Effective Field Theory approach for Dark Energy/ Modified Gravity. Bin HU BNU

Transcription

1 Effective Field Theory approach for Dark Energy/ Modified Gravity Bin HU BNU NAOC Nov. 2016

2 Outline 1. Evidence of late-time cosmic acceleration 2. Effective Field Theory approach for DE/MG 3. The structure of EFTCAMB 4. Planck-2015 results based on EFTCAMB 5. Conclusion

3 How do we know the Universe is accelerating?

4 It is via Measurement of the distance of far away object What we observed is line of sight integration effect Need to know the intrinsic physics! Standard Standard candle ruler fixed luminosity SNIa credit: WiggleZ team BAO fixed transverse scale

5 SNIa (White dwarf) luminosity module Einstein-DeSitter only CDM+baryon

6 BAO baryonic acoustic oscillation The imprint of sound horizon of Recom epoch on the LSS 100 Mpc 10 Mpc

7 BAO EdS transverse distance scale 100 Mpc 10 Mpc

8 Most simplest explanation LCDM 6 param Early universe ns>1 P(k) ns=1 ns<1 (Harrison-Zeldovich spectrum) 1970s k A_s Amplitude of primordial power spectrum (1E-10) n_s The tilt of the primordial power spectrum (0.96)

9 Most simplest explanation LCDM 6 param Late universe Omega_cdm Fraction of CDM(23%) Omega_b Fraction of baryons (4%) H0 Expansion rate (70 [km/s/mpc]) tau Optical depth of the reionization of hydrogen due to the formation of the first star (0.09), tells us how much percentage of hydrogen is ionised.

10 SN CMB LSS BAO [Planck13 CP paper]

11 Is this the end of story?

12 Tension between high-z and low-z Amplitude matter fluct. at 8 [Mpc/h] matter fluct. Planck (CMB) >> LSS (CFHTLenS) [Planck15-CP paper]

13 Tension between high-z and low-z Lensing amplitude Primary CMB >> Secondary CMB [Planck15-CP paper]

14 Tension between high-z and low-z Mass bias of tsz cluster CMB << LSS [Planck15-SZ paper]

15 Most part is below phantom divide! [Planck15-MG paper]

16 [Planck15-MG paper] GR GR predict, on the large scale, the two gravitational potentials are equal, due to the lack of sources of anisotropic stress!

17 All these motivate us to GR!

18 How to? DE MG Not the math trick of RHS or LHS

19 What do I mean by DE and MG? DE EoS of exotic fluid MG Growth rate of matter fluid LCDM w= w GR z

20 Zeldovich Approximation Continuity eq. Euler eq. Poisson eq. In the linear sub-horizon regime, GR gives The growth rate of CDM only depends on time! The displacement field In GR: CDM particles trajectory is straight line!

21 A video of ZA

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23 Quasic-Static Approx: DE/MG: DE/MG: at linear regime growth rate of CDM depends on the scales! GR: The displacement field

24 Beyond Zeldovich Approximation DE/MG: at linear regime growth rate of CDM depends on the scales! Deflection by the gravitational potential [W. Valkenburg, BH, JCAP 1509 (2015) no.09, 054] Even at linear regime, trajectory of CDM particles are curved!

25 Examples f(r) gravity w ~0.01 n=1 n= ~0.1 ~ B0~1 B0~1 z at most 10% effect! ~0.01 z Most of viable model gives very similar EoS! It is hard to distinguish them via only EoS for the on-going and up-coming surveys! [Hu,Sawicki, PRD 76, (2007)] Need other observables to break the theoretical degeneracy!

26 /5-1 ~ 60% Many k modes!

27 Take home message: Compared with background probe, we should consider perturbation dynamics!

28 2. Effective Field Theory of DE/MG EFT provides a unified parametrisation of the scalar field perturbations in single scalar field DE/MG given background evolution. [Bloomfield et. al. [Gubitosi et. al. JCAP 1302 (2013) * There are 7 independent functions at linear level, EFT functions

29 The logic of construction of the action 1. Choose the time coordinate (clock), by asking (breaking time translation diffemorphism) 2. Build the block of the action by the operators which keep the unbroken 3D spatial Diffs 3. Multiply these operators by a only time dependent function

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31 * relate with background operators, only one are independent * EFT functions depend on time only

32 How we know EFT approach is equivalent to the Covariant approach?

33 Covariant approach p t1 Valid in ALL the gauge t

34 EFT approach p Only Valid in the unitary gauge

35 EFT approach=> Covariant approach Identify pi field: Goldstone boson of breaking time shift symm Stuckburg trick: restore full covariance

36 3. The structure of EFTCAMB We implement the pi field into the Einstein-Boltzmann solver CAMB > EFTCAMB Evolving the full Einstein equation, Klein-Golden equation (pi field), fluid equation (CDM,baryon, massive neutrino),boltzmann hierarchy equation sets (CMB, massless neutrino) [Hu et.al. PRD89,103530(2014); PRD90,043513(2014); PRD91,063524(2015)]

37 Introduction The EFT approach Observational results The next phase EFTCAMB structure v1.0 0: GR code 0: LCDM Standard CAMB 1: wcdm Background DE equation of state: (Flag: EFTwDE) 2: CPL 1: pure EFT Use some parametrized forms for the EFT functions Pure EFT Omega model selection: (Flag: PureEFTmodelOmega) Pure EFT gamma_1 model selection: (Flag: PureEFTmodelGamma1) Pure EFT gamma_2 model selection: (Flag: PureEFTmodelGamma2) Pure EFT gamma_3 model selection: (Flag: PureEFTmodelGamma3) Pure EFT gamma_4 model selection: (Flag: PureEFTmodelGamma4) 0: Zero 1: Constant 2: Linear model 3: Power law model 4: Exponential model EFTCAMB STRUCTURE (Main EFT flag: EFTflag) Pure EFT gamma_5 model selection: (Flag: PureEFTmodelGamma5) Pure EFT gamma_6 model selection: (Flag: PureEFTmodelGamma6) 5: User defined 1: f(r) 2: minimally coupled quintessence 2: designer mapping EFT Use a theory whose background mimics exactly the one specified Mapping EFT model selection: (Flag: MappingEFTmodel) 3: non-minimally coupled quintessence 4: k-essence 5: Brans-Dicke 6: Background DE equation of state: (Flag: EFTwDE) 0: LCDM 1: wcdm 2: CPL... ( B.Hu, MR, N.Frusciante, A.Silvestri, arxiv: : EFTCAMB/EFTCosmoMC: Numerical Notes v1.0 ) Marco Raveri Theoretical Cosmology in the Era of Large Surveys 37

38 Introduction The EFT approach Observational results The next phase EFTCAMB structure v2.0 0: GR code 0: LCDM Standard CAMB 1: wcdm 1: pure EFT Use some parametrized forms for the EFT functions Background DE equation of state: (Flag: EFTwDE) Pure EFT Omega model selection: (Flag: PureEFTmodelOmega) Pure EFT gamma_1 model selection: (Flag: PureEFTmodelGamma1) Pure EFT gamma_2 model selection: (Flag: PureEFTmodelGamma2) Pure EFT gamma_3 model selection: (Flag: PureEFTmodelGamma3) Pure EFT gamma_4 model selection: (Flag: PureEFTmodelGamma4) 2: CPL 3: JBP 4: Turning point 5: Taylor expansion 6: User defined 0: Zero 1: Constant 2: Linear model 3: Power law model 4: Exponential model EFTCAMB STRUCTURE (Main EFT flag: EFTflag) Pure EFT gamma_5 model selection: (Flag: PureEFTmodelGamma5) Pure EFT gamma_6 model selection: (Flag: PureEFTmodelGamma6) Pure EFT Horndeski: (Flag: PureEFTHorndeski) 5: User defined Restricts pure EFT models to Horndeski. Pure EFT choices for gamma_4, gamma_5, gamma_6 will be ignored and handled internally. 1: f(r) 2: minimally coupled quintessence 2: designer mapping EFT Use a theory whose background mimics exactly the one specified Mapping EFT model selection: (Flag: MappingEFTmodel) 3: non-minimally coupled quintessence 4: k-essence 5: Brans-Dicke 6: Background DE equation of state: (Flag: EFTwDE) 0: LCDM 1: wcdm 2: CPL... Planck mass: (Flag: RPHmassPmodel) 3: EFT alternative parametrization Use a parametrization that is mapped to the EFT framework Parametrized EFT model selection: (Flag: AltParEFTmodel) 1: ReParametrized Horndeski... Background DE equation of state: (Flag: EFTwDE) 0: LCDM 1: wcdm 2: CPL Kineticity: (Flag: RPHkineticitymodel) Braiding: (Flag: RPHbraidingmodel) Tensor: (Flag: RPHtensormodel) 0: Zero 1: Constant 2: Power law model 3: User defined 4: full EFT mapping Use a theory by specifying it completely and mapping it to the EFT framework Full EFT mapping model selection: (Flag: FullMappingEFTmodel)... 1: Horava gravity 2: more coming soon! Low-energy Horava gravity Low-energy Horava gravity evading Solar System constraints (Flag: HoravaSolarSystem) ( B.Hu, MR, N.Frusciante, A.Silvestri, arxiv: : EFTCAMB/EFTCosmoMC: Numerical Notes v2.0 ) Marco Raveri Theoretical Cosmology in the Era of Large Surveys 38

39 3.1 Background parametrization EoS EFTCAMB provides 6 different kinds of parametrization of EoS (Flag: EFTwDE), including: LCDM (w=-1), wcdm (w=w0), CPL (w=w0+wa*a),

40 3.2 EFT parametrization: Pure EFT Phenomenological parametrization, e.g.

41 3.2 EFT parametrization: Full mapping designer mapping e.g. Designer f(r) gravity [Song,Hu,Sawicki PRD75:044004,2007] GR limit: B0 > 0, effetive mass > Infty

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43 kinetic friction mass sound speed source Have pass the viability condition:

44 pi field solution: f(r) example pi a

45 CMB spectra example: f(r)

46 Initial Condition for N-body simulations Designer f(r) with LCDM background B0=0.001

47 Designer f(r) with wcdm background B0=0.01 and w=-0.95

48 FalconIC [ [Wessel Valkenburg, BH, arxiv: ]

49 4. Parameter estimation results from EFTCosmoMC and Planck-2015 Designer f(r) CosmoMC >EFTCosmoMC Linear EFT [Planck-2015,MG paper]

50 5. Conclusion EFTCAMB include most of viable single field DE/MG model For scalar field: full perturbative treatment, does not rely on quasistatic approx Support various background, LCDM/wCDM/CPL Check the stability for given parameterization Selected by Planck 2015 data release Selected by Theory Working Group of Euclid

51 Thank you!