xPand: an algorithm for perturbing homogeneous cosmologies. In this paper, we develop in detail a fully geometrical method for deriving perturbation equations about a spatially homogeneous background. This method relies on the 3+1 splitting of the background space-time and does not use any particular set of coordinates: it is implemented in terms of geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with the extension for perturbations xPert. Our algorithm allows one to obtain the perturbation equations for all types of homogeneous cosmologies, up to any order and in all possible gauges. As applications, we recover the well-known perturbed Einstein equations for Friedmann-Lemaître-Robertson-Walker cosmologies up to second order and for Bianchi I cosmologies at first order. This work paves the way to the study of these models at higher order and to that of any other perturbed Bianchi cosmologies, by circumventing the usually too cumbersome derivation of the perturbed equations

References in zbMATH (referenced in 18 articles )

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  1. Brax, Philippe; Lazanu, Andrei: Non-Gaussianity in DHOST inflation (2022)
  2. Bernardo, Reginald Christian: Self-tuning kinetic gravity braiding: cosmological dynamics, shift symmetry, and the tadpole (2021)
  3. Brax, Philippe; Lazanu, Andrei: Scale-dependence in DHOST inflation (2021)
  4. Umeh, Obinna; Koyama, Kazuya; Crittenden, Robert: Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum (2021)
  5. Umeh, Obinna; Maartens, Roy; Padmanabhan, Hamsa; Camera, Stefano: The effect of finite halo size on the clustering of neutral hydrogen (2021)
  6. Markus B. Fröb: FieldsX - An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology (2020) arXiv
  7. Villani, Mattia: Quasi-normal mode of a regular Schwarzschild black hole (2020)
  8. Carrilho, Pedro; Malik, Karim A.: Magnetogenesis from isocurvature initial conditions (2019)
  9. Granda, L. N.; Jimenez, D. F.: Slow-roll inflation in scalar-tensor models (2019)
  10. Umeh, Obinna; Koyama, Kazuya; Maartens, Roy; Schmidt, Fabian; Clarkson, Chris: General relativistic effects in the galaxy bias at second order (2019)
  11. Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino; Scomparin, Mattia: Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity (2018)
  12. Carrilho, Pedro; Malik, Karim A.: Isocurvature initial conditions for second order Boltzmann solvers (2018)
  13. Cabass, G.; Pajer, E.; Schmidt, F.: How Gaussian can our universe be? (2017)
  14. Fidler, Christian; Tram, Thomas; Rampf, Cornelius; Crittenden, Robert; Koyama, Kazuya; Wands, David: General relativistic weak-field limit and Newtonian N-body simulations (2017)
  15. Frusciante, Noemi; Papadomanolakis, Georgios: Tackling non-linearities with the effective field theory of dark energy and modified gravity (2017)
  16. Umeh, Obinna: Imprint of non-linear effects on HI intensity mapping on large scales (2017)
  17. Nutma, Teake: \textitxTras: a field-theory inspired \textitxActpackage for Mathematica (2014)
  18. Pitrou, Cyril; Roy, Xavier; Umeh, Obinna: (\textxPand): an algorithm for perturbing homogeneous cosmologies (2013)