The Cosmic Spacetime

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Section I: Space and Time
	Chapter 1: Introduction
		1.1 HOT BIG BANG COSMOLOGY
		1.2 LARGE-SCALE STRUCTURE
		1.3 THE COSMOLOGICAL PRINCIPLE: HOMOGENEITY & ISOTROPY
	Chapter 2: Theoretical Background
		2.1 BASIC CONSIDERATIONS
		2.2 SPECIAL RELATIVITY
		2.3 FOUR-DIMENSIONAL SPACETIME
		2.4 ACCELERATED FRAMES
		2.5 RELATIVISTIC CONTINUUM MECHANICS
		2.6 THE PRINCIPLE OF EQUIVALENCE
		2.7 EINSTEIN’S FIELD EQUATIONS
	Chapter 3: The Black-hole Spacetime
		3.1 SCHWARZSCHILD METRIC
		3.2 KERR METRIC
	Chapter 4: The Cosmic Spacetime
		4.1 THE METRIC IN COMOVING COORDINATES
		4.2 FRIEDMANN, LEMAˆITRE, ROBERTSON & WALKER
		4.3 PHYSICAL INTERPRETATION OF THE FRIEDMANN EQUATION
Section II: The Metric
	Chapter 5: Special FLRW Solutions
		5.1 MILNE UNIVERSE
		5.2 DE SITTER SPACE
		5.3 EINSTEIN-DE SITTER UNIVERSE
		5.4 STATIC FLRW SOLUTIONS
			5.4.1 Minkowski Spacetime
			5.4.2 The Milne Universe (Revisited)
			5.4.3 de Sitter Space
			5.4.4 The Lanczos Universe
			5.4.5 The Lanczos Universe with
			5.4.6 Anti-de Sitter Space (Negative
	Chapter 6: The Standard Model
		6.1 STANDARD MODEL BASICS
		6.2 THE EARLY UNIVERSE
		6.3 NUCLEOSYNTHESIS
		6.4 THE COSMIC MICROWAVE BACKGROUND
		6.5 THE TEMPERATURE HORIZON PROBLEM
		6.6 BASIC SLOW-ROLL INFLATION
		6.7 QUANTUM FLUCTUATIONS IN THE INFLATON FIELD
	Chapter 7: The Gravitational Horizon
		7.1 BRIEF HISTORICAL BACKGROUND
		7.2 THE BIRKHOFF-JEBSEN THEOREM
		7.3 THE (APPARENT) GRAVITATIONAL HORIZON
		7.4 GEODESICS IN THE FLRW SPACETIME
		7.5 PROPER SIZE OF THE VISIBLE UNIVERSE
		7.6 A COMPARISON OF THE GRAVITATIONAL, PARTICLE AND EVENT HORIZONS
		7.7 GAUGE TRANSFORMATIONS WITH
			7.7.1 de Sitter Space
			7.7.2 A Cosmology with
			7.7.3 Radiation Dominated Universe
			7.7.4 Einstein-de Sitter Universe (
			7.7.5 The Standard (
	Chapter 8: Cosmological Redshift
		8.1 DEFINITION
		8.2 REDSHIFT IN STATIC SPACETIMES
			8.2.1 Minkowski Spacetime
			8.2.2 The Milne Universe
			8.2.3 de Sitter Space
			8.2.4 The Lanczos Universe
			8.2.5 A Lanczos Universe with
			8.2.6 Anti-de Sitter Space
		8.3 EXPANSION OF SPACE
Section III: The Metric
	Chapter 9: Emergence of Zero Active Mass
		9.1 A MOST CURIOUS COINCIDENCE
		9.2 AGE OF THE UNIVERSE VERSUS REDSHIFT
		9.3 HIGH-REDSHIFT QUASARS
		9.4 HIGH-REDSHIFT GALAXIES
		9.5 CONCLUDING REMARKS
	Chapter 10: Theoretical Basis for Zero Active Mass
		10.1 THE LAPSE FUNCTION
		10.2 THE COSMOLOGICAL ORIGIN OF
	Chapter 11: The Horizon Problems
		11.1 INFLATION: A STATUS UPDATE
		11.2 VIABILITY OF SLOW-ROLL INFLATION
		11.3 THE TEMPERATURE HORIZON PROBLEM
		11.4 THE ELECTROWEAK HORIZON PROBLEM
	Chapter 12: Observing Zero Active Mass
		12.1 STATISTICAL METHODS USED IN MODEL SELECTION
			12.1.1 Information Criteria
			12.1.2 Two-point Diagnostics
		12.2 REDSHIFT-DEPENDENT EXPANSION RATE
		12.3 THE HUBBLE DIAGRAM
			12.3.1 Active Galactic Nuclei
			12.3.2 Type Ia Supernovae
		12.4 THE ANGULAR-DIAMETER DISTANCE
		12.5 STRONG GRAVITATIONAL LENSING
		12.6 THE COSMIC EQUATION OF STATE
	Chapter 13: Structure Formation
		13.1 QUANTUM FLUCTUATIONS AT THE PLANCK SCALE
		13.2 STRUCTURE FORMATION
			13.2.1 Perturbed Boltzmann Equation,
			13.2.2 Perturbed Boltzmann Equation, Zero Active Mass
			13.2.3 The Observed Matter Power Spectrum
		13.3 THE OBSERVED HALO MASS FUNCTION
	Chapter 14: Future Prospects
		14.1 A DIRECT TEST OF THE COSMIC SPACETIME
		14.2 OBSERVATIONS OVER THE COMING DECADES
			14.2.1 Dark Energy Surveys
			14.2.2 B-mode Polarization in the CMB
			14.2.3 Re-ionization History
			14.2.4 The Redshift-time Relation
		14.3 MAJOR UNSOLVED PROBLEMS IN
			14.3.1 The Trans-Planckian Problem
			14.3.2 The Horizon Problems
			14.3.3 BBN and the
			14.3.4 Timeline for SMBHs and Early Galaxies
			14.3.5 The Halo Mass Function
			14.3.6 The Hubble Constant
		14.4 OPEN QUESTIONS IN FLRW WITH ZERO ACTIVE MASS
			14.4.1 BBN
			14.4.2 N-Body Simulations
			14.4.3 CMB Power Spectrum Below One Degree
		14.5 CONCLUDING REMARKS
Bibliography
Index