynamics by ► Note that reff can be negative for some z in some part of the parameter space. Then the Universe undergoes an anti-de. Sitter evolution the weak energy condition is violated weff is singular at the points reff = 0. This shows that the definition of weff is not very useful Ø Ø Ø Matts Roos at 43 rd Rencontres de Moriond, 2008

weff (z) for a selection of points along the 1 s contour in the

weff (z) for a selection of points along the 1 s contour in the (Wrc , WA) -plane Matts Roos at 43 rd Rencontres de Moriond, 2008

The deceleration parameter q (z) along the 1 s contour in the (Wrc ,

The deceleration parameter q (z) along the 1 s contour in the (Wrc , WA) -plane Matts Roos at 43 rd Rencontres de Moriond, 2008

V. Conclusions 1. Standard. Chaplygin gas embedded in self-decelerated DGP geometry with the condition

V. Conclusions 1. Standard. Chaplygin 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 43 rd Rencontres de Moriond, 2008

V. Conclusions 6. The conflict between the value of L and theoretical calculations of

V. Conclusions 6. The conflict between the value of L and theoretical calculations of the vacuum energy is absent. 7. weff changed 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 43 rd Rencontres de Moriond, 2008

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