Large-Scale Structure, Nonlinear Growth, and Weak Lensing
From Linear Perturbations to the Cosmic Web
Growth of Structure
Density perturbations grow under gravity after horizon re-entry, with the linear growth factor governed by a second-order differential equation depending on the expansion history. On small scales, nonlinear collapse leads to virialized halos, filaments, and voids, requiring perturbation theory, effective field theory, or numerical simulation.
Structure Probes
| Probe | Primary observable | Cosmological sensitivity |
|---|---|---|
| Galaxy clustering | and correlation functions | BAO, growth, bias |
| Weak lensing | Shear and convergence fields | , , geometry |
| Redshift-space distortions | Anisotropic clustering | Growth rate |
| Clusters of galaxies | Mass function and abundance | Late-time growth and calibration |
Observable Combination
Large-scale structure provides a complementary view to the CMB by measuring late-time growth, neutrino mass suppression, dark energy, and modified gravity effects.
What does weak gravitational lensing directly measure?
Weak lensing distorts galaxy shapes in response to the integrated gravitational potential.
Correct answer: The projected tidal field along the line of sight
Linear vs Nonlinear Regimes
Linear regime
- Perturbations remain small.
- Analytic growth and transfer functions apply.
- Power spectrum methods are highly effective.
Nonlinear regime
- Mode coupling becomes important.
- Requires simulations or effective field theory.
- Halo bias and baryonic feedback complicate inference.
Why are baryonic effects a major challenge for small-scale cosmology?
These processes alter the matter power spectrum and halo structure, limiting parameter inference on small scales.
Correct answer: Because feedback from gas cooling, star formation, and AGN reshapes matter clustering in ways that are difficult to model precisely.
Which quantity is commonly extracted from redshift-space distortions?
Redshift-space distortions probe the velocity field and growth rate combination .
Correct answer:
Weak Lensing Measurement Pipeline
-
1
Measure galaxy shapes and correct for the point-spread function.
-
2
Estimate shear two-point statistics or higher-order summaries.
-
3
Model intrinsic alignments, photo-z errors, and survey systematics.
-
4
Infer cosmological parameters with a likelihood or simulation-based emulator.
Open Frontier: Summary Statistics Beyond the Power Spectrum
Because nonlinear structure contains non-Gaussian information, modern cosmology increasingly uses bispectra, Minkowski functionals, peak counts, wavelets, graph-based summaries, and simulation-based inference to extract information beyond traditional two-point statistics.