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...
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
Why Modification?
Knowledge of Physics: Standard Model
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
Why Modification?
Knowledge of Physics: Standard Model + General Relativity
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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]
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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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13
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
[Deffayet, Esposito-Farese, Vikman PRD 79]
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15
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]
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45
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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47
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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48
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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49
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
54
54
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
59
59
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
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
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.
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.
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017
62
THANK YOU!
E.N.Saridakis – 9th Aegean, Sifnos. Sept 2017