course dates credits
Large Scale Structure Feb 24 - Mar 19 3
teachers schedule term
Emiliano Sefusatti Mon-Thu, 8:30-10:00 2

Program:

  • Introduction. Large-scale structure. Homogeneity. FRW metric. Redshift. Friedmann's equations.
  • Random Fields. Matter density and galaxy number density. Random fields. Correlation functions and statistical homogeneity & isotropy. Power Spectrum. Gaussian Random Fields.
  • Initial Conditions.Evolution of fluctuations. Primordial curvature perturbations. Large-scales matter perturbations. Small scales, transfer function.
  • Linear Eulerian Perturbation Theory. Vlasov equation. Single-stream approximation. Equations of motion. Linear theory. Einstein de-Sitter solutions. Vorticity. Linear propagator. Growth factor and growth rate in ΛCDM.
  • Nonlinear Evolution. Nonlinear solutions in SPT. ΛCDM approximation. Non-Gaussianity. Bispectrum from gravitational instability. Nonlinear power spectrum in Standard PT. Nonlinear propagator in Renormalised PT. Effective Field Theory of LSS.
  • Lagrangian Perturbation Theory. Lagrangian dynamics. Zeldovich approximation. Zeldovich pancakes. 2LPT. Relation to Eulerian PT. Applications.
  • Galaxy bias. Local bias. The galaxy power spectrum and bispectrum with local bias. Nonlocal bias. Higher-derivatives corrections. Bias loop corrections and bias renormalisation.
  • Baryonic Acoustic Oscillations. BAO as a standard ruler. Nonlinear evolution of acoustic oscillations. Reconstruction.
  • Redshift Space Distortions. Kaiser effect. Finger-of-God effect. Models.
  • Spherical Collapse. Equation of motion and parametric solution. Onset of collapse. Linear and nonlinear density. Turnaround and collapse. Relation to Eulerian PT.
  • Dark Matter Halos. Mass function. Press-Schechter. Halo bias and the peak-background split. Nonlinear predictions for the matter and galaxy power spectrum in the Halo Model. The Halo Occupation Distribution.
  • Errors. Finite volume and the DFT. Poisson sampling. Shot-noise. Power Spectrum covariance.

Prerequisites:

  • General Relativity,
  • Cosmological Perturbation Theory

Books:

  • Bernardeau et al., Large-scale structure of the Universe and cosmological perturbation theory, Physics Reports 367 (2002) [mainly]
  • Peebles, The large-scale structure of the Universe, Princeton University Press (1980) [some parts]
  • Padmanabhan, Structure formation in the Universe, Cambridge University Press (1993) [spherical collapse]

Online Resources:

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