Beecroft Institute for Particle Astrophysics and Cosmology

Abstract:

We present LimberJack.jl, a fully auto-differentiable code for cosmological analyses of 2 point auto- and cross-correlation measurements from galaxy clustering, CMB lensing and weak lensing data written in Julia. Using Julia’s auto-differentiation ecosystem, LimberJack.jl can obtain gradients for its outputs an order of magnitude faster than traditional finite difference methods. This makes LimberJack.jl greatly synergistic with gradient-based sampling methods, such as Hamiltonian Monte Carlo, capable of efficiently exploring parameter spaces with hundreds of dimensions. We first prove LimberJack.jl’s reliability by reanalysing the DES Y1 3×2-point data. We then showcase its capabilities by using a O(100) parameters Gaussian Process to reconstruct the cosmic growth from a combination of DES Y1 galaxy clustering and weak lensing data, eBOSS QSO’s, CMB lensing and redshift-space distortions. Our Gaussian process reconstruction of the growth factor is statistically consistent with the ΛCDM Planck 2018 prediction at all redshifts. Moreover, we show that the addition of RSD data is extremely beneficial to this type of analysis, reducing the uncertainty in the reconstructed growth factor by 20% on average across redshift. LimberJack.jl is a fully open-source project available on Julia’s general repository of packages and GitHub.

Abstract:

Aims
We combined the LOw-Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS) second data release (DR2) catalogue with gravitational lensing maps from the cosmic microwave background (CMB) to place constraints on the bias evolution of LoTSS-detected radio galaxies, and on the amplitude of matter perturbations.
Methods
We constructed a flux-limited catalogue from LoTSS DR2, and analysed its harmonic-space cross-correlation with CMB lensing maps from Planck, Cℓgk, as well as its auto-correlation, Cℓgg. We explored the models describing the redshift evolution of the large-scale radio galaxy bias, discriminating between them through the combination of both Cℓgk and Cℓgg. Fixing the bias evolution, we then used these data to place constraints on the amplitude of large-scale density fluctuations, parametrised by σ8.
Results
We report the significance of the Cℓgk signal at a level of 26.6σ. We determined that a linear bias evolution of the form bg(z) = bg,D/D(z), where D(z) is the growth rate, is able to provide a good description of the data, and we measured bg,D = 1.41 ± 0.06 for a sample that is flux limited at 1.5 mJy, for scales ℓ < 250 for Cℓgg, and ℓ < 500 for Cℓgk. At the sample’s median redshift, we obtained b(z = 0.82) = 2.34 ± 0.10. Using σ8 as a free parameter, while keeping other cosmological parameters fixed to the Planck values, we found fluctuations of σ8 = 0.75−0.04+0.05. The result is in agreement with weak lensing surveys, and at 1σ difference with Planck CMB constraints. We also attempted to detect the late-time-integrated Sachs-Wolfe effect with LOFAR data; however, with the current sky coverage, the cross-correlation with CMB temperature maps is consistent with zero. Our results are an important step towards constraining cosmology with radio continuum surveys from LOFAR and other future large radio surveys.