Dark Matter Dark Energy Interactions · 2017. 10. 4. · Dark Matter – Dark Energy Interactions...
Transcript of Dark Matter Dark Energy Interactions · 2017. 10. 4. · Dark Matter – Dark Energy Interactions...
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Dark Matter – Dark Energy
Interactions
Emmanuel N. Saridakis
Physics Department, National and Technical University of Athens, Greece
Physics Department, Baylor University, Texas, USA
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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Goal
We investigate cosmological scenarios in a universe where dark sectors are allowed to mutually interact
Note:
A consistent or interesting cosmology is not a proof for the consistency of the underlying gravitational theory
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Why Modification?
Knowledge of Physics: Standard Model
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Why Modification?
Knowledge of Physics: Standard Model + General Relativity
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Why Modification? Universe History:
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Modified Gravity
Non-minimal gravity-matter coupling
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
(Gen. Proca)
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Scalar-Tensor Theories
Add a scalar field:
Conformal Transf. to Jordan frame:
,)()(2)()(16
1ghLsRfgL m
ggh )(
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Scalar-Tensor Theories
Add a scalar field:
Conformal Transf. to Jordan frame:
Redefinition of :
Brans-Dicke for
GR for
,)()(2)()(16
1ghLsRfgL m
ggh )(
,)(2
)(
16
1gLVRgL m
0., Vconst
.,0/', 2 constV
[Brans,Dicke, PR 124] [Santos,Gregory, Annals Phys. 258]
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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Scalar-Tensor Theories
Field equations:
□
For Brans-Dicke:
PPN parameters:
Newton’s constant: with
TgVG 8)(
2
2
)32(
400002
1,1
PPNPPN
1
23
24
G
TVV 8'24)(' 2
112107.1 yrG
G
[D.F. Toress, PRD 66]
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Brans-Dicke Cosmology
Friedmann-Robertson-Walker metric:
Friedmann equations:
Scalar-field equation:
Matter equation:
ji
ij dxdxtadtds )(222
2
22
63
8
HH m
HpHH m 2
28
132
22
0332
83
mm pH
3
V
V
d
dVV2
32
2
03 mmm pH
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Inflation in Brans-Dicke Cosmology
[La,Steinhardt PRL 62], [Green, Liddle PRD 54]
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Dark Energy in Brans-Dicke Cosmology
Effective Dark Energy sector:
2
68
3 HDE 8
V
HpDE 2
28
1 2
8
V
DE
DEDE
pw
2
0)(
V
V
[D.F. Toress, PRD 66] E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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Horndeski Theories
Most general 4D scalar-tensor theories having second-order field equations:
5
2i
iH LL
),(][2 XKKL
),(][ 333 XGGL
2
,4444 ),(][ XGRXGGL
2)(36
1),(][
3
,5555 XGGXGGL
[G. Horndeski, Int. J. Theor. Phys. 10 ]
2/ X
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Horndeski Theories
Most general 4D scalar-tensor theories having second-order field equations:
[Nicolis, Rattazzi, Trincherini, PRD 79]
5
2i
iH LL
),(][2 XKKL
),(][ 333 XGGL
2
,4444 ),(][ XGRXGGL
2)(36
1),(][
3
,5555 XGGXGGL
[G. Horndeski, Int. J. Theor. Phys. 10 ]
Coincides with Generalized Galileon theories
bc ,
2/ X
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[Deffayet, Esposito-Farese, Vikman PRD 79]
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Horndeski Cosmology (background)
Field Equations:
In flat FRW:
with
SHRSHL ....
mXXXX
XXXXXX
XGGXHXGGXH
GHGHXXGGXHGHXGHGXKXK
)23(6)25(2
612)(246262
,5,5
2
,5,5
3
,4,4,4,4
2
4
2
,3,3,
mX
XXXX
XXXXXX
pGHXGXHXHXHGHXXHX
GXHGHHHHXGHXXGGH
GXHXXGHGXHXGHGHHGGXK
,5,5
2
,5
,5
22
,5
23
,4,4,4
,4,4,4,4
2
4
2
,3,3
43)(22)(4
4)322(2)2(44)2(2
88412)23(2)(2
PJadt
d
a)(
1 3
3
)(6)23(212)2(626 ,5,5
2
,5,5
3
,4,4,4
2
,3,3, XXXXXXXXXX XGGHXGGXHHXGXGGHGHXGKJ
XXX GXHXGHGHXXHGHHGGXKP ,5
3
,5
2
,4,4
2
,3,3, 26)2(6)2(6)(2
[De Felice,Tsujikawa JCAP 1202]
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Horndeski Cosmology (perturbations)
Scalar perturbations:
No-ghost condition:
No Laplacian instabilities condition:
with
[De Felice,Tsujikawa JCAP 1202]
ji
ij dxdxadtds )21()21( 222
0
3
942
2
2
2311
w
wwwwQS
094
6244232
2311
2
12
2
11214
2
22
2
12
wwww
pwwwwwwwwHwwc mm
S
,5,5,441 222w GHGXXGG XX
,5,5,5,5,5
22
,5
2
,4
2
,4
2
,4,4,44,4
3
,3,3,3,3,,3
18152713626
21675418
63623w
GGHXGGXHGXXGHXH
GXGHXXHGGGXHGGHXH
HGGXGHGXXXKKX
XXXXXXXXX
XXXXXXXXX
XXXXXXX
SHRSHL ....
XXGXGG ,5,544 222w
22
,5,5,5,5
2
,4,4,4,4
2
4,32
45628
2441642w
HXGHGGHXHGX
GXHGGHGXHGXG
XXXX
XXXXX
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Inflation in Horndeski Theories
0,),(),(),( 543
33 GGX
M
cXGVXXK
22
2
1)( mV 4
4
1)( V
[Ohashi,Tsujikawa, JCAP 1210]
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Inflation in Horndeski Theories
G-Inflation (Shift-symmetric):
0,),(),(),( 543
33 GGX
M
cXGVXXK
22
2
1)( mV 4
4
1)( V
[Ohashi,Tsujikawa, JCAP 1210]
0,1
),(,2
),( 54333
2
GGXM
XGM
XXXK
17.0r
[Kobayashi,Yamaguchi,Yokoyama PRL 105] [Banerjee, Saridakis PRD 95] E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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Dark Energy in Horndeski Theories
Background evolution: Universe thermal history
554332 ,1,),(,),( cGGcXGXcXK
[Ali,Gannouji,Sami PRD 82] [Leon, Saridakis JCAP 1303]
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Dark Energy in Horndeski Theories
Background evolution: Universe thermal history
Perturbations:
with
Clustering growth rate:
γ(z): Growth index.
554332 ,1,),(,),( cGGcXGXcXK
[Ali,Gannouji,Sami PRD 82]
),,,,( 543 GGGKGG effeff
mmeffmm GH 42
)(ln
lna
ad
dm
m
[Leon, Saridakis JCAP 1303]
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Fab Four
ringogeorgepauljohnFF LLLLL
GVL johnjohn )(
PVL paulpaul )(
RVL georgegeorge )(
GVL ringoringoˆ)(
][][][ 22
RRRRP
24ˆ RRRRRG
[Charmousis,Copeland,Padilla,Saffin PRL 108]
[Copeland,Padilla,Saffin JCAP 1212] E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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Nonminimal Derivative Coupling
In flat FRW:
rm SSVGgRG
gxdS
)()(
2
1
16
14
rmVH
GH
)(91
23
8 22
2
rm ppV
HHHGHH )(
4321
2832 2
22
[Saridakis,Suskov PRD 81]
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Nonminimal Derivative Coupling – Dark Energy
In flat FRW:
rm SSVGgRG
gxdS
)()(
2
1
16
14
rmVH
GH
)(91
23
8 22
2
rm ppV
HHHGHH )(
4321
2832 2
22
[Saridakis,Suskov PRD 81]
[Dent,Dutta,Saridakis,Xia JCAP 1311]
eVV 0)( nVV 0)(
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Nonminimal Derivative Coupling - Inflation
New Higgs Inflation:
[Skugoreva,Sushkov,Toporensky PRD 88]
[Dalianis,Koutsoumbas,Ntrekis,Papantonopoulos JCAP 1702]
[Germani,Kehagias PRL 105] 05.0r
2
0)( VV
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Beyond Horndeski Theories
Beyond Horndeski, free from Ostrogradski instabilities but still propagating 2+1 dof’s:
with
Primary constraint prevents the propagation of extra degrees of freedom
5
2i
iBH LL
][ 222 ALL H
][]2[ ,32,3333 XCLXCCLL H
X
H 1
2
,444
,42,443444
2][]2[][ galXH
X
HH LX
XBABXCLXCCLBLL
2
21 XLgal
[Gleyzes,Langlois,Piazza,Vernizzi, PRL 114], [Crisostomi,Hull,Koyama,Tasinato, JCAP 1603 ]
2/ X
2
2/5
5,5
,52,553544553
3][]2[][][ galXH
X
HHH LX
AXBXDLXDDLCLGLL
2
23
23
2
32 XLgal
),( XAA ii
),( XBB ii
dXXAC 2/3
33 )(2
1
dXXBC 2/1
,44 )(
dXXBXC 2/3
,55 )(4
1
dXXCD 2/1
,55 )( dXXBG X
2/1
,55 )(
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Bi-scalar Theories
Modified gravity propagating 2+2 dof’s
For
RRRfgxdS ,)(, 24
RRRQRRKRRRf 222 )(,)(,,)(,
geBBGGBKK 32
2,,,,
[Naruko,Yoshida,Mukohyama CQG 33 ]
3
23
23
223
24
4
1ˆ2
1
4
1ˆ
6
1ˆ
2
1ˆ2
1eQeKeQgegRgxdS
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Bi-scalar Theories
Modified gravity propagating 2+2 dof’s
For
eg.:
[Saridakis,Tsoukalas PRD 93 ]
RRRfgxdS ,)(, 24
RRRQRRKRRRf 222 )(,)(,,)(,
3
23
23
223
24
4
1ˆ2
1
4
1ˆ
6
1ˆ
2
1ˆ2
1eQeKeQgegRgxdS
geBBGGBKK 32
2,,,,
BBGBK
,,2
,
HeeDE 66218
1
2
1 33/23/222
663
121
8
1
2
1 23/23/222 eepDE
[Naruko,Yoshida,Mukohyama CQG 33 ]
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Dark Matter – Dark Energy Interaction
Theoretical argument: In principle, since the underlying theory and the microphysics of both dark energy and dark matter is unknown, possible mutual interactions cannot be excluded.
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Dark Matter – Dark Energy Interaction
Theoretical argument: In principle, since the underlying theory and the microphysics of both dark energy and dark matter is unknown, possible mutual interactions cannot be excluded.
Phenomenological argument: Alleviate the coincidence problem: Why are the DE and DM densities nearly equal today, although they scale independently through the expansion history
[Mimoso, Nunes, Pavon, PRD 73] [Billyard, Coley, PRD 61]
[Wang, Gong, Abdalla, PLB 624] [Chen, Gong, Saridakis JCAP 0904]
[Caldera-Cabral, Maartens, Urena-Lopez, PRD 79] [Clifton, Barrow, PRD 73]
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DM – DE Interaction
Assume that DE and DM are effectively described by perfect fluids.
DMSSRG
gxdS
16
14
bS
DMDE
GH
3
82
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DMDMDEDE ppGH 4
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DM – DE Interaction
Assume that DE and DM are effectively described by perfect fluids.
Equations give only the total conservation, namely
If we assume DM conservation, i.e then DE is also conserved:
DMSSRG
gxdS
16
14
0)()()( DM
ab
DE
ab
btot
ab
b TTT
bS
DMDE
GH
3
82
DMDMDEDE ppGH 4
0)( DM
ab
bT 0)( DE
ab
bT
03 DMDMDM pH
03 DEDEDE pH
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DM – DE Interaction
However, it is not forbidden to assume DM – DE interaction by arbitrarily splitting as:
with a phenomenological descriptor of the interaction (positive
corresponds to energy transfer from DE to DM and vice versa).
a
DM
ab
b QT )(
a
DE
ab
b QT )(
aQ aQ
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DM – DE Interaction
However, it is not forbidden to assume DM – DE interaction by arbitrarily splitting as:
with a phenomenological descriptor of the interaction (positive
corresponds to energy transfer from DE to DM and vice versa).
Despite possible pathologies (curvature perturbation blowing up in super-Hubble scales [Valiviita,Majerotto,Maartens, JCAP 0807]) it leads to interesting cosmological behavior.
a
DM
ab
b QT )(
a
DE
ab
b QT )(
aQ
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Phenomenological Models
I)
II)
III)
etc…
DMDMDEDEHQQ 30
DMQQ 0
nnn
DMHQQ 232
0
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Phenomenological Models
I)
II)
III)
etc…
Obtain late time attractors with
DMDMDEDEHQQ 30
1~/ DMDER
DMQQ 0
nnn
DMHQQ 232
0
[Valiviita,Majerotto,Maartens, MNRAS 402] [Chen, Gong, Saridakis JCAP 0904]
[Caldera-Cabral, Maartens, Urena-Lopez, PRD 79]
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More general phenomenological models
with . known
Solve coincidence problem, can lead to intermediate acceleration
DEaHQ )(3 aa 0)( )(aDE
[Chen, Gong, Saridakis JCAP 0904]
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Observational constraints
Impose SNIa, BAO and CMB observational constraints
Incorporate relativistic effects in the large-scale power spectrum.
[Clemson, Koyama, Zhao, Maartens, Valiviita PRD 85]
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[Duniya, Bertacca, Maartens, PRD 91]
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Another approach to phenomenological models
If Q=0 then . Instead of imposing Q one can parametrize its effect assuming:
(perturbations can also be studied; obtain matter overdensity)
3
0 / aDMDM
3
0 /aDMDM [Wang, Meng CQG 22]
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Another approach to phenomenological models
If Q=0 then . Instead of imposing Q one can parametrize its effect assuming:
(perturbations can also be studied; obtain matter overdensity)
H0+SNIa+BAO+CMB
Slight tendency towards interacting DE
δ<0 implies energy flow DM -> DE
3
0 / aDMDM
3
0 /aDMDM [Wang, Meng CQG 22]
[Nunes, Pan, Saridakis PRD 94]
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Lagrangian? Covariant formulation?
Microscopic Lagrangian of DM-DE interaction is unknown. Effective Lagrangians are also absent.
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Lagrangian? Covariant formulation?
Microscopic Lagrangian of DM-DE interaction is unknown. Effective Lagrangians are also absent.
Two interacting fluids:
Covariant approach (two “not-tilted” fluids, i.e with common 4-velocity):
is a current energy density that describes the energy transfer between the fluids
(time dependent due to spacial isotropy)
[Faraoni, Dent Saridakis PRD 90]
QpH 111 3
QpH 222 3
abbaabbaab uquqgpuupT 111
)1(
abbaabbaab uquqgpuupT 222
)2(
cc utq )(
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Lagrangian? Covariant formulation?
Microscopic Lagrangian of DM-DE interaction is unknown. Effective Lagrangians are also absent.
Two interacting fluids:
Covariant approach (two “not-tilted” fluids, i.e with common 4-velocity):
is a current energy density that describes the energy transfer between the fluids
(time dependent due to spacial isotropy)
Imperfect fluids with
Hence, not a robust Lagrangian description for imperfect fluids
[Faraoni, Dent Saridakis PRD 90]
QpH 111 3
QpH 222 3
abbaabbaab uquqgpuupT 111
)1(
abbaabbaab uquqgpuupT 222
)2(
cc utq )(
23)( ii
i pT
b
b
aiiab
b
iiiai
b
baib
b
a
i
ab
b uupuuppuupuuT 222)(
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Lagrangian? Covariant formulation?
Inspired by the Lagrangian formulation of classical dissipative oscillator we can remove the “imperfectness” by transforming the metric as:
baabab uugg 2
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Lagrangian? Covariant formulation?
Inspired by the Lagrangian formulation of classical dissipative oscillator we can remove the “imperfectness” by transforming the metric as:
Hence:
Describes a perfect fluid with and in spacetime metric
: Lagrangian description in a fictitious metric that depends on the fluid
Still not ideal for multiple fluids.
baabab uugg 2
abbaab gpuuppT 22
22 p pp abg
0 ab
bT
pgL
[Faraoni, Dent Saridakis PRD 90]
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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Another approach to phenomenological models
Matter fluid:
are Lagrange multipliers, and are the Lagrange coordinates of the fluid
vector-density particle-number flux
Dark Energy is described by a scalar field:
A
AM sJsngL ,,,),(
A ,, A
J
)(
2
1
VgL
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Another approach to phenomenological models
Matter fluid:
are Lagrange multipliers, and are the Lagrange coordinates of the fluid
vector-density particle-number flux
Dark Energy is described by a scalar field:
DM-DE interaction:
Algebraic coupling:
Derivative Coupling:
Al. coupl.:
Der. Coupl.:
Perturbations, structure formation, quasi-static limit etc
A
AM sJsngL ,,,),(
[Koivisto, Saridakis, Tamanini JCAP 1509]
A ,, A
J
)(
2
1
VgL
A
AM sJsngLL ,,,int ),,(
A
AM sJJsnfsngLL
,,,int ),,(),(
)()( dmTQT
),(nQ
u
n
nfnQ
),(2
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Dark energy - dark matter interaction/unification from generalized Galileons
Most general 4D scalar-tensor theories having second-order field equations:
[Nicolis,Rattazzi,Trincherini, PRD 79]
5
2i
iH LL
),(][2 XKKL
),(][ 333 XGGL
2
,4444 ),(][ XGRXGGL
2)(36
1),(][
3
,5555 XGGXGGL
[G. Horndeski, Int. J. Theor. Phys. 10 ]
Coincides with Generalized Galileon theories
bc ,
2/ X
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
[Deffayet, Esposito-Farese, Vikman PRD 79]
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Dark energy - dark matter interaction/unification from generalized Galileons
Field Equations In flat FRW:
with
mXXXX
XXXXXX
XGGXHXGGXH
GHGHXXGGXHGHXGHGXKXK
)23(6)25(2
612)(246262
,5,5
2
,5,5
3
,4,4,4,4
2
4
2
,3,3,
mX
XXXX
XXXXXX
pGHXGXHXHXHGHXXHX
GXHGHHHHXGHXXGGH
GXHXXGHGXHXGHGHHGGXK
,5,5
2
,5
,5
22
,5
23
,4,4,4
,4,4,4,4
2
4
2
,3,3
43)(22)(4
4)322(2)2(44)2(2
88412)23(2)(2
PJadt
d
a)(
1 3
3
)(6)23(212)2(626 ,5,5
2
,5,5
3
,4,4,4
2
,3,3, XXXXXXXXXX XGGHXGGXHHXGXGGHGHXGKJ
XXX GXHXGHGHXXHGHHGGXKP ,5
3
,5
2
,4,4
2
,3,3, 26)2(6)2(6)(2
[De Felice,Tsujikawa JCAP 1202]
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Dark energy - dark matter interaction/unification from generalized Galileons
In flat FRW:
GXXRgxdS22
1 53
2
2
4
0933 2
53
2
2
2 XHXXXH
023232 2
53
2
2
2 XHXHHXXXHH
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
02
369236
23 23
523
XXHXXHXXHHX
XHX
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Dark energy - dark matter interaction/unification from generalized Galileons
We can rewrite as:
with
Klein-Gordon becomes:
Define Equation-of-State parameter:
3
82 GH
pGH 4
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
03 pH
XHXXX 2
53
2
2 93
XHXHHXXXp 232 2
53
2
2
/pw
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Dark energy - dark matter interaction/unification from generalized Galileons
Shift symmetry allows to write:
with and
)(9)()27(6))(2(3672
)()32()(6)27(2)(12)(
32
5
2
525522
2
2
32
2
2
5252
2
2
fff
fffp
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
2
525 )3(123)( f3 /pw
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Dark energy - dark matter interaction/unification from generalized Galileons
Shift symmetry allows to write:
with and
Allows for a unified description of universe evolution. (Generalized) Chaplygin gas:
)(9)()27(6))(2(3672
)()32()(6)27(2)(12)(
32
5
2
525522
2
2
32
2
2
5252
2
2
fff
fffp
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
2
525 )3(123)( f3
/Ap
03 pH
11
)1(3
000
1
a
AA
1
)1(3
0000
1
a
AAAp
/pw
a
az 01
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Simplest case:
Model I :
53 53
Dark energy - dark matter interaction/unification from generalized Galileons
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
)(362
1
)(366
1
)(2
2
2
2
2
2
zH
zHzw
0,0 52 1w
0,0,0 52
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Dark energy - dark matter interaction/unification from generalized Galileons
Simplest case:
Model I :
we demand and
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
)(362
1
)(366
1
)(2
2
2
2
2
2
zH
zHzw
0,0 52 1w
0,0,0 52
-0.70)w(z 0H0)H(z
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Model II :
55 55
Dark energy - dark matter interaction/unification from generalized Galileons
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
)(6)(9
)(15)(
2
5
2
5
2
2
5
zHzH
zHzw
0,0,0 52
we demand and -0.70)w(z 0H0)H(z
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Model II :
56 56
Dark energy - dark matter interaction/unification from generalized Galileons
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
)(6)(9
)(15)(
2
5
2
5
2
2
5
zHzH
zHzw
0,0,0 52
we demand and -0.70)w(z 0H0)H(z
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Model II :
57 57
Dark energy - dark matter interaction/unification from generalized Galileons
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
)(6)(9
)(15)(
2
5
2
5
2
2
5
zHzH
zHzw
0,0,0 52
580 SN Ia data points
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Model II :
58 58
Dark energy - dark matter interaction/unification from generalized Galileons
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
)(6)(9
)(15)(
2
5
2
5
2
2
5
zHzH
zHzw
0,0,0 52
we demand and -0.70)w(z 0H0)H(z
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Dark energy - dark matter interaction/unification from generalized Galileons
Scalar perturbations:
No-ghost condition:
No Laplacian instabilities condition:
with
[De Felice,Tsujikawa JCAP 1202]
ji
ij dxdxadtds )21()21( 222
0
3
942
2
2
2311
w
wwwwQS
094
6244232
2311
2
12
2
11214
2
22
2
12
wwww
pwwwwwwwwHwwc mm
S
,5,5,441 222w GHGXXGG XX
,5,5,5,5,5
22
,5
2
,4
2
,4
2
,4,4,44,4
3
,3,3,3,3,,3
18152713626
21675418
63623w
GGHXGGXHGXXGHXH
GXGHXXHGGGXHGGHXH
HGGXGHGXXXKKX
XXXXXXXXX
XXXXXXXXX
XXXXXXX
SHRSHL ....
XXGXGG ,5,544 222w
22
,5,5,5,5
2
,4,4,4,4
2
4,32
45628
2441642w
HXGHGGHXHGX
GXHGGHGXHGXG
XXXX
XXXXX
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Model II :
60 60
Dark energy - dark matter interaction/unification from generalized Galileons
[Koutsoumbas,Ntrekis,Papantonopoulos,Saridakis, 1704.08640]
0,0,0 52
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
Healthy scalar perturbations. Necessary to see tensor perturbations, and the speed of gravitational waves.
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61
Conclusions
i) Modification of our knowledge is probably required for the explanation of cosmological evolution.
ii) There is a huge variety of modifications.
iii) Dark Energy (or Modified Gravity) - Dark Matter interaction cannot be excluded, and it can alleviate the coincidence problem.
iv) Many phenomenological approaches. Can become Covariant. A full Lagrangian description is still missing.
v) DE - DM interaction/unification from generalized Galileons with shift-symmetry. Unified universe evolution.
vi) SN Ia data OK. Necessary: Confront with CMB, BAO, and LSS data. Need to add baryonic matter separately. Perform full perturbation analysis, confront with data.
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THANK YOU!
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017