The Early Universe

by

Ricardo de Ruiter

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

Assumptions & Density Parameters

Assumptions:

• Instantaneous transition radiation dominated era to matter dominated era

Relativistc density parameter ,

Non-relativistic density parameter

Matter-Radiation Equality

Ratio of relativistic and non-relativistic matter:

Using that at equality:

As comparison at the time of decoupling

Matter Dominated Era

From and :

•

Since and , then:

Holds for

Or or

Radiation Dominated Era

From and :

•

Since and , then:

Or:

Describing the (T,t)-relation

Schematic plot of T(t)

𝑇𝑇𝑒𝑞

=( 𝑡𝑒𝑞𝑡 )1/2

𝑇𝑇0

=( 𝑡0𝑡 )2 /3

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

Timescales in the Early Universe

Timescales can be related to energy:

Different physical manifestations at different energies, thus time and temperature!

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

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

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

Recent Observations

Concerning the Early Universe

The Situation

The Problem:What problem?

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

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?

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

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

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

Data Acquisition

• Six different GRBs have been analyzed

• Host galaxies are found using astrometry• “Why measure distance again?”

• Pinpointing allows for obtaining spectra

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

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!

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.

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.

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

Questions?