Alexey Anisimov and Alexander Vikman- The Classical Stability Of The Ghost Condensate

8/3/2019 Alexey Anisimov and Alexander Vikman- The Classical Stability Of The Ghost Condensate

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arXiv:h

ep-ph/0411089v3

3Mar2005

Hinf M

Hinf M
http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3http://arxiv.org/abs/hep-ph/0411089v3


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L(,)

Cs

w

L(,)

L = M4

P(X) + Q(X)S

g

M3

,

M

X

X 12

g

M2

M2

,

P(X) Q(X) Sg

M3

g g

P(X)

X = 0 X X = X X

= M2

2Xt


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= M2

2Xt +

()2 2

S

d4x M4(h00 )2.

M4Q(X)S(g/M3) = 2(g)2/2M2

2 k4/M2

(X) = 0

P(X) X X X

X

H

H/M


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X = X

X < X.

X > X X < X.

X = X

X

()2

X

()2

()4 ()6

H

X Q(X) S(X)


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Hinf M 1

H M

H M

S = M4

d4x

gP(X), M

1g gP(X)

= 0,

P(X)

P(X) = P(0) X+ O(X2) X = 0 P(X) X = 0

X = X

X = 1 P(X) = 12

(X 1)2

ds2 = dt2

a2(t) dx2,


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t [P(X)t] + 3HP

(X)t 1a2

i [P(X)i] = 0,

H = a/a a(t)

a(t)

P(X) =const

a3(t) 0 as t +,

X = 0 X P(X) = 0

X

X > X

C2s P(X)

(X),

X = X (X) = 2XP(X) P(X)

X C2s > 0 (C2s < 0) X

X > X

X X

= M2

2Xt +

L = M4 [2XP(X) + P(X)] 2 P(X)()2

X > X 2 ()2 Xd < X < X

X < Xd X > X

X

X

S =

d4x

g

M4P(X) 2(g)

2

2M2


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X

X

P(X)

C2s

0

0

X

Xd

2

Xd X = 0 X = X

C2s 2

C2s

H(t)

H = const H = 2

3t

(0, 0,

0) H M

M/Mpl 1 tot > 0

0 < 0


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X

M

a3t

a3P(X)

=

2

(4) + 6H

+

6H+ 9H2

+

9HH+ 3H

P(X)

X > X

P(X)

P(X) =12(X 1)

2

y

y + 6Hy + 9H2y + 2 (y + 3yH P) = 0.

X = 1 =

2

P(X) =12(X 1)

2

y = 2 +

+ 6H +

9H2 +

2

2

+

6H

2= 0.

3 + 6H2 +

9H2 +

2

2

+

6H

2= 0.

1 = 3H, = 3

2H

1 1 8(3H)2 2 ,

H M

M 1 |1,+| 1013 232H1

exp(3HT) 2 exp(T) T T = Mt

N


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N = (H/M)2

N H 1013 M 1 1026 H/M =

2

100 200 300 400 500 600

1.02

1.04

1.06

1.08

1.1

1.12

1.14

X

T

H/M= 1013

H/M= 102

=2 + 0.1, = 0.1,

= 0.1 HM

= 102 X

X = 1 HM

= 1013 X

300

100

400

200

500

300 400 500 600

5107

1106

1.5106

2106

2.5106

8109

6109

4109

2109

T

T

= 0.1,

= 0.1 HM

102

=

2 + 0.1

H M


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M

M

X0 > X 0 =

0 = 0

H M H

X

10

5

20

10

30

15

40

20

0.995

0.995

1.005

0.9975

1.01

1.0025

1.005

1.0075

1.01

1.0125

X

X

T

T

H/M= 102

H/M= 101

=2 + 0.001, = 0.01,

= 0.001 H M

X0 > X

M


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H = 23t

y y

y + 6Hy + + 12

(y + 3yH P) = 0.

X = 1 P(X) =12(X 1)2 H(t) = 23t1

+4

t

+

2

+

2

2 = 0.

t2/

+2

(2 + ) + = 0

() =1

2[c + (a cos + b sin )] +

1

(a sin b cos ) .

()

=

2 + 0 = 0

= 0 ()

() = 0[20 1

2+

1

2cos( 0) + 1

sin( 0)].

M

1

2

sin( 0)

= 0

= 0

()2

0 1 202

1

,

tover MH2

,

H

M H

M = 1 H = 103

tover 109 1


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t

106

H 1013sec1 M = 1 1022sec tover 1041

25 50 75 100 125 150

1.005

1.01

1.015

1.02

1.025

1.03

X

T

0 = 10 =

2 + 0.1, = 0,

= 0

20

90 100 110 120

1.001

1.002

1.003

1.004

X

T

X

X= 1

()2


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50 100 150 200 2500.98

0.99

1.01

1.00

1.02

1.03

1.04

X

T

0 = 10 =

2 + 0.1, = 0.1,

= 0.1

a

b

0

0

() =c

2+

a2 + b2

2cos( ) +

a2 + b2

sin( ),

cos() a/a2 + b2 sin( ) 2

(0)

(0)

max 020

a2 + b2,

a b

a = b = 0 X


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H/M

M H

H M X

M

X > X X < X

V

M3

Z2

M

103

()2/M2

P(X)


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http://arxiv.org/abs/hep-th/0311312http://arxiv.org/abs/hep-th/9904176http://arxiv.org/abs/astro-ph/0310344http://arxiv.org/abs/astro-ph/0212003http://arxiv.org/abs/hep-th/0312100http://arxiv.org/abs/astro-ph/0201229http://arxiv.org/abs/gr-gc/0112012http://arxiv.org/abs/gr-gc/9908058http://arxiv.org/abs/astro-ph/0105068http://arxiv.org/abs/hep-th/0005016http://arxiv.org/abs/astro-ph/9912463http://arxiv.org/abs/astro-ph/0004134http://arxiv.org/abs/astro-ph/0006373http://arxiv.org/abs/hep-th/9904075http://arxiv.org/abs/hep-th/0312099


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http://arxiv.org/abs/hep-th/0409241http://arxiv.org/abs/hep-th/0404005http://arxiv.org/abs/hep-ph/0403308http://arxiv.org/abs/hep-th/0502189http://arxiv.org/abs/hep-th/0404216http://arxiv.org/abs/hep-ph/0407081http://arxiv.org/abs/hep-ph/0110002http://arxiv.org/abs/astro-ph/9307002http://arxiv.org/abs/astro-ph/0301273

Alexey Anisimov and Alexander Vikman- The Classical Stability Of The Ghost Condensate

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