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TheThe Darkness Darkness of the Universeof the Universe

Eric Linder Lawrence Berkeley National Laboratory

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The Night Sky is DarkThe Night Sky is Dark

The dark night sky is a profound cosmological observation!

The universe is filled with stars emitting photons.

Number of stars at distance r goes as r2; Intensity dies as 1/r2, so total flux received

Ftot = dr F(r) N(r) = 0 dr (L/4r2) (4nr2)

= Ln 0 dr

Why aren’t we cooked?

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The Night Sky is DarkThe Night Sky is Dark

More rigorously:

Energy density of light today

E = tit0 dt L (1+z)-1

If constant comoving luminosity density L, then finite past gives finite limit E < Lt0.

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The Night Sky is DarkThe Night Sky is Dark

Liouville’s Theorem approach:

Photon phase space density N = N/d3xd3p is conserved, so

I = N/(At)dd = N 3

Therefore, I -3 is conserved and the surface brightness I0 = Ie (1+z)-4.

Looking far enough, every line of sight should end on a star, and so the sky should be as bright as the surface of a star.

The answer again is that we can’t look far enough, due to a finite past.

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Optical Depth of the UniverseOptical Depth of the Universe

What is the probability of a line of sight intersecting a star?

Consider a marble rolling on a tabletop.

•

Will the marble hit another marble before rolling off the table top?

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Optical Depth of the UniverseOptical Depth of the Universe

Mean free path is L = 1/(n)

Cross section to intersect a star is = r

2 = (1011 cm)2 = 1022.5 cm2

Number density of stars is n = /m = (10-31 g cm-3)/1033 g = 10-64 cm-3

Effective volume V = 1/n = 1064 cm3 = (1021 cm)3 = [(1/3)kpc]3

MFP L = 1/(n) = V/A = 1041.5 cm = 1017 Mpc

= 1013.5 H0-1

Finite horizon solves Olbers’ paradox by 13 OOM!

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Expanding Universe?Expanding Universe?

What role does the expanding universe play in Olbers’ Paradox? Almost none!

I0 = Ie (1+z)-4 dimming arises from any frequency shift, not just expansion.

E = tit0 dt L (1+z)-1 has little dependence on

redshift. Expansion has factor of ~2 effect.

So Newton could not have “discovered” the expanding universe.

The solution is not expansion in Big Bang cosmology, but the Big Bang itself!

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Expanding Universe?Expanding Universe?

Caveat 1 (CMB):

Photons can be absorbed, and reradiated, e.g. IR degradation. For a diffuse glow like the CMB the sky is dark (E << Mp

4) because of the expansion.

Caveat 2 (Inflation):

In an inflationary epoch, 1+z ~ eH(t0-t), we are saved by the redshift, giving a finite energy density E=L/H even for an infinite past.

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What if Our Eyes Saw Dark (Energy)?What if Our Eyes Saw Dark (Energy)?

The night sky is dark in photons, implying a finite past (Big Bang).

The sky is bright in (dark energy density dominates), implying an infinite future.

Will this turn out to be as significant a discovery as the Big Bang?

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Cornerstones of CosmologyCornerstones of Cosmology

Another simple observation is that the universe appears rather isotropic.

This is most notable in the cosmic microwave background (CMB) radiation. Isotropic to a part in 103, or part in 105 in comoving frame.

Also holds (with less precision) in counts of galaxies, quasars, etc.

Cosmological Principle (Copernican principle, principle of cosmic modesty) argues we are not in special location, so isotropy implies homogeneity.

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Cornerstones of CosmologyCornerstones of Cosmology

The global spatial geometry is isotropic and homogeneous.

The theory of gravity characterizes the spacetime geometry, and relates the dynamics to the matter and energy contents.

General relativity accurately describes gravity as far as it has been tested.

Robertson-Walker metric:

ds2 = dt2+a2(t)[dr2/(1-kr2)+r2d2]

scale factor a(t) ; spatial curvature k

1212

Expansion of the UniverseExpansion of the Universe

The universe is expanding: Photons received from distant galaxies exhibit a change to lower frequencies (redshift).

This shift is at lowest order proportional to the distance:

z = H0r

Isotropic, radial: suggests vector relation

v = H0r

Linearity predicted by Weyl, before Hubble.

Note v12 = v2-v1 = H0(r2-r1) = H0r12.

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Expansion of the UniverseExpansion of the Universe

Approximate timescale of the expansion is the Hubble time H0

-1.

Since distances r ~ a, i.e. r = r0(a/a0), then r = r (a/a). So

H = a/a

Volumes behave as V ~ a3. So number densities n ~ a-3. Photon frequencies (inverse wavelengths) ~ a-1, so radiation energy density ~ a-4 (T ~ a-1).

Early universe was hot and dense.

. .

.

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Big BangBig Bang

This is the hot Big Bang theory:

Expansion of the universe from a hot, dense state over a finite time.

Tested by

1) Expansion redshift

2) Cosmic microwave background radiation

3) Primordial nucleosynthesis

4) Cosmic ages

5) General relativity

6) Dark night sky

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Our Expanding UniverseOur Expanding Universe

Bertschinger & Ma ; courtesy Ma

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

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Our Cosmic AddressOur Cosmic Address

Earth 10Earth 1077 meters meters

Solar system 10Solar system 101313 m m

Milky Way galaxy 10Milky Way galaxy 102121 m m

Local Group of galaxies 3x10Local Group of galaxies 3x102222 m m

Local Supercluster of galaxies 10Local Supercluster of galaxies 102424 m m

The Visible Universe 10The Visible Universe 102626 m m

Our SunOur Sun is one of 400 billion stars is one of 400 billion stars in the in the Milky Way galaxyMilky Way galaxy, which is , which is one of more than 100 billion one of more than 100 billion galaxies in galaxies in the visible universethe visible universe. .

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The Cosmic CalendarThe Cosmic Calendar

InflationInflation 10101616 GeV GeV

Quarks Quarks Hadrons Hadrons 1 GeV1 GeV

Nuclei formNuclei form 1 MeV1 MeV

Atoms formAtoms form 1 eV1 eV

Stars and galaxies Stars and galaxies

first form:first form: 1/40 eV1/40 eV

Today:Today: 1/4000 eV1/4000 eV

[Room temperature 1/40 eV][Room temperature 1/40 eV]

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Characteristic ScalesCharacteristic Scales

Physics today:

Cosmic size (Hubble scale) -- H0-1 = 1028 cm

Cosmic time (Hubble age) -- H0-1 = 1010 yr

Mass scale -- H0 = 10-33 eV

Energy density scale -- H02MP

2 = (10-3 eV)4

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Mapping Our HistoryMapping Our History

The subtle slowing down and speeding up of the expansion, of distances with time: a(t), maps out cosmic history like tree rings map out the Earth’s climate history.

STScI

2020

Discovery! AccelerationDiscovery! Acceleration

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acceler

ating

deceler

atingacc

elerating

decelerating

cf. Tonry et al. (2003)

Cosmic ConcordanceCosmic Concordance

• Supernovae alone

Accelerating expansion

> 0

• CMB (plus LSS)

Flat universe

> 0

• Any two of SN, CMB, LSS

Dark energy ~75%

222295% of the universe is unknown!

Frontiers of CosmologyFrontiers of Cosmology

STScI

Us

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Dark Energy Is!!!Dark Energy Is!!!Dark Energy Is...Dark Energy Is...

• 70-75% of the energy density of the universe

• Accelerating the expansion, like inflation at 10-35s

• Determining the fate of the universe

! 70-75% of the energy density of the universe

95% of the universe unknown!

! Accelerating the expansion, like inflation at 10-35s

Repulsive gravity!

! Determining the fate of the universe

Fate of the universe!

Is this mysterious dark energy the original cosmological constant , a quantum zeropoint sea?

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: Ugly Duckling: Ugly Duckling

Astrophysicist:

Einstein equations –

gab

p = -

Naturally, =const= PL

= 10120

Today M

Field Theorist:

Vacuum – Lorentz invariant

Tab ~ab = diag { -1, 1, 1, 1}

p = -

Naturally, Evac ~ 1019 GeV

E ~ (meV)4

=0?

• Fine Tuning Puzzle – why so small?

• Coincidence Puzzle – why now?

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What’s the Matter with Energy?What’s the Matter with Energy?

They are off by a factor of 1,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000.

This is modestly called the fine tuning problem.

Why not just bring back the cosmological constant ()?

When physicists calculate how big should be, they don’t quite get it right.

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Matter

Dark energy

Today Size=2 Size=4Size=1/2Size=1/4

But it gets worse: Think of the energy in as the level of the quantum “sea”. At most times in history, matter is either drowned or dry.

Cosmic CoincidenceCosmic Coincidence

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On Beyond On Beyond !!

We need to explore further frontiers in high energy physics, gravitation, and cosmology.

New quantum physics? Energy of the vacuum (nothing weighs something)?

New gravitational physics? Quantum gravity, supergravity, extra dimensions?

We need new, highly precise data

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Cosmic ArchaeologyCosmic Archaeology

CMB: direct probe of quantum fluctuations

Time: 0.003% of the present age of the universe.

(When you were 0.003% of your present age, you were 2 cells big!)

Supernovae: direct probe of cosmic expansion

Time: 30-100% of present age of universe

(When you were 12-40 years old)

Cosmic matter structures: less direct probes of expansion

Pattern of ripples, clumping in space, growing in time.

3D survey of galaxies and clusters - Lensing.

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The Universe: Early and LateThe Universe: Early and Late

Relic imprints of quantum particle creation in inflation - epoch of acceleration at 10-35 s and energies near the Planck scale (a trillion times higher than in any particle acclerator).

These ripples in energy density also occur in matter, as denser and less dense regions.

Denser regions get a “head start” and form into galaxies and clusters of galaxies. How quickly they grow depends on the expansion rate of the universe (traced by SN).

It’s all connected!

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CosmicCosmic Archaeology Archaeology

Inflation sets seeds of structure, patterning both radiation (CMB) and matter (galaxies)

CMB

Large scale structure:Baryon acoustic oscillationsLensing (weak and strong)Galaxy clusteringSunyaev-Zel’dovich effect

}NASA GSFC/COBE

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Fundamental PhysicsFundamental Physics

Astrophysics Cosmology Field Theory

a(t) Equation of state w(z) V()

V ( ( a(t) ) )SN

CMB

LSS

Map the expansion history of the universe

The subtle slowing and growth of scales with time – a(t) – map out the cosmic history like tree rings map out the Earth’s climate history.

STScI

3232

What if Our Eyes Saw Dark (Energy)?What if Our Eyes Saw Dark (Energy)?

The night sky is dark in photons, implying a finite past (Big Bang).

The sky is bright in (dark energy density dominates), implying an infinite future.

Will this turn out to be as significant a discovery as the Big Bang?

Next: The Darkness of the Universe 2: Acceleration and Deceleration