Patterns Across the Universe: Clusters and the Cosmic Web

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Patterns Across the UniverseClusters and
the Cosmic Web
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Patterns Across the Universe

• Rien van de Weijgaert
• Kapteyn Institute, Groningen
• Summerschool
• Guillermo Haro 2005
• A Pan-Chromatic View of Clusters of Galaxies
• the Large-Scale Structure
• June 27-July 8, 2005, Puebla, Mexico

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Preliminaries
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Lecture Theme
Cosmic Matter and Galaxy Distribution displays
salient geometric patterns, the Cosmic Web.
Clusters are found at the densest spots, the
interstices, of this network. These lectures seek
to address the issue of the origin, formation and
dynamics of the Cosmic Web. It will investigate
the position and setting of clusters within the
cosmic web, and the role of the web for the
formation and evolution of clusters.
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Lecture Outline

• The Cosmic Foam
• Census (observational)
• Formation of the Cosmic Web
• Linear Theory Gravitational
  Instability
• Gaussian random fields
• Peaks in Gaussian random fields
• Constrained Random Fields
• Formation of the Cosmic Web
  
• Nonlinear Structure Growth
• Anisotropic Collapse
• Hierarchical Clustering
• Voids
• Analysis of the Cosmic Web
• Modelling superclustering
• Measures Weblike Patterns/Topologies

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Historical Precedents
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Academia of Plato, Athens
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With warm thanks to my organizer-friends,
Manolis Omar
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Cosmology GeometryPlatos Cosmic Scheme
Demiurge, divine craftsman, is a
mathematician Universe constructed according
to Geometric Principles The Platonic Solids
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Cosmology GeometryPlatos Cosmic Scheme
? Four basic constituents
of nature - fire Pyramid
- air Octahedron -
earth Cube - water
Icosahedron ? The Cosmos itself
Dodecahedron
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Cosmological Background
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The Hot Big Bang Universe
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the Hot Big Bang

• One of the greatest and most astonishing
  triumphs of
• science, the unravelling of
• nature, origin and evolution
• of the Universe

Einstein and de Sitter discussing the Universe,
in Leiden
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Let no one unversed in geometry enter here
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Einsteins Field Equations
Spacetime becomes a dynamic continuum,
integral part of the structure of the cosmos
curved spacetime becomes force of gravity
its geometry rules the world, the world
rules its geometry
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Geometry of the UniverseCosmological Principle
God is an infinite sphere whose centre is
everywhere and its circumference nowhere
Empedocles, 5th cent
BC
Cosmological
Principle Describes the symmetries in
global appearance of the Universe
? Homogeneous ?
Isotropic ? Universality
? Uniformly Expanding
The Universe is the same everywhere -
physical quantities (density, T,p,) The
Universe looks the same in every
direction Physical Laws same everywhere The
Universe grows with same rate in -
every direction - at every location
all places in the Universe are alike
Einstein, 1931
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Geometry of the Universe
Fundamental Tenet (Non-Euclidian Riemannian)
Geometry ? there exist no more
than THREE uniform spaces 1)
Euclidian (flat) Geometry
Euclides 2) Hyperbolic Geometry
Gauß,

Lobachevski, Bolyai
3) Spherical Geometry
Riemann
uniform homogeneous isotropic
(cosmological principle)
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Geometry of the UniverseRobertson-Walker Metric
The geometry of the 3 homogenous and isotropic
space-times can be expressed in terms of its
metric, specifying the distance between any 2
points in space-time (t,r,?,f). These may be
shown to have the above expression
Robertson-Walker metric
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Friedmann-Robertson-Walker-Lemaitre Universe
for an expanding Universe with ?
matter density ?(t) ? pressure p(t)
? cosmological constant ? or
elusive dark energy ?v (t)
whose dynamics is ultimately set by the
geometrical term k
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Geometry DynamicsFriedmann-Robertson-Walker-Le
maitre Universe
Evolution Fate of the universe determined by
one major factor
the ratio of the cosmic (energy) density
to , the critical density needed
to have a flat Universe .
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DynamicsFriedmann-Robertson-Walker-Lemaitre
Universe
Cosmological (energy) densities are typically in
the order of that of the critical energy density
of the universe. Its value at the current cosmic
epoch is
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Friedmann-Robertson-Walker-Lemaitre Universe
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Friedmann-Robertson-Walker-Lemaitre Universe
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Friedmann-Robertson-Walker-Lemaitre Universe
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EADN summerschool, Leiden, July 1995
Friedmann-Robertson-Walker-Lemaitre Universe
of course, since some years ?CDM Universe
deemed concordant
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Friedmann-Robertson-Walker-Lemaitre Universe
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Hubble Expansion
Edwin Hubble (1889-1953)
discovers that galaxies move
apart in a systematic fashion, the
universe flies apart v
H r This expansion of the universe
is real, and is now indicated with
the name Hubble Expansion
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Hubble Expansion
Hubbles original Hubble diagram (1929)
universe expands !!!!
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Hubble Expansion
Hubble Diagram Supernovae I
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Cosmic Constituents
The total energy content of the Universe is made
up by various different constituents, of which
the main ones are
matter
?b
baryonic matter
?m
?DM
dark matter
radiation
??
photons
?rad
?tot
??
neutrinos
?v
dark/vacuum energy
In addition to the constituents mentioned in the
diagram, there are contributions by e.g.
gravitational waves, magnetic fields, etc.
However, given the poor constraints on their
contribution henceforth we will not take them
into consideration.
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Cosmic Energy Inventory
Fukugita Peebles 2004
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Cosmic Energy Inventory
Fukugita Peebles 2004
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Cosmic Energy Inventory
Cosmic Baryons
Fukugita Peebles 2004
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Cosmic Energy Inventory
The Dark Sector
Fukugita Peebles 2004
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Cosmic Constituents
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the Hot Big BangCosmic Timeline
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Adiabatic Expansion
From the Friedmann equations, it is
straightforward to appreciate that cosmic
expansion is an adiabatic process
In other words, there is no external power
responsible for pumping the tube
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Adiabatic Expansion
Translating the adiabatic expansion into the
temperature evolution of baryonic gas and
radiation (photon gas), we find that they cool
down as the Universe expands
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Thus, as we go back in time and the volume of the
Universe shrinks accordingly, the temperature of
the Universe goes up. This temperature behaviour
is the essence behind what we commonly denote as
Hot Big Bang
From this evolution of temperature we can thus
reconstruct
the detailed
Cosmic Thermal History
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Cosmic Microwave Background

• Primordial plasma
• protons, electrons en photons
• opaque
• (major share photons produced after 1 min)
• 379.000 years after Big Bang
• Universe cooled to T 3000 K
• pn ? H protons electrons
• hydrogen atoms
  
• Decoupling photons and atoms
• Cosmos becomes
  transparent
• Surface of last scattering
• Cosmic Microwave Background Radiation
• (expansion
  Universe
• cooled down to
  T2.725 K)

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Cosmic Microwave Background

• Primordial plasma
• protons, electrons en photons
• opaque
• (major share photons produced after 1 min)
• 379.000 years after Big Bang
• Universe cooled to T 3000 K
• pn ? H protons electrons
• hydrogen atoms
  
• Decoupling photons and atoms
• Cosmos becomes
  transparent
• Surface of last scattering
• Cosmic Microwave Background Radiation
• (expansion
  Universe
• cooled down to
  T2.725 K)

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Cosmic Microwave Background
Big Bang The CMB photons produced at
z109 visible as
a perfectly thermal and isotropic radiation
blanket
T2.725 K
Discovered in 1965 by Penzias Wilson
(Nobelprize 1978)
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Cosmic Microwave Background
COBE (1992) Accurate measurement
Planck spectrum CMB First detection angular
temperature perturbations (? 7o)
Sachs-Wolfe effect
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Cosmic Microwave Background

• WMAP
• (2003)
• Accurate mapping
• primordial
• temperature
• perturbations at
• sub-horizon scale

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Post-Recombination Universe the Emergence of
Structure
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the Universe Infrastructure
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The Stars
a journey
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The Galaxy
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Galaxies
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Groups Clusters
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... A Cosmic Filigree
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Up to the depths of the
visible Universe

Our Galaxy