Lecture Notes on Gravitational Waves in Cosmology

Key Lecture Topics

• Gravitational waves and their significance in cosmology
• Bayesian parameter estimation
• Selection effects (if time permits)
• Projections for future research and open questions

Gravitational Waveforms

Key Characteristics

• Amplitude and Phase
• Sensitive to both amplitude and phase (unlike electromagnetic astronomy, which primarily measures intensity)
• Ability to track phase evolution
• Importance of amplitude and phase sensitivity in cosmology

Differences Between Optical Astronomy and Gravitational Wave Astronomy

• Gravitational wave astronomy looks for coherent sources
• Relationship between amplitude and distance
  • Amplitude falls off as (1/R) while intensity in optical astronomy falls off as (1/R^2)
  • Sensitivities: Doubling detector sensitivity extends observational range twices for gravitational waves, whereas only (\sqrt{2}) times for electromagnetic methods

Types of Gravitational Wave Sources

• Transients (short duration)
  • Compact Binary Coalescence (CBC)
  • Unmodeled burst signals (e.g., supernovae)
• Long Duration or Background
  • Continuous waves (e.g., from neutron stars with distortions)
  • Stochastic backgrounds (accumulated from many sources)

Non-Event Sources

• Primordial background: Key for cosmology, but difficult to detect currently
• Stochastic background: Combination of various sources like CBCs, supernovae, etc.

Modeling Gravitational Waveforms

Three Phases of a Waveform

1. In-spiral: Can be calculated using post-Newtonian expansions
2. Merger: Requires numerical relativity
3. Ring-down: Can utilize black hole perturbation theory but needs fitting from numerical relativity

Source Parameters

• Black Holes: Masses, Spins (6 parameters for double black holes)
• Neutron Stars: Additional parameters for matter (tidal deformability, etc.). Neutron star parameters increase total to 8+ parameters

Parameter Extraction and Distance Measurement

• Gravitational wave data allows direct measurement of distance independent of a “distance ladder”
• Intrinsic parameters affect phase; extrinsic affect amplitude

Gravitational Wave Detection & Parameter Estimation

• Initial searches identify interesting data portions
• Rigorous parameter estimation follows, separating into high-latency (accurate) and low-latency (fast, for real-time applications)

Importance of Redshift in Cosmology

• Redshift affects time intervals and frequencies, impacting phase measurement
• Amplitude depends on total mass and angles; distance inferred from amplitude

Parameters of Importance in Amplitude and Phase Determination

• Intrinsic: Masses, Spins (In-band for phase modeling)
• Extrinsic: Distance, Sky Position, Orbital Phase, etc. (mainly affect amplitude)

Summary and Outlook

• Gravitational waves offer a powerful tool for cosmological studies due to their unique measurement capabilities.
• Future discussions will include detailed cosmology applications using gravitational wave data.

Questions and Interactions

• Encouragement to ask questions during/after the lecture.
• Clarifications provided on complex topics as needed.