Transcript Transparencies - Rencontres de Moriond

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
II.
The DGP model
III. The Chaplygin gas model
IV. A combined model
V.
Observational constraints
VI. Conclusions
I.
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. L or self-accelerating DGP)

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.)

LCDM works, but is not understood theoretically.

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
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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 is MPl ,
the corresponding scale in the 5-dim. bulk is M5 .
 Matter fields act on the brane only, gravity throughout 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 =+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 43rd Rencontres de Moriond, 2008
Replace rm by
, 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 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 43rd Rencontres de Moriond, 2008
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 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 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.
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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 43rd Rencontres de Moriond, 2008
IV A combined model
We fit supernova data, redshifts and magnitudes, to H(z)
using the 192 SNeIa in the compilation of Davis & al.*
Magnitudes:
Luminosity distance:
Additional constraints:
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Wm0 = 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
*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.
Matts Roos at 43rd Rencontres de Moriond, 2008
IV A combined model
The best fit has c2 = 195.5 for 190 degrees of freedom
(LCDM scores c2 = 195.6 ).
The parameter values are
The 1s errors correspond to c2best + 3.54.
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 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
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This confirms that the data contain no information on F ,
F can 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)-space
at WA values +1s (1), central (2), and -1s (3).
Best fit (at +) and 1s contour in 3-dim. space.
Constraints from SNeIa and 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 that reff can 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
weff is singular at the points reff = 0.
This shows that the definition of weff is not very useful
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Matts Roos at 43rd Rencontres de Moriond, 2008
weff (z) for a selection of points along the 1s
contour 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
1.
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. 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 43rd Rencontres de Moriond, 2008