1

On Generalized Chaplygin Gas

Yungui Gong

龚云贵

重庆邮电学院

超弦 /理论、粒子物理及宇宙学专题研讨会 10月 21日 -11月 3日

10/23/2004

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Motivation

2210 )1()1( zAzAAQ )1()1/( 110 zBzBBQ

z

zaQ

10

20 )1( z

zaQ

20

))1ln(1( zbQ

)1ln(10

zbQ

)1ln(10 za

Q

3

4

Chaplygin gas

A

p

)1( ,, gAL

As a perfect fluid with the equation of state

Motivation: Nambu-Goto action for a d-brane moving in a (d+2)-dimensional spacetime in the light-cone parameterization

Quintessence filed potential

13/8 Take

)3cosh/13(cosh2

1)(

G

AV

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Cosmological Solution

22

2

4 6

44 6

44 6

4

6

])/(1arctan2/

/[ln

6

1

/

Apc

Ap

AaBAaBA

AaBA

At

aBA

s

6

Generalized Chaplygin Gas

0 ,

Ap

)1/(2/)1(,, )])(1([

gAL

Quintessence filed potential

13/8 Take

)]2/)1(3(cosh)2/)1(3([cosh2

1)( )1/(2)1/(2)1/(1

G

AV

As a perfect fluid with the equation of state

Flat universe, Chaplygin gas is the only source

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Cosmological Solution: Possible Unification of dark matter and dark energy

)]/()1(

1[

)]/()1(

1[

]/[

22)1(3

)1/(1

22)1(3

)1/(1

12

1

)1/(1)1(3

ABOAa

BAp

ABOAa

BA

Apc

Ap

aBA

s

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Chaplygin gas as dark energy

)1(3000

0

)/)(1(

aacc

cc

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Constraints

1. The total energy density is non-negative

2. The current density is not increasing

3. Sound speed 10 20 sc

00 00

00

0

20

20

3)1(41

01

1

qj

q

Ha

k

kk

k

k

(1)

(2)

(3)

32

aH

aj

aH

aq

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Constraints on GCG

0)1)(1(

0)1(

0)1(

1

)1(2

91

)1(2

3

2

31

0000

000

000

00

0000

0000

chchchm

chchch

chchm

chkm

chchchk

chchkm

j

q

(1)

(2) Used (1)

(3) Used (1)

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Physical Constraints01 ,01 00 chm

0 if 10 ch

0 ch

From (2), we get

0 if 10 ch

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SN Fitting Method

13

14

004.0044.00 m

15

16

17

18

19

Age fitting

20

21

Current Measurements on matter density

Peebles, PJE, astro-ph/0410284