Evaluating the variance of individual halo properties in constrained cosmological simulations
Abstract:
Constrained cosmological simulations play an important role in modelling the local Universe, enabling investigation of the dark matter content of local structures and their formation. We introduce an internal method for quantifying the extent to which the variance of individual halo properties is suppressed by the constraints imposed on the initial conditions. We apply it to the Constrained Simulations in BORG (CSiBORG) suite of 101 high-resolution realizations across the posterior probability distribution of initial conditions from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. The method is based on the overlap of the initial Lagrangian patch of a halo in one simulation with those in another, measuring the degree to which the haloes' particles are initially coincident. This addresses the extent to which the imposed large-scale structure constraints reduce the variance of individual halo properties. We find consistent reconstructions of M≳1014M⊙h-1 haloes, indicating that the constraints from the BORG algorithm are sufficient to pin down the masses, positions, and peculiar velocities of clusters to high precision, though we do not assess how well they reproduce observations of the local Universe. The effect of the constraints tapers off towards lower mass, and the halo spins and concentrations are largely unconstrained at all masses. We document the advantages of evaluating halo consistency in the initial conditions and describe how the method may be used to quantify our knowledge of the halo field given galaxy survey data analysed through the lens of probabilistic inference machines such as BORG.No evidence for anisotropy in galaxy spin directions
A precise symbolic emulator of the linear matter power spectrum
Abstract:
Context. Computing the matter power spectrum, P(k), as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used.
Aims. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert As to σ8 given the other cosmological parameters.
Methods. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and σ8. We learn the ratio between an existing low-accuracy fitting function for P(k) and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation.
Results. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between k = 9 &³Ù¾±³¾±ð²õ; 10−3 &³¾¾±²Ô³Ü²õ; 9 h M±è³¦−1 and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than CAMB and 36 times faster than the neural network based matter power spectrum emulator BACCO. We also provide a simple analytic approximation for σ8 with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain As as a function of σ8 and the other cosmological parameters, if preferred.
Conclusions. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.