Origin of Accelerating Universe: Dark-Energy and Particle Cosmology Yong-Yeon Keum Institute for Early Universe, Ewha Womans Univ, Korea & CTP-BUE in Egypt Talk at WHEPP XI workshop Jan 03, 2010

Motivations: What is the origin of the accelerating Universe What is the origin of the accelerating Universe and Dark-Energy ? and Dark-Energy ? The connection between cosmological observations and particle physics is one of the interesting and hot topic in astro-particle physics. The connection between cosmological observations and particle physics is one of the interesting and hot topic in astro-particle physics. Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to prove neutrino mass with greater precision than current laboratory experiments. Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to prove neutrino mass with greater precision than current laboratory experiments.

Contents Experimental evidence of accelerating universe Experimental evidence of accelerating universe Candidates of Dark Energy Candidates of Dark Energy Neutrino Model of Dark Energy Neutrino Model of Dark Energy (An example of interacting dark matter and dark energy model) (An example of interacting dark matter and dark energy model) Conclusion and discussions on some issues. Conclusion and discussions on some issues.

Breakthrough of 1998: the Winner ASTRONOMY: Cosmic Motion Revealed

Breakthrough of 2003: the Winner Illuminating the Dark Universe

Closed Universe Flat Universe Open Universe Measurement of the geometry AT A GIVEN DISTANCE Known physical sizeangle depends on geometry Known luminosity flux depends on geometry CMB SN Ia

Standard Candle-SNIa

Hubble diagram: Redshift z m = log F + cst = 5 log (H 0 D L ) + M - 5 log H H 0 D L cz z  0 measure of H 0 Large z : measure of  m,   Magnitude m older fainter 1+z = a(t obs )/a(t em ) At a given z Supernova Cosmology Project Accelerated expansion = smaller rate in the past = more time to reach a given z = larger distance of propagation of the photons = smaller flux 

Back to thermal history Density perturbations (inflation?) Nucleosynthesis t = s t ~ 1 mn t ~ yrs Matter: Gravitational collapse Photons: Free propagation observable Galaxies, clustersCMB Recombination: p+e -  H+ 

What Penzias & Wilson saw in 1965

Should the CMB sky be perfectly smooth (or isotropic)? No. Today ’ s Universe is homogeneous and isotropic on the largest scales, but there is a fair amount of structure on small scales, such as galaxies, clusters of galaxies etc. No. Today ’ s Universe is homogeneous and isotropic on the largest scales, but there is a fair amount of structure on small scales, such as galaxies, clusters of galaxies etc.

What are these primordial fluctuations (at the level of 100 micro-Kelvin)?

What are the C ℓ s? Qualitatively: ~power in each multipole mode Qualitatively: ~power in each multipole mode Quantitatively: Quantitatively:

3 regimes of CMB power spectrum Large scale plateau Damping tail Acoustic oscillations

In general…. ↓Ωmh2↓Ωmh2 ↑Ωbh2↑Ωbh2 ← ← Ωm+ΩΛ← ← Ωm+ΩΛ ←Age of Universe ↓z re

Max. scale of anisotropies  Max scale relates to total content of Universe  tot Limited by causality (remember?)  maximum scale

What we know so far Our universe is flat, accelerating. Our universe is flat, accelerating. The dominance of a dark energy component with negative pressure in the present era The dominance of a dark energy component with negative pressure in the present era is responsible for the universe’s accelerated expansion. is responsible for the universe’s accelerated expansion.

Contents of Matter

Title Dark Energy 73% (Cosmological Constant) Neutrinos Neutrinos 0.1  2% 0.1  2% Dark Matter 23% Ordinary Matter 4% (of this only about 10% luminous) 10% luminous)

Perfect fluid – the zeroth-order approximation Einstein Equation geometric structurematter distribution P : pressure : functions of time : energy density

(00): (1) (i i): (2)  (3) Supernova Cosmology Projects (1999): or Quintessence (“Dark Energy”) Einstein’s General Relativity (GR) & Cosmological Principle (CP): Negative Pressure

Puzzles in Accelerating Universe Cosmological Constant Problem: Cosmological Constant Problem: Why is the energy of the vacuum so much small ? Why is the energy of the vacuum so much small ? Dark Energy Puzzle: Dark Energy Puzzle: What is the nature of the smoothly-distributed What is the nature of the smoothly-distributed energy density which appears to determine the universe. energy density which appears to determine the universe. Coincidence Scandal: Coincidence Scandal: Why is the dark energy density approximately equal to the matter density in present epoch. Why is the dark energy density approximately equal to the matter density in present epoch.

Candidates of Dark Energy (A) Cosmological Constant (B) Dynamical Cosmological constant (Time-dependent; Quintessence ) (Time-dependent; Quintessence ) - quintessence: potential term + canonical kinetic term - quintessence: potential term + canonical kinetic term - K-essence: non-canonical kinetic term - K-essence: non-canonical kinetic term - phantom - quintom - Tachyon field - phantom - quintom - Tachyon field (C) Modified Gravity (Modified friedman eq.) (D) Cosmological Back Reaction (E) Others ……

(A)Cosmological Constant Typical scale ： Hence a new energy density is too lower Hence a new energy density is too lower from the particle physics point. from the particle physics point.

Cosmological constant problem Many different contributions to vacuum energies: Many different contributions to vacuum energies: (a) QCD ~ (a) QCD ~ (b) EW physics ~ (b) EW physics ~ (c) GUT ~ (c) GUT ~ (d) SUSY ~ (d) SUSY ~ All these contributions should conspire to cancel down to. Extreme fine tuning !!!

( B ) Quintessence Quintessence = dark energy as a scalar field = dynamical cosmological constant Quintessence = dark energy as a scalar field = dynamical cosmological constant No evidence for evolving smooth energy, but attractive reasons for dynamical origins ! No evidence for evolving smooth energy, but attractive reasons for dynamical origins ! (a) why small, why not zero, why now ??? (a) why small, why not zero, why now ??? (b) suggest the physical cosmological evolution. (b) suggest the physical cosmological evolution. Canonical quintessence: Canonical quintessence:

Quintessence (2) If potential energy dominates over the kinetic energyIf potential energy dominates over the kinetic energy Slow-roll limit: Slow-roll limit: Stiff matter: Stiff matter: Accelerating exp.: Accelerating exp.:

Quintessence Potentials

K-essence Originally kinetic energy driven inflation, called K-inflation [Armendariz-Picon] ; Originates from string theory.  First applied to dark energy by Chiba et al. K-essence is characterized by a scalar field with non- canonical kinetic energy Transformed to the Einstein-frame action:

Phantom(ghost field) Negative sign in the kinetic term;Negative sign in the kinetic term; We obtain forWe obtain for

Quintom Feng,Wang and Zhang proposed a hybrid model of quintessence and Phantom (so the name quintom) quintessence and Phantom (so the name quintom) when while when when while when

Big-Rip Singularity in phantom field Hubble rate diverges as t -> ts, which corresponds to an infinitely large energy density at a finite time in the future. The curvature also glows to infinity. Hubble rate diverges as t -> ts, which corresponds to an infinitely large energy density at a finite time in the future. The curvature also glows to infinity. It should be emphasized that we expect quantum effects to become important when the curvature of universe become large. It should be emphasized that we expect quantum effects to become important when the curvature of universe become large.

Tachyon field (A. Sen) An acclerated expansion occurs for

Chaplygin gas A special case of a tachyon with a constant potential

( C ) Idea of the Modified Gravity Newtonian Cosmology: Newtonian Cosmology: Gravitational Force law determines the evolution Gravitational Force law determines the evolution Combining the above eqs: Moreover, E = constant and decelleration !!

Modified Force For simplicity g=1 (1) Early times t << tc so that matter domination, no acceleration matter domination, no acceleration (2) Later time, t > tc when Accelerated expansion !!! Accelerated expansion !!!

Classification of the Modified Gravity Cardassian : Cardassian : Different brane world scenarios: Different brane world scenarios: a) Dvali, Gabadadze and Porrati (DGP) a) Dvali, Gabadadze and Porrati (DGP) b) Deffayet, Devali and Gabadadez(DDG) b) Deffayet, Devali and Gabadadez(DDG) c) Randall and Sundrum c) Randall and Sundrum d) Shtanov brane Model d) Shtanov brane Model e) non-linear gravity e) non-linear gravity

Candidates of DE (Modified Gravity) Modification of GravityModification of Gravity 1. Modified Newtonian Dynamics (Milgrom. 83) 1. Modified Newtonian Dynamics (Milgrom. 83) 2. Brane Models (Binetaury. 98) 2. Brane Models (Binetaury. 98) 3. Cardassian Expansion (Freese. 02) 3. Cardassian Expansion (Freese. 02)

Top-ten accelerating cosmological Models Akaike information: AIC = -2 lnL + 2d: d = # of model param. Bayesian factor: BIC = -2 lnL + d lnN: N = # of data point used in the fit.

(B,n), (z eq,n) or (  m,n) (B,n), (z eq,n) or (  m,n) Hubble Parameter as Function of z, H=H 0 E(z) Hubble Parameter as Function of z, H=H 0 E(z) The Critical/Matter Density The Critical/Matter Density Parameters of MFE cosmology Observational Constraints on MFE Cosmology

From turnaround redshift z q=0 Observational Constraints on MFE Cosmology z q=0 depends on both of  m and n. (see eq. below)z q=0 depends on both of  m and n. (see eq. below) For each  m, there exists one n peak (  m ), which leads to a maximum of z q=0.For each  m, there exists one n peak (  m ), which leads to a maximum of z q=0. Higher  m is, lower z q=0 is.Higher  m is, lower z q=0 is. For each z q=0, there exists an upper limit for  m, e.g., z q=0 >0.6, then  m 0.6, then  m <0.328.

Observational Constraints on MFE Cosmology The thick solid line is z q=0.The thick solid line is z q=0. The cross-hatched area is the present optimistic  m = The cross-hatched area is the present optimistic  m = The dashed lines are  m =0.2 and 0.4 respectively.The dashed lines are  m =0.2 and 0.4 respectively. The shaded area gives 0.6 < z q=0 <1.7.The shaded area gives 0.6 < z q=0 <1.7. From turnaround redshift z q=0 Zhu & Fujimoto 2004, ApJ, 602, 12

Observational Constraints on MFE Cosmology A  2 minimization method is used to determine (  m,n). A  2 minimization method is used to determine (  m,n). The best fit happans at (  m,n)=(0.38,-0.20).The best fit happans at (  m,n)=(0.38,-0.20). The 68.3% and 95.4% confidence level in the (  m,n) plane are shown.The 68.3% and 95.4% confidence level in the (  m,n) plane are shown. Zhu, Fujimoto & He 2004, ApJ, 603,365 From SNeIa and Fanaroff-Riley type IIb radio galaxies

A Brane World Model (BWM): DGP A self-accelerating 5-dimensional BWM A self-accelerating 5-dimensional BWM With a noncompact, infinite volume extra dimension With a noncompact, infinite volume extra dimension An ordinary 5-dimensional Einstein-Hilbert action An ordinary 5-dimensional Einstein-Hilbert action A 4-dimensional Ricci scalar term induced on the brane A 4-dimensional Ricci scalar term induced on the brane Dvali, Gabadadze & Porrati 2000

Comments: MFE is an alternative to DE as acceleration mechanism. Combinations of current astronomical data can provide stringent constraints on its model parameters. MFE is an alternative to DE as acceleration mechanism. Combinations of current astronomical data can provide stringent constraints on its model parameters. MFE cosmology can not be the mechanism for acceleration starting from z > 1.0. MFE cosmology can not be the mechanism for acceleration starting from z > 1.0. DGP model is disfavored by current SNeIa and f gas of galaxy clusters. DGP model is disfavored by current SNeIa and f gas of galaxy clusters.

Equation of State (EoS) W = p/ r It is really difficult to find the origin of dark-energy with non-interacting dark-energy scenarios.

Summary of EoS Canada-France-Hawaii Wide Synoptic Survey: Canada-France-Hawaii Wide Synoptic Survey: w o < based on cosmic share data alone w o < based on cosmic share data alone Supernova Lagacy Survey (SNLS): Supernova Lagacy Survey (SNLS): Combined with SDSS measurement of BAO Combined with SDSS measurement of BAO WMAP3 and WMAP5 data: WMAP3 and WMAP5 data: 1) assume flat universe with SNLS data: 1) assume flat universe with SNLS data: 2) Drop prior of flat universe, WMAP+LSS+SNLS data: 2) Drop prior of flat universe, WMAP+LSS+SNLS data:

Interacting Dark-Energy models o interacting between dark-matter and dark-energy: (Farrar and Peebles, 2004) o interacting between photon and dark-energy: (Feng et al., 2006; Liu et al., 2006) o interacting between neutrinos and dark-energy: (Zhang et al, Fardon et al. 2004, yyk and Ichiki, 2006,2008)

S Lee. IoPAS Models of Interacting DE-Photon Coupled Quintessence (S.L, K.Olive, M.Pospelov, 04) Coupled Quintessence (S.L, K.Olive, M.Pospelov, 04) Potentials : Potentials : Coupling : Coupling :

S Lee. IoPAS Evolution of Background I

S Lee. IoPAS57 Evolution of Background

S Lee. IoPAS58 Time Varying Alpha (Late time)

10 Motivations for Interacting DE-Massive Neutrinos: Why does the mass scale of neutrinos so small ? Why does the mass scale of neutrinos so small ? about eV ~ Eo: accidental or not ? about eV ~ Eo: accidental or not ? If not accidental, are there any relation between Neutrinos and Dark Energy ? If not accidental, are there any relation between Neutrinos and Dark Energy ?

Interacting dark energy model Example At low energy, The condition of minimization of V tot determines the physical neutrino mass. n v m v  Scalar potential in vacuum Interacting Neutrino-Dark-Energy Model

Mass Varying Neutrino Model Zhang et al, Fardon,Kaplan,Nelson,Weiner: PRL93, 2004 Fardon, Nelson and Weiner suggested that Fardon, Nelson and Weiner suggested that tracks the energy density in neutrinos tracks the energy density in neutrinos The energy density in the dark sector has two-components: The energy density in the dark sector has two-components: The neutrinos and the dark-energy are coupled because it is assumed that dark energy density is a function of the mass of the neutrinos: The neutrinos and the dark-energy are coupled because it is assumed that dark energy density is a function of the mass of the neutrinos:

Since in the present epoch, neutrinos are non-relativistic (NR), Since in the present epoch, neutrinos are non-relativistic (NR), Assuming dark-energy density is stationary w.r.t. variations in the neutrino mass, Assuming dark-energy density is stationary w.r.t. variations in the neutrino mass, Defining Defining

Lessons: Wanted neutrinos to probe DE, but actually are DE. Wanted neutrinos to probe DE, but actually are DE.  flat scalar potential (log good) choice,  flat scalar potential (log good) choice, m v < few eV. m v < few eV. Neutrino mass scales as m v ~ 1/n v : Neutrino mass scales as m v ~ 1/n v : - lighter in a early universe, heavier now - lighter in a early universe, heavier now - lighter in clustered region, heavier in FRW region - lighter in clustered region, heavier in FRW region - lighter in supernovae - lighter in supernovae Couplings of ordinary matter to such scalars strongly Couplings of ordinary matter to such scalars strongly constrained – must be weaker than Planck: 1/M pl constrained – must be weaker than Planck: 1/M pl

b The FNW scenario is only consistent, If there is no kinetic contributions (K=0) and the dark-energy is a pure running cosmological constant !!

Theoretical issue: Adiabatic Instability problem: Afshordi et al Gravitational collapse Gravitational collapse Kaplan, Nelson, Weiner 2004 Kaplan, Nelson, Weiner 2004 Khoury et al Khoury et al Zhao, Xia, X.M Zhang 2006 Zhao, Xia, X.M Zhang 2006 Always positive sound velocity Always positive sound velocity No adiabatic instability No adiabatic instability Brookfield et al, Brookfield et al, YYK and Ichiki, 2007, 2008 YYK and Ichiki, 2007, 2008

Background Equations: We consider the linear perturbation in the synchronous Gauge and the linear elements: Perturbation Equations: K. Ichiki and YYK:2007

The impact of Scattering term:

Varying Neutrino Mass Mn=0.9 eVMn=0.3 eV With full consideration of Kinetic term V( f )=Vo exp[- lf ]

W_eff Mn=0.9 eVMn=0.3 eV

Neutrino Masses vs z

Mn=0.9 eV

Mn=0.3eV

Neutrino mass effects After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than their free streaming scale. After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than their free streaming scale. The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non- relativistic. The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non- relativistic.  Pm(k)/Pm(k) = -8 Ω /Ω m  Pm(k)/Pm(k) = -8 Ω /Ω m Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering when Ω  h^2 > (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at Ω h^2 = Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering when Ω  h^2 > (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at Ω h^2 =

Mass Power spectrum vs Neutrino Masses

Power spectrum P m (k,z) = P * (k) T 2 (k,z) Transfer Function: P m (k,z) = P * (k) T 2 (k,z) Transfer Function: T(z,k) :=  (k,z)/[  (k,z=z * )D(z * )] T(z,k) :=  (k,z)/[  (k,z=z * )D(z * )] Primordial matter power spectrum (Ak n ) Primordial matter power spectrum (Ak n ) z * := a time long before the scale of interested have entered z * := a time long before the scale of interested have entered in the horizon in the horizon Large scale: T ~ 1 Large scale: T ~ 1 Small scale : T ~ 0.1 Small scale : T ~ 0.1  P m (k)/P m (k) ~ -8 Ω / Ω m  P m (k)/P m (k) ~ -8 Ω / Ω m = -8 f = -8 f

Numerical Analysis

Within Standard Cosmology Model (LCDM)

Power-spectrum (LSS) Mn=0.9 eVMn=0.3 eV

Constraints from Observations

Neutrino mass Bound: M n < % C.L.

WMAP3 data on Ho vs W

Neutrino Mass Bounds Without Ly-alpha Forest data (only 2dFGRS + HST + WMAP3) Omega_nu h^2 < ; (inverse power-law potential) Omega_nu h^2 < ; (inverse power-law potential) < ; (sugra type potential) < ; (sugra type potential) < ; ( exponential type potential) < ; ( exponential type potential) provides the total neutrino mass bounds provides the total neutrino mass bounds M_nu < 0.45 eV (68 % C.L.) M_nu < 0.45 eV (68 % C.L.) < 0.87 eV (95 % C.L.) < 0.87 eV (95 % C.L.) Including Ly-alpah Forest data Omega_nu h^2 < ; (sugra type potential) Omega_nu h^2 < ; (sugra type potential) corresponds to corresponds to M_nu < 0.17 eV (68 % C.L.) M_nu < 0.17 eV (68 % C.L.) < 0.43 eV (95 % C.L.) < 0.43 eV (95 % C.L.)

Questions How can we test mass-varying neutrino model in Exp. ? How can we test mass-varying neutrino model in Exp. ? --- by the detection of the neutrino mass variation in space via neutrino oscillations. --- by the detection of the neutrino mass variation in space via neutrino oscillations. --- by the measurement of the time delay of the neutrino emitted from the short gamma ray bursts. --- by the measurement of the time delay of the neutrino emitted from the short gamma ray bursts. How much this model can be constrainted from, BBN, CMB, Matter power spectrum observations ? How much this model can be constrainted from, BBN, CMB, Matter power spectrum observations ?

Solar mass-varying neutrino oscillation V.Barger et al: hep-ph/ ;PRL2005 M.Cirelli et al: hep-ph/ The evolution eq. in the two-neutrinos framework are: The evolution eq. in the two-neutrinos framework are: e -e forward scattering amplitude: e -e forward scattering amplitude: Model dependence in the matter profiles: Model dependence in the matter profiles: - k parameterize the dependence of the neutrino mass on n e -  i is the neutrino mass shift at the point of neutrino production.

MaVaN results:

Conclusions-1 Neutrinos are best probe of SM into DE sector Neutrinos are best probe of SM into DE sector Possible origin for dark energy Possible origin for dark energy Motivates consideration of new matter effects to Motivates consideration of new matter effects to be seen in oscillations: be seen in oscillations: - LSND interpretation - LSND interpretation - Matter/air analyses - Matter/air analyses - Solar MaVaN oscillation Effects - Solar MaVaN oscillation Effects - time delay in the gamma ray bursts. - time delay in the gamma ray bursts.

Conclusions-2 Neutrinoless double beta decays can provides very important properties of neutrinos: Dirac or majorana particles; neutino mass information; Neutrinoless double beta decays can provides very important properties of neutrinos: Dirac or majorana particles; neutino mass information; mass-hierarchy pattern. mass-hierarchy pattern. In conclusion, results of precision analysis of CMB and LSS data don’t follow only from data, but also can rely on theoretical assumptions. In conclusion, results of precision analysis of CMB and LSS data don’t follow only from data, but also can rely on theoretical assumptions. Prospects: Prospects: Future measurements of gravitational lensing of CMB light and/or of photon generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, it might be possible to see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scale. Future measurements of gravitational lensing of CMB light and/or of photon generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, it might be possible to see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scale.  This could allow us to discriminate between normal and inverted neutrino mass hierarchy.

When the neutrino masses are not constant, but vary as a function of time and space, CPT violation occurs naturally even in thermal equilibrium. When the neutrino masses are not constant, but vary as a function of time and space, CPT violation occurs naturally even in thermal equilibrium. CPTV helps to understand the matter-antimatter asymmetry of the universe CPTV helps to understand the matter-antimatter asymmetry of the universe -> spontaneous Baryon Asymmetry -> spontaneous Baryon Asymmetry However, since the laboratory experimental limit on the CPTV in electrons is so stringent that the induced CPTV in neutrino sector will be much below the sensitivity for the current and future experiments. However, since the laboratory experimental limit on the CPTV in electrons is so stringent that the induced CPTV in neutrino sector will be much below the sensitivity for the current and future experiments.

Summary of Methods to Obtain Neutrino Masses Single beta decay   m i 2 |U ei | 2 Sensitivity 0.2 eV Double beta decay m  = |    m i |U ei | 2  i |  i = Majorana phases Sensitivity 0.01 eV Neutrino oscillations  m 2 = m m 2 2 Observed ~ eV 2 Cosmology     m i Observed ~ 0.1 eV Only double beta decay is sensitive to Majorana nature.

Search for the origin of Dark-Energy with Large Scale Structures Baryon Acoustic Oscillation (BAO) Baryon Acoustic Oscillation (BAO) Galaxy Cluster surveys (GL) Galaxy Cluster surveys (GL) Supernova type Ia surveys (SNIa) Supernova type Ia surveys (SNIa) Weak Lensing surveys (WL) Weak Lensing surveys (WL)

luminosity distance-redshift relation: luminosity distance-redshift relation: angular distance-redshift relation: angular distance-redshift relation: volume-redshift relation: volume-redshift relation: linear growth-redshift relation: linear growth-redshift relation: ways to measure dark energy

Dark Energy Probes by LSS samples ProbeMeasurementsRemarks supernovae (SN) GRB(?) GRB(?) dL(z)dL(z)dL(z)dL(z) standard candle evolution effects clusters (CL) QSO’s Ly-alpha absorption d A (z), V (z), & g(z) g(z) standard samples. identifications ( mass—observable relation nonlinear evolution (mass function,..) bias nonlinear evolution, UV photon background baryon acoustic oscillation (BAO) d A (z) & V (z) standard ruler relation between dark matter and galaxies weak Lensing (WL) d A (z) & g(z) How to calibrate Systematic errors

Power of combining techniques

Concordance CMB LSS Expected precision with JDEM (>2013)

Cosmological weak lensing Cosmological weak lensing present z=zs z=zl z= 0 past Large-scale structure Arises from total matter clustering Arises from total matter clustering Note affected by galaxy bias uncertainty Note affected by galaxy bias uncertainty Well modeled based on simulations (current accuracy <10%, White & Vale 04) Well modeled based on simulations (current accuracy <10%, White & Vale 04) Tiny 1-2% level effect Tiny 1-2% level effect Intrinsic ellipticity per galaxy, ~30% Intrinsic ellipticity per galaxy, ~30% Needs numerous number (10^8) of galaxies for the precise measurement Needs numerous number (10^8) of galaxies for the precise measurement

Weak Lensing Tomography- Method

Warning ! In conclusion, results of precision analysis of CMB and LSS data don ’ t follow only from data but also rely on theoretical assumptions. Prospects: Future measurements of gravitational lensing of CMB light and/or of light generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, it might be possible to see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scale.  This could allow us to discriminate between normal and inverted neutrino mass hierachy.

Thanks Thanks For For your attention!

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