Dark Matter Dark Energy Interactions

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

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

E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Why Modification? Knowledge of Physics: Standard Model

E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Why Modification? Knowledge of Physics: Standard Model + eneral Relativity

E.N.Saridakis 9 th Aegean Sifnos. Sept 07 Why Modification? Universe istory:

Modified ravity en. Proca Non-minimal gravitymatter coupling 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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 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

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

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

Inflation in Brans-Dicke Cosmology [asteinhardt PR 6] [reen iddle PRD ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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

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 ] [ [. 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]

orndeski Cosmology background Field Equations: In flat FRW: with R S S.... m K K 6 6 6 6 m p K 8 8 P J a dt d a 6 6 6 K J K P 6 6 6 [De FeliceTsujikawa JCAP 0] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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 8 8 6 K K 6 6 6 6 6 7 j 7 6.. S R.. S 8 0 w [De FeliceTsujikawa JCAP 0] 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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

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

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

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

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

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

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

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

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

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

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 6 6 8 / / 6 6 8 / / e e p DE [NarukoYoshidaMukohyama CQ ] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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]

8 8 Dark energy - dark matter interaction/unification from generalized alileons Field Equations In flat FRW: with m K K 6 6 6 6 m p K 8 8 P J a dt d a 6 6 6 K J K P 6 6 6 [De FeliceTsujikawa JCAP 0] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

9 9 Dark energy - dark matter interaction/unification from generalized alileons In flat FRW: R g x d S 0 9 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis 70.0860] 0 6 9 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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 70.0860] 0 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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 70.0860] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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 70.0860] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

Simplest case: Model I : Dark energy - dark matter interaction/unification from generalized alileons w z 0 w 0 0 0 6 0 6 6 z z [KoutsoumbasNtrekisPapantonopoulosSaridakis 70.0860] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

Dark energy - dark matter interaction/unification from generalized alileons Simplest case: Model I : we demand w z 0 w 0 0 0 6 0 6 6 z z wz 0-0.7 and z 0 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis 70.0860] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

Dark energy - dark matter interaction/unification from generalized alileons Model II : 0 0 0 z w z 9 z 6 z we demand wz 0-0.7 and z 0 0 [KoutsoumbasNtrekisPapantonopoulosSaridakis 70.0860] E.N.Saridakis 9 th Aegean Sifnos. Sept 07

Dark energy - dark matter interaction/unification from generalized alileons Model II : 0 0 0 z w z 9 z 6 z 80 SN Ia data points [KoutsoumbasNtrekisPapantonopoulosSaridakis 70.0860] 7 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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 8 8 6 K K 6 6 6 6 6 7 j 7 6.. S R.. S 8 0 w [De FeliceTsujikawa JCAP 0] 9 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

Dark energy - dark matter interaction/unification from generalized alileons Model II : 0 0 0 ealthy scalar perturbations. Necessary to see tensor perturbations and the speed of gravitational waves. [KoutsoumbasNtrekisPapantonopoulosSaridakis 70.0860] 60 E.N.Saridakis 9 th Aegean Sifnos. Sept 07

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

TANK YOU! 6 E.N.Saridakis 9 th Aegean Sifnos. Sept 07