The matter and halo power spectra in redshift space using effective field theory

The imminent era of large galaxy surveys (Dark Energy Survey, Euclid and Dark Energy Spectroscopic Instrument, among others) will soon drive a step change in our understanding of the standard cosmological model. Analytic control has traditionally come from the use of perturbation theory, but its reach is limited in scale and excludes a significant fraction of the modes visible to the surveys. N-body simulations could provide an alternative, but their computational time is extremely long. These pressures have produced research to enhance the standard perturbation theory and to appropriately model the redshift-space distortion power spectra that real surveys produce. The analysis performed in this thesis is based on the effective field theory of large-scale structure (EFT). This yields encouraging results for the dark matter power spectrum, at the cost of adjustable counterterms that we estimate from a suite of custom N-body simulations performed using the gevolution numerical relativity code. We extend our analysis to haloes –concept used to refer to a more general notion: tracers of large-scale structures. There exists a statistical relation between the distribution of dark matter and haloes given by a set of bias parameters. As part of this analysis, we utilise the WizCOLA simulations –created to obtain covariance matrices for the WiggleZ survey. In summary, we are in broad agreement with other methods employed in the literature. We include for the first time the full time dependence of the one-loop matter power spectrum using EFT and we are capable of probing smaller scales, k ≲ 0.74h/Mpc. Moreover, we achieve, for k ≲ 0.4h/Mpc, a ∼ 2% level of accuracy in real space and ∼ 5% for the monopole in redshift space. We also quantify how more complex modelling improves the fit for the halo multipoles. For future work, we find it relevant to use real observational data, e.g. WiggleZ dataset

Impact of bias and redshift-space modelling for the halo power spectrum: testing the effective field theory of large-scale structure

We study the impact of different bias and redshift-space models on the halo power spectrum, quantifying their effect by comparing the fit to a subset of realizations taken from the WizCOLA suite. These provide simulated power spectrum measurements between kmin = 0.03 h/Mpc and kmax = 0.29 h/Mpc, constructed using the comoving Lagrangian acceleration method. For the bias prescription we include (i) simple linear bias; (ii) the McDonald & Roy model and (iii) its coevolution variant introduced by Saito et al.; and (iv) a very general model including all terms up to one-loop and corrections from advection. For the redshift-space modelling we include the Kaiser formula with exponential damping and the power spectrum provided by (i) tree-level perturbation theory and (ii) the Halofit prescription; (iii) one-loop perturbation theory, also with exponential damping; and (iv) an effective field theory description, also at one-loop, with damping represented by the EFT subtractions. We quantify the improvement from each layer of modelling by measuring the typical improvement in χ2 when fitting to a member of the simulation suite. We attempt to detect overfitting by testing for compatibility between the best-fit power spectrum per realization and the best-fit over the entire WizCOLA suite. For both bias and the redshift-space map we find that increasingly permissive models yield improvements in χ2 but with diminishing returns. The most permissive models show modest evidence for overfitting. Accounting for model complexity using the Bayesian Information Criterion, we argue that standard perturbation theory up to one-loop, or a related model such as that of Taruya, Nishimichi & Saito, coupled to the Saito et al. coevolution bias model, is likely to provide a good compromise for near-future galaxy surveys operating with comparable kmax

The matter power spectrum in redshift space using effective field theory

The use of Eulerian 'standard perturbation theory' to describe mass assembly in the early universe has traditionally been limited to modes with k <= 0.1 h/Mpc at z=0. At larger k the SPT power spectrum deviates from measurements made using N-body simulations. Recently, there has been progress in extending the reach of perturbation theory to larger k using ideas borrowed from effective field theory. We revisit the computation of the redshift-space matter power spectrum within this framework, including for the first time for the full one-loop time dependence. We use a resummation scheme proposed by Vlah et al. to account for damping of the baryonic acoustic oscillations due to large-scale random motions and show that this has a significant effect on the multipole power spectra. We renormalize by comparison to a suite of custom N-body simulations matching the MultiDark MDR1 cosmology. At z=0 and for scales k <~ 0.4 h/Mpc we find that the EFT furnishes a description of the real-space power spectrum up to ~ 2%, for the ell=0 mode up to ~ 5% and for the ell = 2, 4 modes up to ~ 25%. We argue that, in the MDR1 cosmology, positivity of the ell = 0 mode gives a firm upper limit of k ~ 0.74 h/Mpc for the validity of the one-loop EFT prediction in redshift space using only the lowest-order counterterm. We show that replacing the one-loop growth factors by their Einstein-de Sitter counterparts is a good approximation for the ell = 0 mode, but can induce deviations as large as 2% for the ell = 2, 4 modes. An accompanying software bundle, distributed under open source licenses, includes Mathematica notebooks describing the calculation, together with parallel pipelines capable of computing both the necessary one-loop SPT integrals and the effective field theory counterterms