Dark Matter Dark Energy Interactions
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1 E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Dark Matter Dark Energy Interactions Emmanuel N. Saridakis Physics Department National and Technical University of Athens reece Physics Department Baylor University Texas USA
2 oal 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 9 th Aegean Sifnos. Sept 07
3 E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Why Modification? Knowledge of Physics: Standard Model
4 E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Why Modification? Knowledge of Physics: Standard Model + eneral Relativity
5 E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Why Modification? Universe istory:
6 Modified ravity en. Proca Non-minimal gravitymatter coupling 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
7 7 Scalar-Tensor Theories Add a scalar field: Conformal Transf. to Jordan frame: 6 g h s R f g m g g h E.N.Saridakis 9 th Aegean Sifnos. Sept 07
8 8 Scalar-Tensor Theories Add a scalar field: Conformal Transf. to Jordan frame: Redefinition of : Brans-Dicke for R for 6 g h s R f g m g g h 6 g V R g m. 0 V const. 0 / ' V const [BransDicke PR ] [Santosregory Annals Phys. 8] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
9 Scalar-Tensor Theories Field equations: V g 8 T ' V V ' 8 T For Brans-Dicke: PPN parameters: PPN PPN 0000 Newton s constant: with [D.F. Toress PRD 66].7 0 yr 9 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
10 Brans-Dicke Cosmology Friedmann-Robertson-Walker metric: ds dt a t dx ij i dx j Friedmann equations: 8 V m 6 8p m Scalar-field equation: 8 m pm 0 V V dv d Matter equation: m p 0 m m 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
11 Inflation in Brans-Dicke Cosmology [asteinhardt PR 6] [reen iddle PRD ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
12 Dark Energy in Brans-Dicke Cosmology Effective Dark Energy sector: DE 8 6 V 8 p DE 8 V 8 w DE p DE DE V V 0 [D.F. Toress PRD 66] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
13 orndeski Theories Most general D scalar-tensor theories having second-order field equations: i i ] [ K K ] [ ] [ R 6 ] [ [. orndeski Int. J. Theor. Phys. 0 ] / E.N.Saridakis 9 th Aegean Sifnos. Sept 07
![orndeski Theories Most general D scalar-tensor theories having second-order field equations: [Nicolis Rattazzi Trincherini PRD 79] i i ] [ K K ] [ ] [ R 6 ] [ [.](/docs-images/85/92726164/images/14-0.jpg "orndeski Int. J. Theor. Phys. 0 ] Coincides with eneralized alileon theories b c / E.N.Saridakis 9 th Aegean Sifnos.")
14 orndeski Theories Most general D scalar-tensor theories having second-order field equations: [Nicolis Rattazzi Trincherini PRD 79] i i ] [ K K ] [ ] [ R 6 ] [ [. orndeski Int. J. Theor. Phys. 0 ] Coincides with eneralized alileon theories b c / E.N.Saridakis 9 th Aegean Sifnos. Sept 07 [Deffayet Esposito-Farese Vikman PRD 79]
15 orndeski Cosmology background Field Equations: In flat FRW: with R S S.... m K K m p K 8 8 P J a dt d a K J K P [De FeliceTsujikawa JCAP 0] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
16 orndeski Cosmology perturbations Scalar perturbations: No-ghost condition: No aplacian instabilities condition: with w w w ds i dt a dx dx ij w w w 9w Q S 0 w w w w w ww w w w 6w m pm cs w w w 9w K K j S R.. S 8 0 w [De FeliceTsujikawa JCAP 0] 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
17 Inflation in orndeski Theories K V 0 c M [OhashiTsujikawa JCAP 0] V V m 7 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
18 8 8 Inflation in orndeski Theories -Inflation Shift-symmetric: 0 M c V K m V V [OhashiTsujikawa JCAP 0] 0 M M K 0.7 r [KobayashiYamaguchiYokoyama PR 0] [Banerjee Saridakis PRD 9] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
19 Dark Energy in orndeski Theories K c c c Background evolution: Universe thermal history [AliannoujiSami PRD 8] [eon Saridakis JCAP 0] 9 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
20 Dark Energy in orndeski Theories K c c c Background evolution: Universe thermal history [eon Saridakis JCAP 0] Perturbations: with eff eff m m eff K m m Clustering growth rate: γz: rowth index. d ln d ln a m m a [AliannoujiSami PRD 8] 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
21 Fab Four FF john paul george ringo john Vjohn paul Vpaul P george Vgeorge R ringo V ringo ˆ P ˆ R R [CharmousisCopelandPadillaSaffin PR 08] R R [ ] R [ ] R [ ] R R R [CopelandPadillaSaffin JCAP ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
22 Nonminimal Derivative Coupling In flat FRW: S m S r V g R g x d S 6 r m V 9 8 r p m p V 8 [SaridakisSuskov PRD 8] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
23 Nonminimal Derivative Coupling Dark Energy In flat FRW: S m S r V g R g x d S 6 r m V 9 8 r p m p V 8 [SaridakisSuskov PRD 8] [DentDuttaSaridakisia JCAP ] e V V 0 n V V 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
![0 [ermanikehagias PR 0] V V 0](/docs-images/85/92726164/images/24-3.jpg "[SkugorevaSushkovToporensky PRD 88]")
24 Nonminimal Derivative Coupling - Inflation New iggs Inflation: r 0.0 [ermanikehagias PR 0] V V 0 [SkugorevaSushkovToporensky PRD 88] [DalianisKoutsoumbasNtrekisPapantonopoulos JCAP 70] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
25 Beyond orndeski Theories Beyond orndeski free from Ostrogradski instabilities but still propagating + dof s: with Primary constraint prevents the propagation of extra degrees of freedom i B i [ ] A ] [ ] [ C C C ] [ ] [ ] [ gal B A B C C C B gal [leyzesangloispiazzavernizzi PR ] [CrisostomiullKoyamaTasinato JCAP 60 ] / / ] [ ] [ ] [ ] [ gal A B D D D C gal A A i i B B i i d A C / d B C / d B C / d C D / d B / E.N.Saridakis 9 th Aegean Sifnos. Sept 07
26 6 6 Bi-scalar Theories Modified gravity propagating + dof s For R R R f g x d S R R Q R R R K R R R f g e B B B K K [NarukoYoshidaMukohyama CQ ] ˆ ˆ 6 ˆ ˆ e Q e K e Q g e g R g x d S E.N.Saridakis 9 th Aegean Sifnos. Sept 07
27 7 7 Bi-scalar Theories Modified gravity propagating + dof s For eg.: [SaridakisTsoukalas PRD 9 ] R R R f g x d S R R Q R R R K R R R f ˆ ˆ 6 ˆ ˆ e Q e K e Q g e g R g x d S g e B B B K K B B B K e e DE / / / / e e p DE [NarukoYoshidaMukohyama CQ ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
28 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. 8 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
29 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 [Billyard Coley PRD 6] [Mimoso Nunes Pavon PRD 7] [Wang ong Abdalla PB 6] [Chen ong Saridakis JCAP 090] [Caldera-Cabral Maartens Urena-opez PRD 79] [Clifton Barrow PRD 7] 9 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
30 S DM DE Interaction d x g R S 6 S DM Assume that DE and DM are effectively described by perfect fluids. 8 DE DE p DE DM DM p DM S b 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
31 S DM DE Interaction d x g R S 6 S DM Assume that DE and DM are effectively described by perfect fluids. 8 DE DE p DE DM DM p Equations give only the total conservation namely DM S b b T tot ab b DE DM T T 0 ab ab If we assume DM conservation i.e b T DM 0 then DE is also conserved: DM DE DM pdm 0 p 0 DE DE ab b DE Tab 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
32 DM DE Interaction owever it is not forbidden to assume DM DE interaction by arbitrarily splitting as: b DM Tab Qa b with T Q DE ab Qa a a phenomenological descriptor of the interaction positive corresponds to energy transfer from DE to DM and vice versa. Qa E.N.Saridakis 9 th Aegean Sifnos. Sept 07
33 DM DE Interaction owever it is not forbidden to assume DM DE interaction by arbitrarily splitting as: b DM Tab Qa b with T Q DE ab Q a a 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- ubble scales [ValiviitaMajerottoMaartens JCAP 0807] it leads to interesting cosmological behavior. E.N.Saridakis 9 th Aegean Sifnos. Sept 07
34 Phenomenological Models I Q Q 0 DE DE DM DM II Q Q 0 DM III Q etc Q 0 n n n DM E.N.Saridakis 9 th Aegean Sifnos. Sept 07
35 Phenomenological Models I Q Q 0 DE DE DM DM II Q Q 0 DM III Q etc Q 0 n n n DM Obtain late time attractors with R DE / DM ~ [Chen ong Saridakis JCAP 090] [ValiviitaMajerottoMaartens MNRAS 0] [Caldera-Cabral Maartens Urena-opez PRD 79] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
36 More general phenomenological models Q a with a. DE a known DE a 0 Solve coincidence problem can lead to intermediate acceleration [Chen ong Saridakis JCAP 090] 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
37 Observational constraints Impose SNIa BAO and CMB observational constraints [Clemson Koyama Zhao Maartens Valiviita PRD 8] Incorporate relativistic effects in the large-scale power spectrum. [Duniya Bertacca Maartens PRD 9] 7 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
38 Another approach to phenomenological models If Q=0 then DM / a DM 0. Instead of imposing Q one can parametrize its effect assuming: DM DM 0 / a perturbations can also be studied; obtain matter overdensity [Wang Meng CQ ] 8 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
39 Another approach to phenomenological models If Q=0 then DM / a DM 0. Instead of imposing Q one can parametrize its effect assuming: DM 0 / a perturbations can also be studied; obtain matter overdensity DM [Wang Meng CQ ] 0+SNIa+BAO+CMB Slight tendency towards interacting DE δ<0 implies energy flow DM -> DE [Nunes Pan Saridakis PRD 9] 9 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
40 agrangian? Covariant formulation? Microscopic agrangian of DM-DE interaction is unknown. Effective agrangians are also absent. 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
41 agrangian? Covariant formulation? Microscopic agrangian of DM-DE interaction is unknown. Effective agrangians are also absent. Two interacting fluids: p Q p Q Covariant approach two not-tilted fluids i.e with common -velocity: T T p u aub p gab qaub qbua p u aub p gab qaub qbua ab ab c c q t u is a current energy density that describes the energy transfer between the fluids time dependent due to spacial isotropy [Faraoni Dent Saridakis PRD 90] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
42 agrangian? Covariant formulation? Microscopic agrangian of DM-DE interaction is unknown. Effective agrangians are also absent. Two interacting fluids: p Q p Q Covariant approach two not-tilted fluids i.e with common -velocity: T T p u aub p gab qaub qbua p u aub p gab qaub qbua ab ab c c q t u is a current energy density that describes the energy transfer between the fluids Imperfect fluids with b T i ab u a time dependent due to spacial isotropy u b b p i T u i a u p b b ence not a robust agrangian description for imperfect fluids i i b b i a pi pi i u bua pi i u a ub [Faraoni Dent Saridakis PRD 90] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
43 agrangian? Covariant formulation? Inspired by the agrangian formulation of classical dissipative oscillator we can remove the imperfectness by transforming the metric as: g ab g ab u a u b E.N.Saridakis 9 th Aegean Sifnos. Sept 07
44 agrangian? Covariant formulation? Inspired by the agrangian formulation of classical dissipative oscillator we can remove the imperfectness by transforming the metric as: g ab g ab u a u b ence: T ab p p u aub pgab Describes a perfect fluid with p and p p in spacetime metric b T ab 0 gab g p : agrangian description in a fictitious metric that depends on the fluid Still not ideal for multiple fluids. [Faraoni Dent Saridakis PRD 90] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
45 Matter fluid: Another approach to phenomenological models M g A are agrange multipliers and A J vector-density particle-number flux Dark Energy is described by a scalar field: A n s J s A are the agrange coordinates of the fluid g V E.N.Saridakis 9 th Aegean Sifnos. Sept 07
46 6 6 Another approach to phenomenological models Matter fluid: are agrange multipliers and are the agrange 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 A M s J s n g [Koivisto Saridakis Tamanini JCAP 09] A A J V g A A M s J s n g int A A M s J J s n f s n g int dm T Q T n Q u n n f n Q E.N.Saridakis 9 th Aegean Sifnos. Sept 07
47 7 7 Dark energy - dark matter interaction/unification from generalized alileons Most general D scalar-tensor theories having second-order field equations: [NicolisRattazziTrincherini PRD 79] i i ] [ K K ] [ ] [ R 6 ] [ [. orndeski Int. J. Theor. Phys. 0 ] Coincides with eneralized alileon theories b c / E.N.Saridakis 9 th Aegean Sifnos. Sept 07 [Deffayet Esposito-Farese Vikman PRD 79]
48 8 8 Dark energy - dark matter interaction/unification from generalized alileons Field Equations In flat FRW: with m K K m p K 8 8 P J a dt d a K J K P [De FeliceTsujikawa JCAP 0] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
49 9 9 Dark energy - dark matter interaction/unification from generalized alileons In flat FRW: R g x d S [KoutsoumbasNtrekisPapantonopoulosSaridakis ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
50 Dark energy - dark matter interaction/unification from generalized alileons We can rewrite as: 8 p with p 9 Klein-ordon becomes: p 0 Define Equation-of-State parameter: w p / [KoutsoumbasNtrekisPapantonopoulosSaridakis ] 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
51 Dark energy - dark matter interaction/unification from generalized alileons Shift symmetry allows to write: p f 7 6 f f 7 6 f 6 7 f 9 f with f and w p / [KoutsoumbasNtrekisPapantonopoulosSaridakis ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
52 Dark energy - dark matter interaction/unification from generalized alileons Shift symmetry allows to write: p f 7 6 f f 7 6 f 6 7 f 9 f with f and w p / Allows for a unified description of universe evolution. eneralized Chaplygin gas: p A/ p 0 0 A0 p 0A0 A A a 0 0 A a 0 a0 z a [KoutsoumbasNtrekisPapantonopoulosSaridakis ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
53 Simplest case: Model I : Dark energy - dark matter interaction/unification from generalized alileons w z 0 w z z [KoutsoumbasNtrekisPapantonopoulosSaridakis ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
54 Dark energy - dark matter interaction/unification from generalized alileons Simplest case: Model I : we demand w z 0 w z z wz and z 0 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
55 Dark energy - dark matter interaction/unification from generalized alileons Model II : z w z 9 z 6 z we demand wz and z 0 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07
56 Dark energy - dark matter interaction/unification from generalized alileons Model II : z w z 9 z 6 z we demand wz and z 0 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis ] 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
57 Dark energy - dark matter interaction/unification from generalized alileons Model II : z w z 9 z 6 z 80 SN Ia data points [KoutsoumbasNtrekisPapantonopoulosSaridakis ] 7 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
58 Dark energy - dark matter interaction/unification from generalized alileons Model II : z w z 9 z 6 z we demand wz and z 0 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis ] 8 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
59 Dark energy - dark matter interaction/unification from generalized alileons Scalar perturbations: No-ghost condition: No aplacian instabilities condition: with w w w ds i dt a dx dx ij w w w 9w Q S 0 w w w w w ww w w w 6w m pm cs w w w 9w K K j S R.. S 8 0 w [De FeliceTsujikawa JCAP 0] 9 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
60 Dark energy - dark matter interaction/unification from generalized alileons Model II : ealthy scalar perturbations. Necessary to see tensor perturbations and the speed of gravitational waves. [KoutsoumbasNtrekisPapantonopoulosSaridakis ] 60 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
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 ravity - Dark Matter interaction cannot be excluded and it can alleviate the coincidence problem. iv Many phenomenological approaches. Can become Covariant. A full agrangian description is still missing. v DE - DM interaction/unification from generalized alileons with shiftsymmetry. Unified universe evolution. vi SN Ia data OK. Necessary: Confront with CMB BAO and SS data. Need to add baryonic matter separately. Perform full perturbation analysis confront with data. 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
62 TANK YOU! 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07
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