LtU-ILI: An All-in-One Framework for Implicit Inference in Astrophysics and Cosmology
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 × 10−3 − 9 h Mpc−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 Our emulator will be usable long after the codes on which numerical approximations are built become outdated.
SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrum
Constraints on dark matter and astrophysics from tomographic γ-ray cross-correlations
Abstract:
We study the cross-correlation between maps of the unresolved 𝛾-ray background constructed from the 12-year data release of the Fermi Large-Area Telescope, and the overdensity of galaxies in the redshift range 𝑧≲0.4 as measured by the 2MASS photometric redshift survey and the WISE-SuperCOSMOS photometric survey. A signal is detected at the 8−10𝜎 level, which we interpret in terms of both astrophysical 𝛾-ray sources, and weakly interacting massive particles (WIMP) dark matter decay and annihilation. The sensitivity achieved allows us to characterise the energy and redshift dependence of the signal, and we show that the latter is incompatible with a pure dark matter origin. We thus use our measurement to place an upper bound on the WIMP decay rate and the annihilation cross section, finding constraints that are competitive with those found in other analyses. Our analysis is based on the extraction of clean model-independent observables that can then be used to constrain arbitrary astrophysical and particle physics models. In this sense we produce measurements of the 𝛾-ray emissivity as a function of redshift and rest-frame energy 𝜖, and of a quantity 𝐹(𝜖) encapsulating all WIMP parameters relevant for dark matter decay or annihilation. We make these measurements, together with a full account of their statistical uncertainties, publicly available.