Baryon density of the Universe :

a trace of a scalar field?Julien Larena* , Jean-Michel Alimi* , Arturo Serna‡

Albert Einstein Century Conference

July, 20th 2005Paris, Palais de l'Unesco

*LUTh, Observatoire de Paris-Meudon, FRANCE‡Departamiento de física, Universidad Miguel Hernández, Elche, SPAIN

Primordial Nucleosynthesis

Synthesis of the lightest elements : D, 3He, 4He and traces of 7Li Energy scale : 10 MeV to a few keV Complex network of nuclear reactions (28 reactions) Standard nuclear physics is supposed to apply Two main parameters :

10 and H(T)

Hubble parameter :Expansion rate

Baryon to photon ratio

Reaction rate : (T, 10)=Cross section (T) × number densities(10,T

Thermal equilibrium : H > 1Frozen abundances : /H < 1

CMB Experiments : WMAP alone :

(WMAP+CBI+ACBAR) + Ly+ 2dF

bh2=0.0224±0.0009 or

10= 6.14±0.25

Citer les ref

Good agreement !

Large discrepancy

Then, the predicted primordial abundances are :

Cybert & al.,2004, PRD

10-0.730.60-

7

5-0.240.19-

p

10 3.82Li/H

10 2.75D/H

Y

0004.00005.02484.0

And the observed ones :

10-7

10-7

5-

5-

p

p

10 Li/Hor

10 Li/H

10 D/H or

10 D/H

Yor

Y

46.038.0

68.032.0

44.038.0

35.024.0

19.2

23.1

78.2

42.2

0015.02452.0

0020.02391.0

Ryan & al., 2000, ApJ Lett.; Bonifacio & al., 2002,A&ALuridiana & al., 2003, ApJ; Izotov & al., 1999, ApJKirkman & al., 2003, ApJ

27.022.010 25.6

Tegmark & al,2004,PRD

Spergel & al, 2003, ApJ

Scalar-tensor cosmology

mgAVR

gG

,)()(2

1

44

1 2,

*mL

L

gAg )(~ 2Universal coupling Metric theories :

Weak Equivalence Principle holds

Observable quantities must be computed in the Jordan frame.

Einstein frame :

mgUZRFgG

,~~

)(2)(~

)(~16

1~ ,,

*mL

L

Our parameterization : )(

)( and ZF )(

Jordan-Fierz frame :

Flat, homogeneous and isotropic Universe flat FRW metric

222222222 sin)( drdrdrtadtds

)3)((4)(

3

)(22)3(43

3)(

3

2

3

1

3

8

,,,

2,*

,,

2,

*2

pd

dVH

VpGa

a

VG

H

ttt

ttt

t

Where :

d

Ad )(ln)(

General Relativity : 0)(

Effective gravitational coupling : ))(1)(( 22* AGGeff

Observable expansion rate : tHA

H ,)()(

1~

Speed-up factor :GRH

H~

with33

82

NGR

GH

csta ln

d

dV

GwVwVm effeff

)(

)(4

1)()31(')),(,('')),((

*

'ud

du

p

w

Effective potential :

dwG

VVeff )()31(

)(4

)(),(

*

Convergence towards General Relativity requires that Veff has a minimum where vanishes.

Three types of models :

•V=0 and ∫has a minimum where vanishes.

•V0 and has a stationary point where vanishes. Then we need

conditions on the initial values to have convergence.

•V has a minimum where vanishes

; Equation of state for the background :

0

V

a 0

V

a 4

V

a

Three types of effective potentials leading to different convergence mechanisms :

Radiation dominated era

Matter dominated era

grows

grows

Veff Veff Veff

Veff

Solving the lithium problem with a scalar field

When V=0, the scalar field does’nt evolve during the radiation dominated era (if the initial conditions are set so that )

CstAGG iieff ))(1)(( 22*

So, a constant value of the coupling during BBN cannot explain the lithium abundance

We need an evolving scalar field during the radiation dominated era

0' i

Case of a vanishing potential

Model defined by :

ba

1

)(23

With a=4 and b= 2.68 this yields :

107

5

10601.2

10871.2

2405.0

H

LiH

D

Yp

We succeeded inlowering the lithium abundance

We begin slower than in General relativityand finish faster

Case of a quartic potential

Model :

6.0)(

109)(V 42

10

5

10324.2

10082.3

2441.0

H

LiH

D

Y

7

p

3.1i

The speed-up factor crosses 1 at a few MeV

Temperatures of freeze-out arestrongly modified

Be,He 73 less efficient

107

10H

Li

10

a

3.1

V 42

i

a

0020.02391.0 pY

0015.02452.0 pY

No constraint from the lithium abundance

The mechanism responsible for the decrease of the lithium abundance is very general

and constrained by the temperature of freeze-out for the weak interaction processes that interconvert n and p

Conclusion

•We reconcile the lithium abundance with its observed value when the baryon density is supposed high.

•Purely dynamical modification.

•Very general mechanism : a wide variety of models predict the right lithium abundance.

•Importance of the speed-up factor evolution : the expansion starts slower than in General Relativity and finishes faster.

•Consequences on CMB ?