Lagrangian theory of gravitational instability of Friedman-Lemaître cosmologies: a generic third-order model for non-linear clustering

By T. Buchert. 1993

The Lagrangian perturbation theory of Friedman-Lemaitre cosmologies, which was investigated and solved up to the second order in earlier papers, is evaluated up to the third order. Based on this, a model for non-linear clustering applicable to the modelling of large-scale structure in the Universe for generic initial conditions is formulated. A truncated model is proposed which represents the main body of the perturbation sequence in the early non-linear regime by neglecting all gravitational sources that describe interaction of the perturbations. I also, however, give the irrotational solutions generated by the interaction terms to the third order, which induce vorticity in Lagrangian space. The consequences and applicability of the solutions are put into perspective

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Citations in the corpus

Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing (2013, methodology): “We rely on 2LPT for the long-range component: Ψ2LPT = −D∇φ (1) +D2∇φ (2) , (1) whereD is the linear growth factor andD2 ≃ −3/7Ω−1/143D2 (for details on 2LPT see Buchert 1994; Bouchet et al. 1995; Catelan 1995).”
The Initial Conditions of the Universe from Constrained Simulations (2012, background): “For technical detailswe refer to Buchert (1994); Bouchet et al. (1995); Bernardeau et al. (2002).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: modelling the clustering and halo occupation distribution of BOSS CMASS galaxies in the Final Data Release (2015, methodology): “…field is estimated using augmented Lagrangian perturbation theory (Kitaura & Heß 2013) which combines the second-order perturbation theory (see e.g. Buchert 1994; Bouchet et al. 1995; Catelan 1995) and spherical collapse approximation (see Bernardeau 1994; Mohayaee et al. 2006; Neyrinck 2013).”
PTHALOS: a fast method for generating mock galaxy distributions (2001, background): “It is possible to improve on 2LPT by going to third-order in the displacement field (3LPT), however it becomes more costly due to the need of solving three additional Poisson equations (Buchert 1994).”
Transients from initial conditions in cosmological simulations (2006, methodology): “Here we present the basics of 2LPT, we refer the reader to the literature (Buchert 1994; Buchert et al. 1994; Bouchet et al. 1995; Catelan 1995; Scoccimarro 2000b) for more information.”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release (2015, methodology): “We rely on second order LPT (2LPT) for the long-range component 2LPT (for details on 2LPT, see Buchert 1994; Bouchet et al. 1995; Catelan 1995).”