Shant Baghram. Séminaires de l'iap. IPM-Tehran 13 September 2013

Transcription

1 Structure Formation: à la recherche de paramètre perdu Séminaires de l'iap Shant Baghram IPM-Tehran 13 September 013 Collaborators: Hassan Firoujahi IPM, Shahram Khosravi Kharami University-IPM, Mohammad Hossien Namjoo IPM, Nareg Mirathuny Sharif University of technology, Hosien Moshafi Institute in Advance Studies in Basic Sciences arxiv: arxiv: , arxiv: JCAP

2 Content of the tal: 6 parameter standard Cosmology model and open Questions Accelerated Expansion of the Universe Modified gravity as a source of accelerated expansion Initial Conditions Non-Gaussian, Anisotropic inflationary models and LSS Simultaneous effect of MG and NG inflationary models Conclusion and further remars

3 Cosmology in Bacground Cosmology is a Science of measuring two quantities Alan Sandage, Physics Today 1970 H,q Geometrical tests of Bacground Cosmology We are measuring distances in the Universe Standard candles Standard Rulers d L H G aa q a d H

4 Bacground is boring: Cosmology with Perturbations Precision Cosmology with perturbations T T ~ 10 5 R g n g R n n g g Planc 013

5 The Tale of two Power Spectrums Establishment of standard model of Cosmology

6 The tale of two standard model A Universe is made up of Baryons 5% Standard Model of Particles Cold Dar Matter 7% Dar Energy 68% Known as CDM with Initial Conditions Gaussian, isotropic, adiabatic and scale invariant A n s b c h h

7 3 Questions for 1th Century 1Why is the Universe accelerating? Dar Energy What is Missing Matter? Dar Matter 3What is the physics of early Universe? Inflation Large Scale Structure can address these three questions. We will need to add free parameters to our nown 6

8 Content of the tal: 6 parameter standard Cosmology model and open Questions Accelerated Expansion of the Universe Modified gravity as a source of accelerated expansion Initial Conditions Non-Gaussian, Anisotropic inflationary models and LSS Simultaneous effect of MG and NG inflationary models Conclusion and further remars

9 How to explain the Accelerated Expansion of the Universe? Cosmological Principle +CDM/baryons+ GR

10 How to explain the Accelerated Expansion of the Universe? Cosmological Principle +CDM/baryons+ GR Does the Cosmological Constant cause the acceleration of the Universe? Old-new Cosmological constant problem

11 How to explain the Accelerated Expansion of the Universe? Cosmological Principle +CDM/baryons + GR Cosmological Principle: Homogenous and Isotropic Universe Non homogenous Universe

12 How to explain the Accelerated Expansion of the Universe? Cosmological Principle +CDM/baryons + GR Is Dar Energy a dynamical exotic entity e.g. quintessence, -essence,? w DE p DE DE w DE w 0 w a 1 w 0 w a ~ 0.01 ~ 0.1 Euclid goal Planc 013

13 How to explain the Accelerated Expansion of the Universe? Cosmological Principle +CDM/baryons + GR Is GR the correct classical theory of Gravity? Modification of GR e.g. fr gravities

14 What we mean by Modified Gravity? Model Dar Matter Problem Dar Energy Problem CDM MG e.g. MOND CDM CDM. Cosmological Constant Cosmological Constant MG Quintessence.

15 Modified Gravity Massive Gravity Models Brane Cosmology Models DGP, fr models fr that evade solar system tests by screening mechanism fr=r - μ /R fr=r-λ

16 Why fr gravity? Modified gravity Theories and where the scale dependence come? F R F M, 3, 1 4 m S m g R f g x d S R R f F

17 Large Scale Structure Formation : GR vs MG Distribution of luminous matter Correlation functions-power spectrum, cluster count BAO Wea Gravitational Lensing SNIa: distance measurements CMB lensing 1 cm ISW

18 Statistical Properties of our Universe We need to define the two point correlation function as: where the correlation function is the excess of particles from randomness. Where power-spectrum is the Fourier transform of correlation function as: r x x r b b x x 3 P D

19 Correlation function and Power Spectrum of matter

20 What is the matter Power-Spectrum? The matter power spectrum nowing: P, in present time can be found by

21 What is the matter Power-Spectrum? The matter power spectrum nowing: 1Primordial power spectrum: P, in present time can be found by encoded in spectral index and the amplitude of perturbations A,n s

22 What is the matter Power-Spectrum? The matter power spectrum nowing: 1Primordial power spectrum: P, in present time can be found by encoded in spectral index and the amplitude of perturbations A,n s Physics of baryons, photons and CDM and the evolution of modes during equality and horion crossing. T

23 What is the matter Power-Spectrum? The matter power spectrum nowing: 1Primordial power spectrum: P, in present time can be found by encoded in spectral index and the amplitude of perturbations Physics of baryons, photons and CDM and the evolution of modes during equality and horion crossing. T 3The Evolution of density contrast due to expansion of universe A,n s D P, A ns T D D 0

24 What is the matter Power-Spectrum? The matter power spectrum nowing: 1Primordial power spectrum: P, in present time can be found by encoded in spectral index and the amplitude of perturbations Physics of baryons, photons and CDM and the evolution of modes during equality and horion crossing. T 3The Evolution of density contrast due to expansion of universe A,n s D P, A ns T D Growth function D 0

25 How do we find the growth rate D? G 8GT ds dt a t dx ij i dx j

26 How do we find the growth rate D? G 8GT ds dt a t dx ij i dx j Linear Perturbation theory: 1The perturbed metric : 10 degrees of freedom and the gauge g g g 00 0i ij x, t 1 x, t x, t 0 x, t a 1 x, t ij G 8G T x 4Ga

27 How do we find the growth rate D? Linear Perturbation theory: G 8G T 1The perturbed metric : 10 degrees of freedom and the gauge g g g G 8GT 00 0i ij x, t 1 x, t x, t 0 x, t a 1 x, t ij ds dt x a t dx ij 4Ga i dx j T Energy-momentum tensor of perturbations p u u pg q u v q u T T T i i i T c s i 0 1 v i

28 What are the players of linear Perturbation theory? Geometry terms t, x t, x Energy momentum terms t, x. v gauge issue: gauge-invariant quantities

29 Equations you have to Solve! T ; 0 G 8G T [ pressure garvity] 0 H 4G c cs H [ a s 4G ] 0 bacground Law of gravity D 0

30 Growth function: MG vs GR GR D 0 m H 4G m m 0 We choose Hu-Sawici model f R R We choose the free parameter of the model: f0 RR 1 0 m H 4G, m eff m m 0 f growth d d ln ln a

31 Scale dependent Growth rate 0, 1 3, 1 / 1,, 0 0 G G H H f H d dh f d df eff m growth growth growth

32 Scale dependent Growth rate N. Mirathuny, Sh. Khosravi, SB and H.Moshafi arxiv: , 1 3, 1 / 1,, 0 0 G G H H f H d dh f d df eff m growth growth growth R R R R f f

33 Scale dependent Growth rate N. Mirathuny, Sh. Khosravi, SB and arxiv: H.Moshafi 0, 1 3, 1 / 1,, 0 0 G G H H f H d dh f d df eff m growth growth growth

34 Scale dependent Growth rate by Euclid 0, 1 3, 1 / 1,, 0 0 G G H H f H d dh f d df eff m growth growth growth

35 Discussion Modified gravity theories introduce a scale dependence in growth of the structures. What other cosmological effects can introduce a scale dependence growth?

36 Content of the tal: 6 parameter standard Cosmology model and open Questions Accelerated Expansion of the Universe Modified gravity as a source of accelerated expansion Initial Conditions Non-Gaussian, Anisotropic inflationary models and LSS Simultaneous effect of MG and NG inflationary models Conclusion and further remars

37 3 Questions for 1 Centaury 1Why is the Universe accelerating? Dar Energy What is Missing Matter? Dar Matter 3What is the physics of early Universe? Inflation Non Gaussianity + Anisotropy can introduce a scale dependence behavior in the growth of the structures through bias.

38 Planc Results Deviation from a single field Inflationary models? Non-Gaussianity Multi-fields, non Bunch Davis vacuum, entropic perturbations, loc equi f NL ortho f 5 39 NL f NL

39 Is there a room for Non Gaussianity NG? Anisotropy introduce a NG Mohammad Hossein Namjoo, Shant Baghram, Hassan Firoujahi: arxiv: LSS observations to detect NG in sub-cmb scales. Scale dependence of NG Non-trivial NG shapes Planc 013

40 CMB and Anisotropy CMB anomalies 1Cold Spot hemispherical asymmetry 3 alignment of quadrupole and octupole 4 Power deficiency in low multipoles Measure problem

41 Intrinsic Anisotropy of CMB Geometric origin, vector fields, long mode modulation P 1/ R, x P 1/ iso R, x 1 A LM Y LM nˆ Planc 013

42 Anisotropic- Non Gaussian Bias Anisotropic Inflationary model: Squeeed Wavenumber direction 3 Preferred direction SB, Mohammad Hossien Namjooi, Hassan Firoujahi JCAP

43 Anisotropic- Non Gaussian Bias Anisotropic Inflationary model: The direction dependent bispectrum Where the free parameter g shows itself in: SB, Mohammad Hossien Namjooi, Hassan Firoujahi JCAP

44 Where we can find the signature of Early Universe?

45 Where we can find the signature of Early Universe? CMB f Nl 3000 f NL 0 Komatsu, Spergel 001

46 Finger Print of Inflationary Physics in LSS 1 Galaxy Power Spectrum The Bispectrum of galaxy distributions 3 Number of rare objects in Universe 4The Bias parameter Non linear Structure formation Dalal et al. 008; Desjacques, Selja & Iliev 009; Slosar et al. 008; Matarrese & Verde 008; Nishimichi et al. 009

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48 Bias What we observe in the Universe is the luminous matter b, x g h X cosmolog y local m P b g P m

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50 1 PDF e x x M R

51 How to find bias for a general NG density field Intrinsic halo bias via bacground model mass function modification nm b l and nm h bm n M

52 What does Non Gaussianity do to bias!!! Type equation here. 3

53 Bias in Pea Bacground splitting There is an intrinsic bias nown as halo bias: b, We can split the perturbations to large-scale and small scale h m 1 s l And the halo number contrast is obtained as: Long wavelength mode R.Scoccimarro et al.phys. Rev. D 85,

54 The effect of NG on PDF The PDF and Cumulates are effected by NG potential NG field PDF depend on higher cumulatses and als0othey depend to NG field. The first term of Taylor Expansion, is the linear bias :

55 How Non-Gaussianity effect this: The PDF and Cumulates are effected by NG potential The Scale dependence bias Shows UP in second term of Taylor Expansion, introduced by bispectrum

56 Can we see the anisotropic NG effects in LSS? b NG f bl 1 c M, T D NL Cˆ 3, nˆ M, 0 5 H 0 m Observation direction 3 Preferred direction

57 Can we see the anisotropic NG effects in LSS? Non Gaussianity + Anisotropy can introduce a scale dependence behavior in the growth of the structures through bias Observation direction 3 Preferred direction

58 Content of the tal: 6 parameter standard Cosmology model and open Questions Accelerated Expansion of the Universe Modified gravity as a source of accelerated expansion Initial Conditions Non-Gaussian, Anisotropic inflationary models and LSS Simultaneous effect of MG and NG inflationary models Conclusion and further remars

59 Redshift Space distortion The peculiar velocity dependents on mass distribution v ihf Where f is the growth rate and bias parameter appears in: v ih f b g f b

60 Redshift Space distortion f b The galaxy distances are mainly measured by they redshift. And the redshift include the Peculiar Velocity of galaxies. n r dv n P s r r dv u r du dr P 1 r

61 Simultaneous effect of MG and NG, 1 M b f b MG c L NL NG 0 0, 5, m MG eff MG H D T G G M

62 Simultaneous effect of MG and NG Redshift Space distortion,, b f First part of the tal Second part of the tal, 1 M b f b MG c L NL NG 0 0 5, m MG eff MG H D T G G M 0, 1 3, 1 1,, 0 0 G G H H f H H f f eff m

63 Simultaneous effect of MG and NG Redshift Space distortion f, b,

64 Galaxy Power Spectrum Luminous Red galaxies of SDSS as a test For galaxy power Spectrum

65 Galaxy growth rate Complementary observation : Galaxy growth rate The redshift space distortion parameter is an observable, We need N-body simulations for MG theories to determine the bias parameter.

66 Conclusion and future prospects Anisotropic inflationary: candidate to address the CMB anomalies. Anisotropic initial conditions introduce a scale dependent, direction dependent bias parameter. There is a degeneracy between Modified gravity theories and anisotropic NG initial conditions because of redshift space distortion parameter. We need complementary observations to brea the degeneracy. We need N-body simulations for MG theories We need Euclid-lie Observations for more statistics

67 Than You