11

Cosmologia em Tempo-RealCosmologia em Tempo-Realcomcom

Efeito Sandage Efeito Sandage ee

Paralaxe CósmicaParalaxe Cósmica

Miguel QuartinMiguel QuartinInstituto de FísicaInstituto de Física

Univ. Federal do Rio de JaneiroUniv. Federal do Rio de Janeiro

USP – Out 2011USP – Out 2011

22

Dark Energy in 2 slidesDark Energy in 2 slides Observational evidence for dark energy:Observational evidence for dark energy:

Cosmic Background Radiation (CMB) →Cosmic Background Radiation (CMB) → Nobel Prize 2006Nobel Prize 2006 Supernovae →Supernovae → Nobel Prize 2011Nobel Prize 2011 Matter power spectrum in large scale structureMatter power spectrum in large scale structure Age of the Universe > age of oldest starsAge of the Universe > age of oldest stars Baryon Acoustic OscillationsBaryon Acoustic Oscillations

A universe with only A universe with only standard model particlesstandard model particles + + dark dark mattermatter cannot explain cannot explain anyany of the above! of the above!

33

Dark Energy Dark Energy in 2 slidesin 2 slides

N.B.: BAO →N.B.: BAO →Baryon Acoustic Baryon Acoustic Oscillations ↔Oscillations ↔matter power matter power spectrumspectrum

­m + ­¤ = 1¡ ­k :

:

44

SupernovaeSupernovaeType Ia SupernovaeType Ia Supernovae

55

100

25

Type Ia Supernovae (2)Type Ia Supernovae (2) Standardizable candlesStandardizable candles

66

Cosmic Microwave Background Cosmic Microwave Background Radiation (CMB)Radiation (CMB)

Oldest photons in the Universe: redshift Oldest photons in the Universe: redshift z ~ 1100z ~ 1100 Nearly-isotropic 2.725 K radiationNearly-isotropic 2.725 K radiation

Anisotropies: ~ 1 part in 10Anisotropies: ~ 1 part in 1055

Temperature of CMB 13.6 eV (ionization of H)↔Temperature of CMB 13.6 eV (ionization of H)↔

77

CMB (2)CMB (2) Angular power spectrum ( spher. harmon. decompos.)↔Angular power spectrum ( spher. harmon. decompos.)↔

88

Matter Power Spectrum (linear)Matter Power Spectrum (linear)

Initial conditions Initial conditions (CMB) (CMB)

++ linear linear perturbation perturbation theory theory

small scales

large scales

99

Matter Power Spectrum (non-linear)Matter Power Spectrum (non-linear)

1010

Baryon Acoustic OscillationsBaryon Acoustic Oscillations

1111

Baryon Acoustic Oscillations (2)Baryon Acoustic Oscillations (2)

1212

Baryon Acoustic Oscillations (3)Baryon Acoustic Oscillations (3)

1313

Dark Energy: the 3-fold way outDark Energy: the 3-fold way out

Usual 2 ways of explaining dark energy:Usual 2 ways of explaining dark energy:

Actually, there is a Actually, there is a thirdthird way out! way out! Keep Einstein theory and “normal” (cold + baryonic) matterKeep Einstein theory and “normal” (cold + baryonic) matter Change the Change the metricmetric

Modified Gravity New fundamental fieldsΛ, f(R), f(G), Unimodular, DGP, Horava-Lifshitz, extra dimensions, Einstein-Aether, degravitation, Cardassian, branes, strings...

Quintessence, Quartessence, K-essence, Chaplygin gas, interacting fields, n-Forms,vector fields, Braiding fields...

G¹º = 8¼G T¹ºperfect °uid :

1414

Homogeneity and IsotropyHomogeneity and Isotropy The most basic (and old) tenets of cosmologyThe most basic (and old) tenets of cosmology

Friedmann-Lemaître Robertson Walker (FLRW) metric:Friedmann-Lemaître Robertson Walker (FLRW) metric: most general homogeneous and isotropic metricmost general homogeneous and isotropic metric overwhelmingly successful at describing the universe in overwhelmingly successful at describing the universe in

large-scaleslarge-scales ConsistentConsistent with all current observations with all current observations

Hard to probe directly →Hard to probe directly → lightconelightcone vs. vs. const. timeconst. time slices: slices: Possibility Possibility →→ more exotic models may also be more exotic models may also be consistentconsistent

with datawith data e.g.: void models; e.g.: void models; anisotropic models; ...anisotropic models; ...

ds2 = ¡dt2 + a2(t)

1¡ kr2 dr2 + r2a2(t)d­2 :

:

1515

Homogeneity?Homogeneity? LTB metric (spher. symmetric, inhomogeneous) Gpc →LTB metric (spher. symmetric, inhomogeneous) Gpc →

Void modelsVoid models

SurprinsinglySurprinsingly successful as an accelerating model without successful as an accelerating model without Dark Energy;Dark Energy;

Can fit all observations in the light cone SNe, BAO & CMBCan fit all observations in the light cone SNe, BAO & CMB But may fail for observations inside the light cone (kSZ, But may fail for observations inside the light cone (kSZ,

redshift drift & CMB blackbody spectrum)redshift drift & CMB blackbody spectrum)

Quartin, Amendola 0909.4954 (PRD)Caldwell, Stebbins 0711.3459 (PRL)Zhang, Stebbins 1009.3967 (PRL)

Marra, Notari 1102.1015 (CQG)

ds2 = ¡dt2 + [R0(t; r)]2

1¡ k(r) dr2 + R2(t; r)d­2 :

1616

Isotropy?Isotropy? People usually consider People usually consider 2 possible anisotropies2 possible anisotropies

ShearShear VorticityVorticity

But there is a 3But there is a 3rdrd type of anisotropy: (spatial) type of anisotropy: (spatial) curvature curvature anisotropyanisotropy Basically: the 3-curvature can be different in different Basically: the 3-curvature can be different in different

directionsdirections There exists aniso. curv. models which areThere exists aniso. curv. models which are

HomogenousHomogenous IrrotationalIrrotational Shear-freeShear-free

Are we taking supposed symmetries Are we taking supposed symmetries too seriouslytoo seriously??

Koivisto, Mota, Quartin, Zlosnik 1006.3321 (PRD)

1717

Precision CosmologyPrecision Cosmologyvs.vs.

Accurate CosmologyAccurate Cosmology

1%

1818

Void ModelsVoid Models Huge (Gpc) voids can mimic the Hubble diagram Huge (Gpc) voids can mimic the Hubble diagram

withoutwithout the need for the need for dark energydark energy!! Acceleration Acceleration →→ artifactartifact of wrong assumption on of wrong assumption on

homogeneityhomogeneity Not over complicatedNot over complicated Could arise from Could arise from

back-reaction effects back-reaction effects → → one of many bubblesone of many bubbles eternal inflation scenarioseternal inflation scenarios … … ??

Isotropic, if observer is in the centerIsotropic, if observer is in the center No No a priori a priori reason for that reason for that → → unlikelyunlikely!!

1919

Lemaître-Tolman-Bondi modelsLemaître-Tolman-Bondi models LTB metrics describe LTB metrics describe void modelsvoid models

Exact solution in a matter-dominated eraExact solution in a matter-dominated era

R0 ´ @R

@r:

:

R(t; r) = (cosh ´ ¡ 1)®(r)

2k(r)

t =(sinh ´ ¡ ´) ®(r)

2k(r)3=2:

:

ds2 = ¡dt2 + [R0(t; r)]2

1¡ k(r) dr2 + R2(t; r)d­2 :

2020

LTB models (2)LTB models (2) Void matter density profileVoid matter density profile

z = 0

2121

LTB models (3)LTB models (3) Hubble parameter is no longer uniqueHubble parameter is no longer unique

R0 ´ @R

@r:

:

Baryon Acoustic Oscillation signal depends on Baryon Acoustic Oscillation signal depends on HH||||

SNe observations are only related to SNe observations are only related to HH⊥⊥

Hjj =1

R0@R0

@t; H? =

1

R

@R

@t:

:

García-Bellido & Haugbolle: 0802.1523 (JCAP)

ds2 = ¡dt2 + [R0(t; r)]2

1¡ k(r) dr2 + R2(t; r)d­2 :

2222

Constraints on Void ModelsConstraints on Void Models Voids which are too large (> 3 Gpc) are in conflict withVoids which are too large (> 3 Gpc) are in conflict with

CMB blackbody spectrum CMB blackbody spectrum Caldwell & Stebbins: 0711.3459 (PRL) Caldwell & Stebbins: 0711.3459 (PRL)

Kinematic Sunyaev-Zeldovich eKinematic Sunyaev-Zeldovich effectffect from large clusters from large clusters García-Bellido & Haugbolle: 0807.1326 (JCAP)García-Bellido & Haugbolle: 0807.1326 (JCAP)

kSZ at small scales due to free ekSZ at small scales due to free e __

Zhang & Stebbins 1009.3967Zhang & Stebbins 1009.3967 Recent work:Recent work:

Biswas, Notari & Valkenburg:Biswas, Notari & Valkenburg:1007.30651007.3065

Marra & Notari: 1102.1015Marra & Notari: 1102.1015

2323

The Redshift DriftThe Redshift Drift Even in Even in ΛΛCDM, the redshift CDM, the redshift z z of a source is not constant of a source is not constant

The evolution of The evolution of zz was first estimated by Sandage in was first estimated by Sandage in 1962!1962!

This effect is called This effect is called Redshift-Drift Redshift-Drift (or Sandage effect)(or Sandage effect) Model dependent!Model dependent!

Very accurate spectroscopy can be used to distinguish Very accurate spectroscopy can be used to distinguish between such models.between such models.

Uzan, Clark & Ellis, 0801.0068 (PRL)

Balbi & Quercellini, 0704.2350 (MNRAS)

¢tzs = H0¢t0

µ1 + zs ¡

H(zs)

H0

¶:

2424

2525

E-ELT and CODEX in 1 slideE-ELT and CODEX in 1 slide

Gilmozzi & Spyromilio, The Messenger 127, 11 (2007)

J. Liske et al., 0802.1532 (MNRAS)

European Extremely Large telescope (E-ELT):European Extremely Large telescope (E-ELT): Estimated completion: 2020-22Estimated completion: 2020-22 Aperture (diameter): Aperture (diameter): 39-42m39-42m Type: optical to mid-infraredType: optical to mid-infrared Cost: ~1 B€ (including 1Cost: ~1 B€ (including 1stst generation instruments) generation instruments) BrazilBrazil is joining ESO! is joining ESO!

Cosmic Dynamics Experiment (CODEX):Cosmic Dynamics Experiment (CODEX): High resolution super-stable spectrograph in E-ELTHigh resolution super-stable spectrograph in E-ELT Precursor in VLT (2014): ESPRESSOPrecursor in VLT (2014): ESPRESSO (Echelle SPectrograph for (Echelle SPectrograph for

Rocky Exoplanet- and Stable Spectroscopic Observations)Rocky Exoplanet- and Stable Spectroscopic Observations)

2626

Redshift Drift in Dark Energy Redshift Drift in Dark Energy modelsmodels

Balbi & Quercellini, 0704.2350 (MNRAS)

2727

Redshift Drift Redshift Drift in LTBin LTB

The Sandage Effect The Sandage Effect (or redshift drift) in (or redshift drift) in LTB is LTB is very very differentdifferent from from ΛΛCDM!CDM!

10 years

5 years

15 yearsQuartin & Amendola 0909.4954 (PRD)

M odel 5 year s 10 years 15 yearsModels I / I I 1:1¾ 6:2¾ 12:5¾

cGBH Model :5¾ 4:3¾ 9:2¾

:

2828

Gaia in 1 slideGaia in 1 slide

Cost: ~ 700Cost: ~ 700M € M €

Broad scientific goalsBroad scientific goals

Allows us to Allows us to detectdetect large-scale deviations from isotropy large-scale deviations from isotropy through observations ofthrough observations of proper motions of quasars proper motions of quasars

GaiaGaia for cosmologists: for cosmologists: astrometry measurements with an astrometry measurements with an

accuracy of about accuracy of about 10 – 200 10 – 200 μμasas astrometric measurements of some astrometric measurements of some

500,000+500,000+ distant quasars distant quasarsLaunch: 2013

Quercellini, Quartin & Amendola 0809.3675 (PRL)

Quercellini, Cabella, Amendola, Quartin & Balbi 0905.4853 (PRD)

2929

The Cosmic Parallax effectThe Cosmic Parallax effect

In a FRW metric, In a FRW metric, ΔΔttγγ ≡≡ γγ22 – – γγ11 = 0. = 0.

In any anisotropic metric, however, ΔIn any anisotropic metric, however, Δttγ γ ≠≠ 0, and we have 0, and we have cosmic parallax.cosmic parallax.

3030

20 years

10 years

30 years

Cosmic Parallax Cosmic Parallax with Gaiawith Gaia

Off-center distance →Off-center distance → 30 Mpc30 Mpc..

Quartin & Amendola 0909.4954 (PRD)

M odel 20 years 30 year s

Model I 1:8¾ 4:9¾

Model II :5¾ 2:2¾

cGBH Model :6¾ 2:6¾

:

3131

SNe off-center dist. d→SNe off-center dist. d→ obsobs ≤≤ 15%15% of void radius of void radius (~250 Mpc)(~250 Mpc)

CMB dipole off-c. dist. d→CMB dipole off-c. dist. d→ obsobs ≤≤ 2%2% of void radius of void radius (~30 Mpc)(~30 Mpc)

Cosmic Parallax with Gaia (2)Cosmic Parallax with Gaia (2)

Off-center distance constrains (Mpc)Off-center distance constrains (Mpc)

M odel 6 year s 10 years 20 years

Model I 143 66 23

Model II 235 109 39

cGBH Model 214 99 35

:

3232

Cosmic Parallax in other modelsCosmic Parallax in other models The cosmic parallax effect is sensitive to “any kind” of The cosmic parallax effect is sensitive to “any kind” of

anisotropy anisotropy (technically, to the (technically, to the shearshear);); Measurement of Measurement of late-time anisotropylate-time anisotropy!! Primordial anisotropy gets diluted with expansionPrimordial anisotropy gets diluted with expansion

Present anisotropy →Present anisotropy → anisotropic pressure fieldanisotropic pressure field!! Overall effect can be Overall effect can be higherhigher in, e.g., Bianchi I in, e.g., Bianchi I Different anisotropic models Different anisotropic models → → different different multipole multipole

dependencedependence;;

Koivisto & MotaarXiv:0707.0279 (ApJ)arXiv:0801.3676 (JCAP)

3333

The “Bianchi I” MetricThe “Bianchi I” Metric Bianchi I metricBianchi I metric

Flat, no overall vorticityFlat, no overall vorticity

Non-zero shearNon-zero shear

ds2 = ¡dt2 + a2(t)dx2 + b2(t)dy2 + c2(t)dz2

§x ´ HxH

¡ 1 6= 0

H ´ 1

abc

d

dt

¡abc¢

3434

Cosmic Parallax in Bianchi ICosmic Parallax in Bianchi I~ 0.2 μas / year

Quercellini, Cabella, Amendola, Quartin & Balbi 0905.4853 (PRD)

3535

Anisotropies in Cosmology (2)Anisotropies in Cosmology (2)

People usually consider People usually consider 2 possibilities2 possibilities ShearShear VorticityVorticity

But there is a 3But there is a 3rdrd type of anisotropy: (spatial) type of anisotropy: (spatial) curvature curvature anisotropyanisotropy 3-curvature can be different in different directions3-curvature can be different in different directions There exists aniso. curv. models which areThere exists aniso. curv. models which are

HomogenousHomogenous IrrotationalIrrotational Shear-freeShear-free

NO Cosmic Parallax!NO Cosmic Parallax!

3636

CP and the CMB DipoleCP and the CMB Dipole CMB Dipole assumed to be ~ →CMB Dipole assumed to be ~ → 99%99% due to our own due to our own

peculiar velocity;peculiar velocity;

No bulk motion No bulk motion between Quasars and CMBbetween Quasars and CMB

Reasonable, but how do we test this?Reasonable, but how do we test this? Look at other diffuse backgrounds!Look at other diffuse backgrounds!

E.g.: cosmic rays, X-rays, gamma-rays, FIRE.g.: cosmic rays, X-rays, gamma-rays, FIR Very hard to isolate the background!Very hard to isolate the background!

Look at off-diagonal CMB correlations!Look at off-diagonal CMB correlations!

Amendola, Catena, Masina, Notari, Quartin & Quercellini 1008.1183

3737

CP and the CMB Dipole (2)CP and the CMB Dipole (2) Gaia in 6 years with 1,000,000 QSOs Gaia in 6 years with 1,000,000 QSOs (preliminary)(preliminary)::

Measure pec. veloc. with Measure pec. veloc. with ΔΔv = v = ±± 150 – 250 km/s 150 – 250 km/s 2 – 3σ2 – 3σ distinction between “tilted universe” & standard model distinction between “tilted universe” & standard model

Quartin & Atrio-Barandela (in prep)

3838

Real-Time CosmologyReal-Time Cosmology Cosmic parallax and the Sandage Effect are but two of Cosmic parallax and the Sandage Effect are but two of

the recently proposed the recently proposed Real-Time CosmologyReal-Time Cosmology observable observable effects.effects.

Quercellini, Amendola, Balbi, Cabella & Quartin (1011.2646)

radialradial transverse

redshift drift cosmic parallax

peculiaracceleration

properacceleration

global (velocity)

local(acceleration)

3939

Real-Time Cosmology (2)Real-Time Cosmology (2)radialradial transverse

redshift drift

cosmic parallax

peculiaracceleration

properacceleration

global (velocity)

local(acceleration)

Pecul. accel. measure →Pecul. accel. measure → accel. of stars inside Milky Way →accel. of stars inside Milky Way →e.g. distinguish between Newton or MoNDe.g. distinguish between Newton or MoND

Proper accel. measure dz/dt objects in a cluster → → →Proper accel. measure dz/dt objects in a cluster → → →independent measure of mass (no need to assume independent measure of mass (no need to assume virializationvirialization))

Amendola, Quercellini & Balbi 0708.1132 (Phys.Lett.B)

Quercellini, Amendola, Balbi, Cabella & Quartin (1011.2646)

4040

ConclusionsConclusions LTB is less symmetric than FLRWLTB is less symmetric than FLRW

FLRW less symmetric than static universeFLRW less symmetric than static universe

Redshift-drift competitive consistency test of FLRW →Redshift-drift competitive consistency test of FLRW →metric;metric; 5σ5σ with 10 years of operation with 10 years of operation

““Cosmic parallax”Cosmic parallax” is is notnot a regular parallax! a regular parallax! Anisotropy test measures →Anisotropy test measures → presentpresent anisotropy anisotropy It may be observable by Gaia, but not in void modelsIt may be observable by Gaia, but not in void models

4141

Conclusions (2)Conclusions (2) Cosmic Parallax Cosmic Parallax vs.vs. other anisotropy probes other anisotropy probes

CMB dipole is 100% degenerated with our peculiar velocityCMB dipole is 100% degenerated with our peculiar velocity Other CMB multipoles: Other CMB multipoles: assumeassume anisotropy is not growing anisotropy is not growing Complementary with supernovae:Complementary with supernovae:

Need ~ 700 SNe for same sensitivity of GaiaNeed ~ 700 SNe for same sensitivity of Gaia Gaia's sky map can be compared with the next global-Gaia's sky map can be compared with the next global-

astrometry missionastrometry mission

One of the One of the fewfew probes of our peculiar velocity probes of our peculiar velocity and the and the intrinsicintrinsic CMB dipole! CMB dipole!

4242

Conclusions (3)Conclusions (3) 2 light cones are better than 12 light cones are better than 1

Redshift drift – Redshift drift – inhomogeneityinhomogeneity probe probe

Cosmic parallax – Cosmic parallax – anisotropyanisotropy probe probe

Both signals effectively increase as Both signals effectively increase as ΔΔtt3/23/2

The near future dawn of Real Time Cosmology→The near future dawn of Real Time Cosmology→

4343

““Tudo que se vê não éTudo que se vê não é

Igual ao que a genteIgual ao que a gente

Viu há um segundoViu há um segundo

Tudo muda o tempo todoTudo muda o tempo todo

No mundoNo mundo

Não adianta fugirNão adianta fugir

Nem mentir pra si mesmo agoraNem mentir pra si mesmo agora

Há Há tanta vidatanta vida tantos fótons lá fora lá fora

Aqui dentro sempreAqui dentro sempre

Como uma onda no marComo uma onda no mar

Como uma onda no mar”Como uma onda no mar”

Lulu SantosLulu Santos

Obrigado!

4444

More on GaiaMore on Gaia Astrometric precision depends strongly on magnitudeAstrometric precision depends strongly on magnitude Quasar distrib. peaks at z Quasar distrib. peaks at z ≈≈ 1.4 (mag G = 19 – 20) 1.4 (mag G = 19 – 20)

4545

More on CODEXMore on CODEX Estimated CODEX precision:Estimated CODEX precision:

Signal-to-noise ratio per pixel:Signal-to-noise ratio per pixel:

apparent magnitude

¾¢v = 1:35

µS/N

2370

¶¡1µNQSO30

¶¡ 12µ1 + zQSO

5

¶¡1:7cm/s :

S

N= 700

"100:4(16¡mX)

µD

42m

¶2tint10 h

²

0:25

# 12

:

¢v = c¢tzs=(1 + zs) :

4646

Distinctions between HDistinctions between H|||| and and H H⊥⊥

Baryon Acoustic Oscillation signal depends on Baryon Acoustic Oscillation signal depends on HH||||

SNe observations are only related to SNe observations are only related to HH⊥⊥

García-Bellido & Haugbolle: 0802.1523 (JCAP)

q(z) = ¡1 + d ln Hjj(z)

d ln(1 + z)

w(z) ´ p(z)

½(z)= ¡1 + 1

3

d lnhH2

?(z)H20 (r)

¡ ­M(r)(1 + z)3i

d ln(1 + z)

4747

Noise and SistematicsNoise and Sistematics Most Most obviousobvious source of noise peculiar velocities→ source of noise peculiar velocities→

Overall effect ~ 0.1 →Overall effect ~ 0.1 → μμas / yearas / year On the very large scales involved they are uncorrelated!On the very large scales involved they are uncorrelated!

Competing dipolar signatures: Competing dipolar signatures: changing aberration due to acceleration of the solar systemchanging aberration due to acceleration of the solar system

dipolar signal due to motion of observerdipolar signal due to motion of observer

Kovalevsky 2003 (Reid et al. 2009)

¢t°pec =

Ãvpec

500 kms

!µDA1Gpc

¶¡1µ¢t

10 years

¶¹as

4848

Noise and Sistematics (2)Noise and Sistematics (2)

ΔΔttγ for 2 quasars separated by 90γ for 2 quasars separated by 90oo, at , at different redshiftsdifferent redshifts

Quartin & Amendola 0909.4954 (PRD)

4949

SNe off-center dist. d→SNe off-center dist. d→ obsobs ≤≤ 15%15% of void radius of void radius (~250 Mpc)(~250 Mpc)

CMB dipole off-c. dist. d→CMB dipole off-c. dist. d→ obsobs ≤≤ 2%2% of void radius of void radius (~30 Mpc)(~30 Mpc)

Caveat:Caveat: this this assumes zero velocityassumes zero velocity between observer and between observer and the center of the voidthe center of the void

With a typical velocity of 500 km/s: With a typical velocity of 500 km/s: ddobsobs ≤≤ 60 Mpc 60 Mpc..

Cosmic Parallax with GaiaCosmic Parallax with Gaia

Alnes & Armazguioui: astro-ph/0607334 (PRD)astro-ph/0610331 (PRD)

Blomqvist & Mortsell: 0909.4723 (JCAP)

5050

Other Gaia GoalsOther Gaia Goals Stellar parallax distances without physical assumptions. →Stellar parallax distances without physical assumptions. → Faintest objects a more complete view of the stellar →Faintest objects a more complete view of the stellar →

luminosity function. luminosity function. Large amount of objects examine the more rapid stages of →Large amount of objects examine the more rapid stages of →

stellar evolution. Also important understand the dynamics →stellar evolution. Also important understand the dynamics →of our galaxy: 1 billion stars = 1% of its content.of our galaxy: 1 billion stars = 1% of its content.

Astrometric and kinematic properties of star understand →Astrometric and kinematic properties of star understand →the various stellar populations, especially the most distant.the various stellar populations, especially the most distant.

Tangential speeds of 40 million stars to a precision of better Tangential speeds of 40 million stars to a precision of better than 0.5 km/sthan 0.5 km/s

5151

Cosmic Parallax FoMCosmic Parallax FoM Figure of Merit (FoM) for Cosmic Parallax:Figure of Merit (FoM) for Cosmic Parallax:

Useful quantity to compare future astrometric missions Useful quantity to compare future astrometric missions (for cosmic parallax):(for cosmic parallax):

pNQSO

µ¢t

1 year

¶µ¾p

1¹as

¶¡1

Gaia FoM = 39→Gaia FoM = 39→ SIMLite FoM = 9 →SIMLite FoM = 9 → 2 Gaia Missions 15 years apart FoM = 230!!!→2 Gaia Missions 15 years apart FoM = 230!!!→

pNQSO

µ¢t

1 year

¶µ¾p

1¹as

¶¡1: