Science of the Dark Energy Survey

Josh Frieman

Fermilab and the University of Chicago

Astronomy 41100Lecture 2, Oct. 15, 2010

DES Collaboration Meeting

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Go to:

http://astro.fnal.gov/desfall2010/Home.html

Science Working group meetings on Tuesday.Plenary sessions Wed-Fri.

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Cosmological Constant as Dark Energy

Einstein:

Zel’dovich and Lemaitre:

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Gμν − Λgμν = 8πGTμν

Gμν = 8πGTμν + Λgμν

≡ 8πG Tμν (matter) + Tμν (vacuum)( )

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Tμν (vac) = Λ8πG

gμν

ρ vac = T00 = Λ8πG

, pvac = Tii = − Λ8πG

wvac = −1 ⇒ H = constant ⇒ a(t)∝ exp(Ht)

Cosmological Constant as Dark Energy Quantum zero-point fluctuations: virtual particles continuously fluctuate into and out of the vacuum (via the Uncertainty principle).

Vacuum energy density in Quantum Field Theory:

Theory: Data:

Pauli

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ρvac = Λ8πG

= 1V

12

h∑ ω = hc(k 2 + m2

0

M

∫ )1/ 2 d3k ~ M 4

wvac = pvac

ρ vac

= −1, ρ vac = const.

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M ~ MPlanck = G−1/ 2 =1028 eV ⇒ ρ vac ~ 10112 eV4

ρ vac <10−10eV4

Cosmological Constant Problem

Dark Energy: Alternatives to ΛThe smoothness of the Universe and the large-scalestructure of galaxies can be neatly explained if there was a much earlier epoch of cosmic acceleration that occurred a tiny fraction of a second after the Big Bang:

Primordial Inflation

Inflation ended, so it was not driven by the cosmological constant. This is a caution against theoretical prejudice for Λ as the cause of current acceleration (i.e., as the identity of dark energy).

Light Scalar Fields as Dark Energy

Perhaps the Universe is not yet in its ground state. The `true’ vacuum energy (Λ) could be zero (for reasons yet unknown). Transient vacuum energy can exist if there is a field that takes a cosmologically long time to reach its ground state. This was the reasoning behind inflation. For this reasoning to apply now, we must postulate the existence of an extremely light scalar field, since the dynamical evolution of such a field is governed by

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td ~ 1m

, td >1/H0 ⇒ m < H0 ~ 10−33eV

JF, Hill, Stebbins, Waga 1995

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Scalar Field as Dark Energy(inspired by inflation)

Dark Energy could be due to a very light scalar field j, slowly evolving in a potential, V(j):

Density & pressure:

Slow roll:

)(

)(2

21

221

ϕϕ

ϕϕρ

VP

V

−=

+=

&&

V(j)

j

€

12 ˙ ϕ 2 < V (ϕ )⇒ P < 0 ⇔ w < 0 and time - dependent

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˙ ̇ ϕ + 3H ˙ ϕ + dVdϕ

= 0

Scalar Field Dark Energy

Ultra-light particle: Dark Energy hardly clusters, nearly smoothEquation of state: usually, w > 1 and evolves in timeHierarchy problem: Why m/ϕ ~ 1061?Weak coupling: Quartic self-coupling ϕ < 10122

General features:

meff < 3H0 ~ 10-33 eV (w < 0)(Potential > Kinetic Energy)

V ~ m2j2 ~ ρcrit ~ 10-10 eV4

j ~ 1028 eV ~ MPlanck

aka quintessence

V(j)

j1028 eV

(10–3 eV)4

The Coincidence Problem

Why do we live at the `special’ epoch when the dark energy density is comparable to the matter energy density?

ρmatter ~ a-3

ρDE~ a-3(1+w)

a(t)Today

Scalar Field Models & Coincidence

VV

j

Runaway potentialsDE/matter ratio constant(Tracker Solution)

Pseudo-Nambu Goldstone BosonLow mass protected by symmetry(Cf. axion) JF, Hill, Stebbins, Waga

V(j) = M4[1+cos(j/f)]f ~ MPlanck M ~ 0.001 eV ~ m

e.g., e–ϕ or ϕ–n

MPl

Ratra & Peebles; Caldwell, etal

`Dynamics’ models(Freezing models)

`Mass scale’ models(Thawing models)

j

PNGB Models

Tilted Mexican hat:

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V (Φ) = λ ΦΦ* − f 2

2

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

+M 4 cos(Arg(Φ) −1( )

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M 4 ~ 10−3eV << f ~ MPl

Frieman, Hill, Stebbins, Waga 2005

• Spontaneous symmetry breaking at scale f

• Explicit breaking at scale M

• Hierarchy protected by symmetry

f

M4

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Caldwell & Linder

Dynamical Evolution of Freezing vs. Thawing Models

Measuring w and its evolution can potentially distinguish between physical models for acceleration

Runaway (Tracker) Potentials

Typically ϕ >> Mplanck today.

Must prevent terms of the form

V(ϕ) ~ ϕn+4 / Mplanckn

up to large n

What symmetry prevents them?

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Perturbations of Scalar Field Dark Energy

If it evolves in time, it must also vary in space.

h = synchronous gauge metric perturbation

Fluctuations distinguish this from a smooth “x-matter” or

Coble, Dodelson, Frieman 1997Caldwell et al, 1998

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Dark Energy Interactions

Couplings to visible particles must be small

Couplings cause long-range forces

Carroll 1998

Attractive force between lumps of

Frieman & Gradwohl 1990, 1992

Example: scalar field coupled to massive neutrino

What about w < 1? The Big Rip• H(t) and a(t) increase with time and diverge in finite time e.g, for w=-1.1, tsing~100 Gyr• Scalar Field Models: need to violate null Energy condtion ρ + p > 0: for example: L = (ϕ)2 V

Controlling instability requires cutoff at low mass scale

• Modified Gravity models apparently can achieve effective w < –1 without violating null Energy Condition

Caldwell, etal

Hoffman, etal

Modified Gravity & Extra Dimensions• 4-dimensional brane in 5-d Minkowski space• Matter lives on the brane• At large distances, gravity can leak off brane into the bulk, infinite 5th dimension Dvali, Gabadadze, Porrati• Acceleration without vacuum energy on the brane, driven by brane curvature term• Action given by:

• Consistency problems: ghosts, strong coupling €

S = M53 d5X det g5∫ R5 + MPlanck

2 d4 x det g4∫ R4 + d4 x∫ det g4 Lm

Modified Gravity

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€

gAB = η AB + hAB | h |<<1 A,B = 0,1,2,3,4• Weak-field limit:

• Consider static source on the brane:

• Solution:

• In GR, 1/3 would be ½• Characteristic cross-over scale:

• For modes with p<<1/rc :• Gravity leaks off the brane: longer wavelength gravitons free to propagate into the bulk• Intermediate scales: scalar-tensor theory

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Tμν ( p) μ,ν = 0,1,2,3

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hμν ( p) = 8πGp2 + 2(G /G(5))p

Tμν (p) − 13

η μν Tαα ( p)

⎛ ⎝ ⎜

⎞ ⎠ ⎟

where

G =1/ MPl2 and G(5) =1/ M5

3

€

rc = 12

G(5)

G= MPl

2

2M53

€

hμν ~ p−1, corresponds to V (r) ~ r−2

Cosmological Solutons• Modified Friedmann equation:

• Early times: H>>1/rc: ordinary behavior, decelerated expansion.• Late times: self-accelerating solution for (-)

• For we require

• At current epoch, deceleration parameter is

corresponds to weff=-0.8

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H 2 ± Hrc

= ρ3MPlanck

2

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H0 ~ rc−1 ~ 10−33eV

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M5 ~ 1 GeV

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H → H∞ = rc−1

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q0 = 3Ωm (1+ Ωm )−1 −1 = −0.36 for Ωm = 0.27

Growth of Perturbations

• Linear perturbations approximately satisfy:

• Can change growth factor by ~30% relative to GR• Motivates probing growth of structure in addition to expansion rate€

˙ ̇ δ + 2H ˙ δ = 4πρ m (t)δ(t)Geff (t)

where

Geff = G 1+ 3β

⎛ ⎝ ⎜

⎞ ⎠ ⎟

and

β =1− 2rcH(t) 1+˙ H

3H 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Modified Gravity: f(R)

€

S = d4∫ x −g R ⇒ d4∫ x −g f (R)

€

e.g., f (R) = 116πG

R − μ 2(n +1)

Rn

⎛ ⎝ ⎜

⎞ ⎠ ⎟

This model has self - accelerating vacuum solution, with

R =12H 2 = 3μ 2 .

This particular realization excluded by solar system tests, but variants evade them: Chameleon models hide deviations from GR on solar system scales

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Bolometric Distance Modulus• Logarithmic measures of luminosity and flux:

• Define distance modulus:

• For a population of standard candles (fixed M), measurements of vs. z, the Hubble diagram, constrain cosmological parameters.

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M = −2.5log(L) + c1, m = −2.5log( f ) + c2

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≡m − M = 2.5log(L / f ) + c3 = 2.5log(4πdL2) + c3

= 5log[H0dL (z;Ωm,ΩDE ,w(z))]− 5log H0 + c4

= 5log[dL (z;Ωm,ΩDE ,w(z)) /10pc]

flux measure redshift from spectra

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dL (z) = (1+ z)r = (1+ z)Sk (χ ) = (1+ z)Skdz

H(z)∫ ⎛ ⎝ ⎜

⎞ ⎠ ⎟

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Distance Modulus• Recall logarithmic measures of luminosity and flux:

• Define distance modulus:

• For a population of standard candles (fixed M) with known spectra (K) and known extinction (A), measurements of vs. z, the Hubble diagram, constrain cosmological parameters.

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M i = −2.5log(Li) + c1, mi = −2.5log( f i) + c2

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≡mi − M j = 2.5log(L / f ) + K ij (z) + c3 = 2.5log(4πdL2) + K + c3

= 5log[H0dL (z;Ωm,ΩDE ,w(z))]− 5log H0 + K ij (z) + Ai + c4

denotes passband

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K corrections due to redshiftSN spectrum

Rest-frame B band filter

Equivalent restframe i band filter at different redshifts

(iobs=7000-8500 A)

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f i = Si(λ )Fobs(λ )dλ∫= (1+ z) Si∫ [λ rest (1+ z)]Frest (λ rest )dλ rest

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Absolute vs. Relative Distances• Recall logarithmic measures of luminosity and flux:

• If Mi is known, from measurement of mi can infer absolute distance to an object at redshift z, and thereby determine H0 (for z<<1, dL=cz/H0)

• If Mi (and H0) unknown but constant, from measurement of mi can infer distance to object at redshift z1 relative to object at distance z2:

independent of H0

• Use low-redshift SNe to vertically `anchor’ the Hubble diagram, i.e., to determine

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M i = −2.5log(Li) + c1, mi = −2.5log( f i) + c2

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mi = 5log[H0dL ] − 5logH0 + M i + K(z) + c4

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m1 − m2 = 5log d1

d2

⎛ ⎝ ⎜

⎞ ⎠ ⎟+ K1 − K2

€

M − 5logH0

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SN 1994D

Type Ia Supernovae as Standardizable Candles

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SN Spectra~1 week after maximumlight

Filippenko 1997

Ia

II

Ic

Ib

Type Ia SupernovaeThermonuclear explosions of Carbon-Oxygen White Dwarfs

White Dwarf accretes mass from or merges with a companion star, growing to a critical mass~1.4Msun

(Chandrasekhar)

After ~1000 years of slow cooking, a violent explosion is triggered at or near the center, and the star is completely incinerated within seconds

In the core of the star, light elements are burned in fusion reactions to form Nickel. The radioactive decay of Nickel and Cobalt makes it shine for a couple of months

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Type Ia SupernovaeGeneral properties:

• Homogeneous class* of events, only small (correlated) variations• Rise time: ~ 15 – 20 days• Decay time: many months• Bright: MB ~ – 19.5 at peak

No hydrogen in the spectra• Early spectra: Si, Ca, Mg, ...(absorption)• Late spectra: Fe, Ni,…(emission)• Very high velocities (~10,000 km/s)

SN Ia found in all types of galaxies, including ellipticals• Progenitor systems must have long lifetimes

*luminosity, color,spectra at max. light

SN Ia Spectral Homogeneity(to lowest order)

from SDSS Supernova Survey

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Spectral Homogeneity at fixed epoch

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SN2004ar z = 0.06 from SDSS galaxy spectrum

Galaxy-subtractedSpectrum

SN Ia template

How similar to one another?

Some real variations: absorption-line shapes at maximum

Connections to luminosity?

Matheson, etal, CfA sample

35Hsiao etal

Supernova Ia Spectral Evolution

Late times

Early times

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LayeredChemicalStructureprovidesclues to Explosionphysics

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SN1998bu Type Ia Multi-band Light curve

Extremely few light-curves are this well sampled

Suntzeff, etalJha, etalHernandez, etal

Lum

inos

ity

Time

m15

15 days

Empirical Correlation: Brighter SNe Ia decline more slowly and are bluerPhillips 1993

SN Ia Peak LuminosityEmpirically correlatedwith Light-Curve Decline Rate

Brighter Slower

Use to reduce Peak Luminosity Dispersion

Phillips 1993

Peak

Lum

inos

ity

Rate of declineGarnavich, etal

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Type Ia SNPeak Brightnessas calibratedStandard Candle

Peak brightnesscorrelates with decline rate

Variety of algorithms for modeling these correlations: corrected dist. modulus

After correction,~ 0.16 mag(~8% distance error)

Lum

inos

ity

Time

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Published Light Curves for Nearby SupernovaeLow-z SNe:

Anchor Hubble diagram

Train Light-curve fitters

Need well-sampled, well-calibrated, multi-band light curves

Low-z Data

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CarnegieSupernovaProject

NearbyOptical+NIR LCs

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Correction for Brightness-Decline relation reduces scatter in nearby SN Ia Hubble Diagram

Distance modulus for z<<1:

Corrected distance modulus is not a direct observable: estimated from a model for light-curve shape

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m − M = 5logυ − 5log H0

Riess etal 1996

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Acceleration Discovery Data:High-z SN Team

10 of 16 shown; transformed to SN rest-frame

Riess etalSchmidt etal

V

B+1

Riess, etal High-z Data (1998)

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High-z Supernova Team data (1998)

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Likelihood Analysis

This assume

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€

−2ln L = χ 2 = (μ i − μmod (zi;Ωm ,ΩΛ,H0)2

σ μ ,i2

i∑

Since μmod = 5log(H0dL ) − 5log(H0), let ˆ μ ≡ μmod (H0 = 70) and define Δ i = μ i − ˆ μ . If we fix H0, then we are minimizing

ˆ χ 2 = Δ i2

σ i2

i∑

To marginalize over logH0 with flat prior, we instead minimize

χ mar2 = −2ln d(5logH0)exp −χ 2 /2( )∫

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥= ˆ χ 2 − B2

C+ ln C

2π ⎛ ⎝ ⎜

⎞ ⎠ ⎟,

where

B = Δ i

σ i2

i∑ , C = 1

σ i2

i∑

σ μ ,i2 = σ μ , fit

2 + σ μ ,int2 + σ μ ,vel

2

Goliath etal 2001

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Exercise 5• Carry out a likelihood analysis of using the

High-Z Supernova Data of Riess, etal 1998: use Table 10 above for low-z data and the High-z table above for high-z SNe. Assume a fixed Hubble parameter for the first part of this exercise.

• 2nd part: repeat the exercise, but marginalizing over H0 with a flat prior, either numerically or using the analytic method of Goliath etal.

• Errors: assume intrinsic dispersion of and fit dispersions from the tables and dispersion

due to peculiar velocity from Kessler etal (0908.4274), Eqn. 28, with 50

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Ω , Ωm

€

,int = 0.15

€

z = 0.0012