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Expansion.ppt. J. Jers ák, Technical Univ. Aachen Theoretical Physics Prague, April 2007. Expansion of space in contemporary cosmology. Geschichte des Universums aus einem Schulbuch in D. CMB. History of the expansion paradigm (I). Known since 1920´s

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expansion ppt


J. Jersák,

Technical Univ. Aachen

Theoretical Physics

Prague, April 2007

history of the expansion paradigm i
History of the expansion paradigm (I)
  • Known since 1920´s

(after GR 1915)

  • Originaltheory of expansion

based on general relativity (GR)

De Sitter (Netherland), Friedmann (Russia),

Lemaître(Belgium, L'Hypothèse de l'Atome Primitif), …

history of the expansion paradigm ii
History of the expansion paradigm (II)
  • First observations in 1920´s:
  • Redshift ofclose Galaxies

increases with their distance

  • Evidence ofthe expansion:

Hubble (USA)

  • Since 1995: Observation of distant galaxies
  • Evidence of an

accelerated expansion

understanding of the expansion
Understanding of the expansion
  • 1920-1990´s:

„simple“ explanations of the expansion without GR

(bomb-like explosion in a rigid space,

using Newtonian mechanics or SR only,

evoking Doppler-effect,

assuming energy conservation, etc.)

were wrong

  • Today:consequentely GR

+ dark energy

both introduced into cosmology by Einstein

universe on cosmological time scales giga
Universe on cosmologicaltime-scales (Giga…)
  • 1 Gy = 1 000 000 000y = billion years
  • Solar system age 4,5 Gy
  • Our galaxy age ≈ 10 Gy
  • Universe since the big bang t0 = 14 Gy
  • Cosmic microwave background (CMB) origin 400 000 y= 0.000 4 Gy
  • Big bang t ≈ 0
universe on cosmological length scales giga
Universe on cosmologicallength-scales (Giga…)
  • 1 Gly = 1 000 000 000ly = 1 billion light years
  • Galaxies („dust particles“) 0,000 1 Gly
  • Galaxy clusters 0,001 Gly
  • Uniform mass distribution

(no structures) from 1 Gly

  • Observables Universe (radius) 46 Gly
distribution of galaxies over the whole sky
Distribution of galaxies over the whole sky



Cosmic microwave background (CMB)averaged over all sky directionsT0 = 2.730+/-0.001° (COBE)T-fluctuations onlyvery fine0,000 02 °K (COBE and WMAP satellites)

COBE 1989: Mather, Smoot, Nobel prize 2006

w hu http background uchicago edu 7ewhu beginners introduction html

Cosmic microwave background (CMB)

From all sky directions atlower T-resolution:T0 = 2,7..°K

W. Hu, http://background.uchicago.edu/%7ewhu/beginners/introduction.html
the observable universe is equal everywhere and expands on all distance scales
The observable Universe is equal everywhere and expands on all distance scales

For an understanding of the expansion is

the general theory of relativity (GR) .necessary

[ Attention!!!...!!!

The special theory of relativity (SR) ist

. NOT applicable! ]

cosmic time t
Cosmic time t

applicable in the whole observable Universe

GR => no inertial system is required.(different from SR)

Since the Univere is equal everywhere,

it has also the same age everywhere

  • Cosmic aget

Defined by the expansion as by a sandglass

Today: t = t0 ( = 14 Gy)

cosmic proper distance d t
Cosmic („proper“) distance D(t)
  • All directions are egual
  • It suffices to consider the

± distanceD(t)

between pairs of distant galaxies

in arbitrary directions

  • Demo of1-dimGR-space: a rubber band





The space expands, but remains locally always the same.Galaxies recede from each other,but they are at restin space and do not expand.


2 dim model of expansion c h lineweaver and t m davis scientific american march 2005
2-dim model of expansionC.H.Lineweaver and T.M.Davis,Scientific American, March 2005

Read, please

a curved 2 dim surface of an air balloon is a good model of the whole universe
A curved 2-dim surface of an air balloon is a good model of thewhole Universe



part of the


is ≈ flat

what is the expansion
What is the expansion:
  • Expansion = stretching of the . space .

Therefore galaxies recede from each other

  • Recession velocity v

of the galaxies at rest

is not a mechanicalmotion

of the galaxies through the space!

the hubble law

The Hubble law

(in a modern form)

Recession velocity v of galaxies

is rigorously proportional to their distance D

H(t) … Hubble expansion parameter

measures the expansion velocity of the space

it is in no contradiction with sr
It is in no contradiction with SR
  • Expansion cannot transmit a signal
  • SR holds around any place

. = locally (in any galaxy)

  • Locally,the light velocity is alwaysc
  • Locally, iscthe maximal velocity
  • At large distances (nonlocally),SR is not applicable
cosmological redshift z29
Cosmological redshift z
  • Expansion of the wave length λ of the light

during ist travel to us

through the expanding space

  • It has NOTHING to do with the motion of the source

=>NOT the Doppler effect!

typical observed values of z
Typical observed values ofz
  • First observations by Hubble 1929:

D < 0,04 Gly z < 0.0003

  • Galaxies at the Hubble distance

D =DH= 14 Glyv = cz = 1.5

  • Quasars up to z ≈ 6.4
  • CMB source: v = 3cz = 1090
universe on cosmological velocity scales
Universe on cosmologicalvelocity scales

c = 1Gly/Gy= 300 000 km/s

Mechanical velocities through the space:

  • Earth around Sun 0,0001c
  • Typical motion of galaxies 0,003c

Large recession velocities:

  • Galaxies with z > 1,5(> thousand observed!) > c
  • Source of CMB today (z = 1090) 3c
  • Source of CMB „then“ 50c
cosmic scale a t
Cosmic scale a(t)
  • Distances normalized with respect to the present ones
  • All length scales in cosmology are proportional to the cosmic scale

a(t)determines the expansion

at all distances simultaneously

a t describes the expansion
a(t) describes the expansion
  • a(t0) = 1 D(t0) today
  • a(t´) = 2 D(t´) = 2D(t0)
  • a(t´´) = 1/1000 D(t´´) = D(t0)/1000
z a t relation
z-a(t) relation
  • t… time of emission (t < t0)
  • 1+z measures the expansion of space

between t and t0

  • Z> 0is an evidence of the expansion


how fast does the universe expand
How fastdoes the Universe expand?
  • Hubble-law:v(t) = H(t) D(t)
  • H(t) large … fasterexpansion
  • H(t) small … slowerexpansion

H(t) = ?<=>a(t) = ?

empirical properties of h t
Empirical properties of H(t):
  • H(t) is t-dependent
  • After the big bang decreased for ≈ 7 Gy

H(t) ~1/t=>decelerated expansion

  • Since ≈ 7 Gy

H(t)≈ const=>accelerated expansion

  • The present value („Hubble-constant“): . H(t0) = 70 km/s Mpc (1Mpc = 0.003 Gly)

… and a THEORY ???

qualitative description of changes of the expansion velocity
Qualitative description of changes of the expansion velocity:

Matter decelerates the expansion

Einstein´s cosmological constantΛaccelerates the expansion

theory of space expansion
THEORY of space expansion
  • Equations of the Einstein´s general relativity

. (Friedmann-Lemaître eqs. without the pressure term)

  • Negative contribution to the acceleration
  • Decelerates the expansion
  • Ist density decreases during the Expansion:
cosmological constant
Cosmological constant Λ
  • Positivecontribution to the acceleration
  • Accelerates the expansion
  • Remains constant with t
  • The second greatest discovery by Einstein (next to GR)?
de sitter universe
De Sitter Universe
  • Universe without matter, only Λ
  • De Sitter 1917:

Exponentially accelerated expansion

discovery during the last 10 years
Discovery during the last 10 years:
  • Supernovae observations =>

The expansion accelerates!

Some accelerating term

like Λ is required

the cause of the acceleration
The cause of the acceleration?
  • New constant of Nature

= cosmological constantΛà la Einstein?

  • Quintessence?A new scalar field≈Λ(t)?

Suggested first by Ch. Wetterich (Heidelberg)

  • Energy of the vacuum (quantum effect)?

To be expected, but theoreticians cannot calculate ist value

ch wetterich
Ch. Wetterich

Quintessence !

Fire , air, water, earth!

Standard-model of the antic Greeks

constant of nature quintessence vacuum energy cosmologists need something like that
Constant of NatureΛ,Quintessence, Vacuum energy,???Cosmologists need something like that:


Nobody knows, whatit is,

since it is transparent (unobservable)!

- A completely new (dark) category?

energy in contemporary observable universe
Energy in contemporary observable Universe
  • 73±% dark energy dominates
  • 4% known matter

≈ atoms (stars, H-gas, . ourselves)

  • 23±% unknown matter

(„dark matter“)

  • Matter slows down,

dark energy speeds up

the expansion


  • „Cosmologists are often wrong, but never in doubt“

. L.D. Landau

  • I am not a cosmologist!
  • Is the contemporary understanding of the expansion

. alreadycorrect?

  • Will this bizarre dark energy remain,

and what is it?

  • New surprises possible!

Stay tuned!

light signal in our direction beyond d h t
Light signal in our directionbeyond DH(t)

Recedes from us because

the recession is superluminal there:


light signal speed

Total velocity

of the signal

recession velocity v increases proportionally to the distance
Recession velocity v increases proportionally to the distance


v= c










v < c

v= c

v > c