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

Observatório Nacional – Jun 2010Observatório Nacional – Jun 2010

22

TeaserTeaser Near future high-precision telescopes and satellites will Near future high-precision telescopes and satellites will

vastly improve our knowledge of the universevastly improve our knowledge of the universe

Unprecedented accuracy, broadness and completeness Unprecedented accuracy, broadness and completeness invites us to think outside the boxinvites us to think outside the box

Not necessarily only on crazy ideas such as the ones Not necessarily only on crazy ideas such as the ones proposed by A. Einmann, B. Andere et. alproposed by A. Einmann, B. Andere et. al

… … but also on but also on semi-crazysemi-crazy ideas. ideas.

33

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 :

44

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 modelse.g.: void models

ds2 = ¡dt2 + a2(t)

1 + kr2dr2 + a2(t)d­2 :

:

55

Why study void models?Why study void 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 Correct placement of 1Correct placement of 1stst peak of CMB*peak of CMB* 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 a priori reason for thatNo a priori reason for that** → → unlikely! unlikely!

66

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

R(t; r) = (cosh ´ ¡ 1) ®(r)2¯(r)

t =(sinh ´ ¡ ´)®(r)

2¯(r)3=2:

:

ds2 = ¡dt2 + [R0(t; r)]2

1 + ¯(r)dr2 + R2(t; r)d­2 :

R0 ´ @R

@r:

:

77

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

z = 0

88

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

ds2 = ¡dt2 + [R0(t; r)]2

1 + ¯(r)dr2 + R2(t; r)d­2 :

Hjj =1

R0@R0

@t:

H? =1

R

@R

@t:

R0 ´ @R

@r:

:

99

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)

Constraints on void Constraints on void shape from SDSS LRG shape from SDSS LRG or SNe number counts?or SNe number counts?

1010

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)

1111

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

¶:

1212

1313

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: 2017Estimated completion: 2017 Aperture (diameter): Aperture (diameter): 42m42m Type: optical to mid-infraredType: optical to mid-infrared Cost: 960M € (including 1Cost: 960M € (including 1stst generation instruments) generation instruments)

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)

1414

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

¶¡1µNQSO

30

¶¡ 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) :

1515

Redshift Drift in Dark Energy Redshift Drift in Dark Energy modelsmodels

Balbi & Quercellini, 0704.2350 (MNRAS)

1616

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

:

1717

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: 2012

Quercellini, Quartin & Amendola 0809.3675 (PRL)

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

1818

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)

1919

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.

2020

Estimating the Cosmic ParallaxEstimating the Cosmic Parallax

Calculating the Cosmic Parallax require solving the full Calculating the Cosmic Parallax require solving the full LTB geodesic equationsLTB geodesic equations

Simple, Simple, inconsistentinconsistent estimate flat FRW universe with → estimate flat FRW universe with →H(t) H(t, r)→H(t) H(t, r)→

Assume 2 sources initially at Assume 2 sources initially at (d(da a , θ, θaa)) and and (d(db b , θ, θbb))..

“physical” distancedistance to the

void center dipole effect

¢t° = ¢t(Hobs ¡Hd)dobs

·sinµada

¡ sinµbdb

¸:

:

2121

Actual effect need to solve the LTB geodesic eqs.→Actual effect need to solve the LTB geodesic eqs.→ ΔΔttγ for a pair of quasars at γ for a pair of quasars at z = 1z = 1 (typical for Gaia) (typical for Gaia)

ResultsResults

Angular position

2222

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

!µDA

1Gpc

¶¡1µ¢t

10 years

¶¹as

2323

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)

2424

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)

2525

20 years

10 years

30 years

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

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

:

2626

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 (3)Cosmic Parallax with Gaia (3)

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

:

2727

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; 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)

2828

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 ´ Hx

H¡ 1 6= 0

H ´ 1

abc

d

dt

¡abc¢

2929

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

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

3030

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!

3131

CP and the CMB Dipole (2)CP and the CMB Dipole (2) Gaia rough measure of our own pec. velocity→Gaia rough measure of our own pec. velocity→

Can distinguish between standard and other explanationsCan distinguish between standard and other explanations E.g.: E.g.: Bulk flowsBulk flows

Measured up to 300 Mpc. What if it is superhorizon?Measured up to 300 Mpc. What if it is superhorizon? No bulk motion No bulk motion between Quasars and Local Groupbetween Quasars and Local Group

Physical explanation extant primordial (pre-inflation) →Physical explanation extant primordial (pre-inflation) →perturbations.perturbations.

Cosmic Vision:Cosmic Vision: How did the Universe originate?How did the Universe originate? What are the fundamental laws of physics?What are the fundamental laws of physics?

3232

CP and the CMB Dipole (3)CP and the CMB Dipole (3) 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

3333

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.

Amendola, Balbi, Quartin & Quercellini (in prep)

radialradial transverse

redshift drift cosmic parallax

properacceleration

peculiaracceleration

global (velocity)

local(acceleration)

3434

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

redshift drift

cosmic parallax

properacceleration

peculiaracceleration

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)

Amendola, Balbi, Quartin & Quercellini (in prep)

3535

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, just not for voidsIt may be observable by Gaia, just not for voids

3636

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

Unique probe of our peculiar velocity Unique probe of our peculiar velocity and the and the intrinsicintrinsic CMB dipole! CMB dipole!

3737

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→

3838

““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!

3939

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)

Gaia posisional accuracy

More on Gaia (2)More on Gaia (2)

4040

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

¶µ¾p1¹as

¶¡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

¶µ¾p1¹as

¶¡1:

4141

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

4242

LTB models (2)LTB models (2) The Alnes et al. The Alnes et al. (astro-ph/0607334)(astro-ph/0607334) class of LTB models: class of LTB models:

We will consider 3 such models:We will consider 3 such models: similar void sizes similar void sizes (z ~ 0.3 – 0.4)(z ~ 0.3 – 0.4) different values of Δrdifferent values of Δr transition width

®(r) =¡Hout?;0¢2

r3·1¡ ¢®

2

µ1¡ tanh r ¡ rvo

2¢r

¶¸:

¯(r) =¡Hout?;0¢2

r2¢®

2

µ1¡ tanh r ¡ rvo

2¢r

¶

4343

Let iT BeLet iT Be

LTB – Lemaître-Tolman-BondiLTB – Lemaître-Tolman-Bondi

LBT – Large Binocular TelescopeLBT – Large Binocular Telescope

BLT – Bacon Lettuce TomatoBLT – Bacon Lettuce Tomato

4444

Extras: Constraints on Void Extras: Constraints on Void ModelsModels

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)

4545

Estimating the Cosmic Parallax (Estimating the Cosmic Parallax (2)2)

ZERO inside the void in Model II

Dipole effect

Model IModel II

:HX ' Houtjj;0

¢t° = ¢t(Hobs ¡HX)Xobs

·sinµaXa

¡ sinµbXb

¸: