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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Technical Univ. Aachen
Prague, April 2007
(after GR 1915)
based on general relativity (GR)
De Sitter (Netherland), Friedmann (Russia),
Lemaître(Belgium, L'Hypothèse de l'Atome Primitif), …
increases with their distance
„simple“ explanations of the expansion without GR
(bomb-like explosion in a rigid space,
using Newtonian mechanics or SR only,
assuming energy conservation, etc.)
+ dark energy
both introduced into cosmology by Einstein
(no structures) from 1 Gly
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
For an understanding of the expansion is
the general theory of relativity (GR) .necessary
The special theory of relativity (SR) ist
. NOT applicable! ]
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
Defined by the expansion as by a sandglass
Today: t = t0 ( = 14 Gy)
between pairs of distant galaxies
in arbitrary directions
The space expands, but remains locally always the same.Galaxies recede from each other,but they are at restin space and do not expand.
part of the
is ≈ flat
Therefore galaxies recede from each other
of the galaxies at rest
is not a mechanicalmotion
of the galaxies through the space!
(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
. = locally (in any galaxy)
during ist travel to us
through the expanding space
=>NOT the Doppler effect!
D < 0,04 Gly z < 0.0003
D =DH= 14 Glyv = cz = 1.5
c = 1Gly/Gy= 300 000 km/s
Mechanical velocities through the space:
Large recession velocities:
a(t)determines the expansion
at all distances simultaneously
between t and t0
H(t) = ?<=>a(t) = ?
H(t) ~1/t=>decelerated expansion
H(t)≈ const=>accelerated expansion
… and a THEORY ???
Matter decelerates the expansion
Einstein´s cosmological constantΛaccelerates the expansion
. (Friedmann-Lemaître eqs. without the pressure term)
Exponentially accelerated expansion
The expansion accelerates!
Some accelerating term
like Λ is required
= cosmological constantΛà la Einstein?
Suggested first by Ch. Wetterich (Heidelberg)
To be expected, but theoreticians cannot calculate ist value
Fire , air, water, earth!
Standard-model of the antic Greeks
Nobody knows, whatit is,
since it is transparent (unobservable)!
- A completely new (dark) category?
≈ atoms (stars, H-gas, . ourselves)
dark energy speeds up
. L.D. Landau
and what is it?
Recedes from us because
the recession is superluminal there:
light signal speed
of the signal
v < c
v > c