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The Early Universe
by
Ricardo de Ruiter
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The Aim
Describing the early universe by:• Finding a relation between temperature and time• Describing different epochs in the early universe• Relating the epochs to energy and degrees of freedom
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Assumptions & Density Parameters
Assumptions:
• Instantaneous transition radiation dominated era to matter dominated era
Relativistc density parameter ,
Non-relativistic density parameter
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Matter-Radiation Equality
Ratio of relativistic and non-relativistic matter:
Using that at equality:
As comparison at the time of decoupling
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Matter Dominated Era
From and :
•
Since and , then:
Holds for
Or or
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Radiation Dominated Era
From and :
•
Since and , then:
Or:
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Describing the (T,t)-relation
Schematic plot of T(t)
𝑇𝑇𝑒𝑞
=( 𝑡𝑒𝑞𝑡 )1/2
𝑇𝑇0
=( 𝑡0𝑡 )2 /3
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Describing the (T,t)-relation
1.00E-12 1.00E-09 1.00E-06 1.00E-03 1.00E+00 1.00E+03 1.00E+06 1.00E+09 1.00E+12 1.00E+15 1.00E+181.00E+00
1.00E+02
1.00E+04
1.00E+06
1.00E+08
1.00E+10
1.00E+12
1.00E+14
1.00E+16
Temperture-time relation of the early universe
T
𝑇 ∝ t−2 /3
𝑇 ∝ t−1/2
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Timescales in the Early Universe
Timescales can be related to energy:
Different physical manifestations at different energies, thus time and temperature!
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At higher temperatures, there are much higher energies:
Equipartition theorem: internal energy proportional to degrees of freedom!
, where .
Degrees of Freedom and Energy – I
Time Temperature Energy
t < 10-10 s T > 1015 K > 10n GeV
10-10 s < t < 10-4 s 1015 K > T > 1012 K 10n GeV > E > 100n MeV
10-4 s < t < 1 s 1012 K > T > 1010 K 100n MeV > E > 1n MeV
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Degrees of Freedom and Energy – IIType Appr. Mass Notes g Total
Quarks 174.2 GeV4.2 GeV1.3 GeV95 MeV
5 MeV2 MeV
Spin ½ 3 colors
2 x 2 x 3……………
12……………
72
Gluons 8 massless Spin 1 2 8 x 216
Leptons 1.8 GeV106 MeV
511 kev
< 18.2 MeV< 190 keV
< 2 eV
Spin ½
Spin ½
2 x 2……
2……
4……
122……6
EW Gauge bosons 80 GeV80 GeV91 GeV
< 6 x 10-17 eV
Spin 1 3
2
3……2
11
Higgs 114 GeV Spin 0 1 11
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Degrees of Freedom and Energy – III
• Today:• 4 degrees of freedom
• 100 MeV > E > 1 MeV• 12 degrees of freedom
• 10 GeV > E > 100 MeV• From 106 to 12 d.o.f.
• E > 10 GeV• 106 degrees of freedom
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Recent Observations
Concerning the Early Universe
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The Situation
The Problem:What problem?
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The Situation
The Problem:To understand how the universe at large got reionized by the first generation of stars and galaxies, by determining the abundance of those objects and relate them to the total UV-flux in the early universe
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The Situation
The Problem:
To understand how the universe at large got reionized by the first generation of stars and galaxies, by determining the abundance of those objects and relate them to the total UV-flux in the early universe
• What is reionization?
• Why this research?
• How to do this research?
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First surveys: quasars
Advantages
• High luminosity
• Easily observable on the ground
Disadvantages
• Total number drops fast beyond z = 4 (farthest known quasar at z = 7.1)
• Need to be in the “line of fire”
Earlier Research – I
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Later surveys: near infrared (nIR) detection of z > 7 galaxies using Lyman dropout.
Lyman dropout uses the Lyman limit and its redshift
Disadvantages
• Extreme faintness (magnitude 28 or higher)• Difficulty distinguishing high-z galaxies from moderate-z galaxies and brown dwarfs• Only possible Ly α is bright
Earlier Research – II
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The authors used another way of probing the early universe: (the afterglow of) gamma ray burtsts (GRBs)
Advantages
• High luminosity (opens a path to high-z objects)
• Power law behaviour of the afterglow
Disadvantages
• Distance (observations in nIR)
• Narrow window of observation
An alternative
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Data Acquisition
• Six different GRBs have been analyzed
• Host galaxies are found using astrometry• “Why measure distance again?”
• Pinpointing allows for obtaining spectra
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Results & Analysis – I: Star Formation Rate
Researchers distilled the Star Formation Rate from the observed galaxies.
The SFR is determined by:
(As comparison: a -10 magnitude dwarf galaxy of , which has a approximate value of in the denomi-nator)
Star formation is modest and seems to take place mostly in faint
galaxies
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Results & Analysis – II: Luminosity Functions
Luminosity function: number of galaxies over a certain interval:
, characteristic galaxy luminosity, power-law slope and normalization factor.
GRBs in the sample show
The higher the redshift, the fainter the galaxies seem to
become and the harder it is to observe them!
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Results & Analysis – III: Probability of Detection
Statistical analysis shows the probabililty of NOT detecting a galaxy
The overall probability of NOT finding all the host galaxies is 0.17. Only one of the six has been found with high certainty. This favors an evolving luminosity function.
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Results & Analysis – IV: True and Observed Flux Density
Statistical analysis compares true and observed flux density probabilities.
Correspondence between the blue and red lines suggests that the finding of specific GRB locations should be able to be drawn randomly from a uniform distribution.
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Conclusions
From the data, only one host galaxy was evidently detected. However, the researchers concluded that
The majority of star formation at high redshifts takes place in small galaxies that are too faint to be detected
Results
• Fit a rapidly evolving luminosity function to higher redshifts
• Are inconsistent with non-evolving functions
• Are hung on two main assumptions
• Demonstrate the potential of GRBs in determining the overall UV-flux in the early universe in order to explain reionization at large scales
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Questions?