The Cosmological Constant

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Table of contents

1 Basics of Observational Cosmology 
1.1 Introduction
1.2 Newtonian cosmology
1.3 Einstein’s cosmology
1.4 The Friedmann-Lemaître-Gamow model
1.4.1 The Friedmann’s equations
1.4.2 Primordial Universe
1.5 Contents of the Universe
1.6 Baryonic Acoustic Oscillations
1.7 Dark matter
1.8 The Dark Energy
1.8.1 Models with Scalar Fields
1.8.2 The Cosmological Constant
1.9 Hubble diagram and measure of distances
1.9.1 The Comoving Distance
1.9.2 The Age and the Conformal Time
1.9.3 The Luminosity Distance
1.10 The Magnitude Systems
1.10.1 The Apparent Magnitude
1.10.2 The Vega System
1.10.3 The AB System
1.11 Constrain the cosmological parameters
1.12 Conclusion
2 Quasars samples 
2.1 Introduction
2.2 Spectrum of quasar
2.3 Events in the space-time diagram
2.4 The selection eect
2.5 Modelling a sample of quasars
2.5.1 Statistical modelling
2.5.2 Simulation technique
2.5.3 The k-correction
2.6 Conclusion
3 The null correlation technique 
3.1 Introduction
3.2 Weighting factors
3.3 Luminosity function and selection function
3.4 Kolmogorov-Smirnov test
3.5 The V/Vmax test
3.5.1 Calculation of the V/Vmax terms
3.6 Conclusion
4 Application to quasars data 
4.1 Introduction
4.2 The Sloan Digital Sky Survey data
4.2.1 The k-correction
4.3 Results
4.3.1 The null correlation test
4.3.2 The V/Vmax test
4.3.3 Estimation of the luminosity function and the selection function
4.4 Inferences on cosmological expansion based on QSOs
4.5 Conclusion
5 Application to supernovae type Ia sample 
5.1 Introduction
5.2 Type Ia Supernovae as standard candles
5.2.1 The lightcurve of type-Ia SN
5.2.2 Standardisation of type-Ia SN
5.2.3 Modelling of the Supernova event
5.2.4 5.2.4 Sampling the light curve of type-Ia SN and selection eects
5.2.5 Calibration statistics
5.2.6 Simulation
5.3 The null correlation test on the supernova sample
5.3.1 Luminosity function and Selection function
5.3.2 Precision and error
5.4 Application to the JLA sample
5.4.1 Description of samples
5.4.2 Results
5.5 Conclusion
6 Résumé en français 
6.1 La cosmologie moderne
6.2 Simulation d’échantillon de quasar
6.3 La technique de corrélation nulle
6.4 Résultats avec les données quasars
6.5 Modélisation d’échantillon de supernova et résultats sur les donn ées de SDSS-II/SNLS3
Appendices 
A Probability density functions 
B Calculation of the weighting factor 
C Calculation of V(M) 
D Code Python