Dark Energy: Supernovae and gravitational shear · P. Astier, CdF(12/16) 44 Gravitational...

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Dark Energy: Supernovae and gravitational shear

(seminar at Collège de France)

Pierre Astier (LPNHE-Paris)(IN2P3/CNRS/UPMC)

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The expansion (of the universe)

1929 : Edwin Hubble : « The faster , the fainter»

Recession velocity

Distance

Recession velocityof galaxies vs their « distance »

In fact, a paper by Lemaître in 1927 describes the same feature, usingthe same data, in French, and without a graphic….

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The expansion

D D

VV VV

Us

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The expansion

D D

VV VV

D 2D

VV 2V2V

UsThem

Some other point of view

Us

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The expansion :

Cosmological principle:

No special position nor direction

Velocity and distance are proportional (at least not too far away)

No dynamical argument involved : only symmetries.

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The expansion :velocity variations

D D

VV VV

Because of gravitationgalaxies attract each otherand their relative velocity

goes down

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So,

velocity

Distance

● V = H d is a signature of the expansion of the universe● The variation of the expansion velocity with time (or distance) encodes the forces at play.

Different hypothesesfor matter density

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● General Relativity  relates the trajectories in space­time and the energy densities of the fluids in the universe.

● Einstein Equations + cosmological principle

                    → Friedman's equation(s)  

Expansion rate Energy densities “Cosmological Constant”

Spatialcurvature

Friedman's equation

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History of expansionand content of the universe

● We have to measure (velocity, distance) pairs● For velocities, it is (almost) easy :

– spectral shift (« Doppler »)

● For distances, it is more difficult:– Luminosity distances : « standard candles »

– Angular distances : « standard rulers »

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Standard candles:« supernovae »

Image credit: NASA/JPL-Caltech

Standard rulers:« Baryon AcousticOscillations » (BAO)

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The programme

distance

z ~ spectral shift (to the red): redshift

Measure - distances- ... and the corresponding “z”

In order to evaluatethe gravitationalforces at play andhence the content

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Type “Ia” Supernovae

● Extremely bright● Transient (rise in~ 20 days)● Rare (~1/galaxy/millenium)● Luminosity fluctuations

at peak : ~ 40 % ● Using luminosity indicators           ~14 %

Thermonuclear explosion of stars That appear to be reproducible

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M. Hamuy + ….       (1996)

The first precision Hubble diagramme

z0.10.030.01

«  distance »

Every distance is measured to 

better than 10 %

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Finding supernovae

Nearby supernova

Distant SN : Image subtraction

cfht/cfh12k (2000)

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Spectroscopic Identification

Dispersion direction

An one measures the redshift z

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Measuring « light curves »

Measurement of theobject flux as a functionof time for about 2 months

One has to measure the« colour », i.e. measurelight in at least two spectral bands

Fit of an empirical modelwhich allows to summarisethe data into a few parameters

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Hubble diagram : flux vs redshift

Peak flux

Multi-band photometry => distance

spectroscopy:- identification- redshift

z

Distant SNe  (0.1<z<0.8)

(Perlmutter et al, 1999) 

Nearby SNe  (0.02<z<0.1)(Hamuy et al, 1996)

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Fall 1998 : the twin papers

Riess et al, 1998[High-z team]

Perlmutter et al,1998[SCP]

Matter density

Dar

k E

nerg

y

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What is new in 1998 ?

● One can detect in a systematical way distant supernovae (z~0.5) (both teams used primarily the BTC camera on the CTIO 4-m)

● One can then compare “high-z” supernovae to the “low-z” ones. (Both teams compare to the same nearby sample : Hamuy & co (1996) )

● What for ? the idea was to measure the deceleration parameter q0 :

- Un a universe dominated by matter q0 =

M /2

-> Expansion should decelerate (matter attracts).

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Accelerated expansion

Decelerated expansion The Nobel Prize in Physics 2011

was divided, one half awarded to Saul Perlmutter, the other half jointly to Brian P. Schmidt and Adam G. Riess "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae".

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A universe dominated todayby two components

Expansion (time)

dens

ity

matter

Dark Energy

??

now

How does the dark energy density varies with expansion ?

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Expansion (i.e. scale factor)

Den

sity matter

Dark Energy

now

??

0

-1/3

-2/3

-1

w : “equation of state”

Matter

w describes the evolution of density with expansion ● Matter : w = 0 (just follows expansion)● Cosmological constant : w = -1 (ignores expansion)

Cosmological constant, or what ?

Constraints from supernovae(Perlmutter et al 1999)

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Around 2000, a new instrument

 Canada France Hawaii Telecope :­ diameter 3.6m­ Mauna Kea, Hawaii­ 4200 m­ Exceptional image   quality

MegaCam: ­ 18 000 x 18 000 pixels­ field of view : 1 deg2

­ first light : end of 2002.­ assembled at CEA.

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http://www.cfht.hawaii.edu/images/CFHTLS-D1-Zoom/

1 degree (18000 pixels)

Megacam's field of view

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The SNLS collaboration(SuperNova Legacy Survey)

(circa 2006)

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SNLS observations : rolling search­ Repeated observations every 4th night­ Try next night if the weather was bad­ 4 bands : g,r,i,z [420­950] nm­ 5 years of observations : 2003­2008­ Part of “CFHTLS”

Several active supernovaein every image

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Light curves

SNLS-04D3fkz=0.358

SNLS-04D3gzz=0.91

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And spectra...

Three large telescopes : The Very Large Telescope (ESO) (8m) Gemini (8m) Keck (10m)

In total : more than 1000 h of observing (!) over 5 years

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Data processing

~ 50 To~ 30 000 hours

Centre de calcul de l'IN2P3, Villeurbanne

Data model residuals weights Kernel

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Supernova surveys The SDSS SN survey SNLS @ CFHT

300 deg2 x 3 years0.1<z<0.45~2000 SNe~500 spectra

4 deg2 x 5 years0.3<z<1~1000 SNe~500 spectra

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Estimating distances● The luminosity of supernovae exhibits event to

event variations which are independent of distance

Slower supernovae are brighter

Bluer supernovae are brighter

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Distance estimation Résidual to Hubble

diagram

Width of the Light curve

Colour : « B-V » Green flux/Blue flux

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Distance estimation

B = m

B ­ M + (s­1) – c  

Measurements for a supernova

Global ParametersFitted (e.g.) at the same timeas cosmological parameters

DistanceModulus (~ log(d) )

Tripp (1998)

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Cosmological results (2014)

● 118 nearby● 366 SDSS● 242 SNLS● 14 HST

740 events

Betoule et al (2014)

“JLA”

~Log(dL(z))

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Equation of state in a flat universe

Planck + BAO: w = −1.01 ± 0.08

Planck + SN: w = −1.018 ± 0.057

Improvements w.r.t previous results : - improved calibration - SDSS data - direct cross-calibration

Betoule et al (2014)Betoule et al (2013)

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Incertainties

JLA sample, flat LCDMPhotometric calibrationdominates systematicuncertainties

...and systematic uncertainties represent half of the totaluncertainty.

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From the discoveryof accelerated

expansion to a recent

compilation

Betoule et al (2014)

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Betoule et al (2014)

From the discoveryof accelerated

expansion to a recent

compilation

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Betoule et al (2014)

From the discoveryof accelerated

expansion to a recent

compilation

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What did we learn in 15 years?

● That accelerated expansion is real. Other probes observe it.

● If one interprets acceleration on the framework of General Relativity, it looks very much like a cosmological constant.

● That improving distance measurements to supernovae is going to be difficult: one should absolutely improve the photometric standards.

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And now:

● The two last years of SNLS (~150 SN) ● Pan STARSS (+ 100?)● Dark Energy Survey (2012-2017) (+1000?)● LSST (2022- ) : + 10000● Euclid (2021-) : + 0 -> 1500 at z>1 (being

discussed)● WFIRST (202x-) : + 2000 ?

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Gravitational shear

In a non-homogeneousUniverse, light is (slightly)bent.

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Gravitational distortions● Image plane transfomations

– Weak lensing : one to one mapping.

– Strong lensing : multiple images of the same object

● Order 0: a shift (~ un-observable).● Order 1 (2x2 matrix = 4 parameters):

– Magnification (1 parameter)

– Shear (symmetric, det=1 → 2 parameters)

– Rotation (1 parameter)

– Magnification and shear are observable statistically. The rotation is not observable and absent for single-plane lenses.

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Distortions schematics

"Shear-components" by TallJimbo

Convergence/magnification

One shear component

The other shear component

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Relation to gravitation sources

Lensing potential

Cosmological physics (Peacock).

“Poisson Equation” :

The observables derive from a potential sourced by the « projected mass ».

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Example : a galaxy cluster

Cluster

Image plane : galaxies are(on average)tangentiallyelongated

Michael Sachs(wikipedia)

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Galaxy cluster MACS 1621+38

XEmission

Convergence (i.e. lensing)

Shear vs distanceto center

Weighing the Giants (1208.0597)

Null component

A. von der Linden& co

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present

z=zs

z=zl

z=0

past

Large-scale Structures

Observables :

- ellipticity

- orientation

• Sensitive to matter (dark or not)• Sensitive :

– To structures– To distances

• A ~ 1% effect: one needs millions of galaxies to measure it.

Cosmic shear

Graphic from M. Takada.

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Cosmological constraintsderived from cosmic shear

● The cosmological model predicts structure formation : in practice density contrasts increase as time goes, in a way related to expansion.

● This is a precise prediction, which is encoded into density fluctuations.

● Cosmic shear is sensitive to density fluctuations, so shear correlations trace density correlations.

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The CFHTLS wide survey

● About 200 degrees², 5 bands, ~ 200 nights on CFHT, (2003-2008)

● ~10 millions of usable galaxies.

1 degré² field of viewExcellent image quality

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Shear measurements

Shear signal : correlations of distant galaxy ellipticities (as a function of their angular separation )

Sources of ellipticity: Natural ellipticity : ~ 30% -> just average over many galaxies Imaging system : 0 – 10 % -> One should measure stellar ellipticities Cossmological signal : ~ 1%

Measured stellar ellipticities (CFHT/Megacam) Hoekstra et al 2005

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L. Van Waerbeke et al. (2013)Converting into mass maps

Coulours, contours :- mass

White dots: :- galaxy densitypeaks

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Angular correlations of shear

M. Kilbinger et al. (2013)

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Cosmological constraints (2D)

M. Kilbinger et al. (2013)

CMB+BAOLensing (shear)

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Cosmological constraints (3D)

● One uses galaxy colours to assign a redshift to them. One can then « cut slices » along redshift.

● One has to measure in 5 bands in order to get the required colours. (visible bands “ugriz”).

Kitching et al. (2014)

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Perspectives : constrain gravity

Distances H(z)

Linear perturbations P(k,z)

Prediction of perturbation observables

Numerical simulations

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Perspectives : scientific questions

● Constrain the source of accelerated expansion

– Cosmological constante

– Quasi-static scalar field

– Modified Gravity

● (Dark) matter on large scales– To be measured directly from

correlations ....

– ... with their time evolution.

Shear correlations

SupernovaeBAO

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Large imaging surveys : the programme

Area (deg2) bands depth (lim. Mag) star/end #SNe

VST @ ESO 1000 4 (vis) ~23 12/17

Dark Energy Survey 5000 5 (vis) ~24 12/17 2000

HyperSuprimeCam 2000 5 (vis) ~26 15/19 300

Pan StarsS 30000 4 (vis) ~23 11/16 300

LSST 20000 6 (vis) 26,5 21/31 10000

Euclid 15000 1 vis + 3 NIR 24,5 21/26 ?

Wfirst 3000 4 NIR H=26 26 ? 2000 ?

Spa

ce

Gro

und

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Conclusions● Dark energy is there. It looks like a cosmological

constant (w = -1.02 +/- 0.05)● Supernovae are moving on.● Gravitational shear is difficult, but two major

have been designed to measure : LSST and Euclid