51ÁÔÆæÈë¿Ú

Abstract:

The tomographic approach to analysing the 3 × 2 pt signal involves dividing the observed galaxy sample into a configuration of redshift bins. We present a simulation-based method to explore the optimum tomographic binning strategy for Euclid, focussing on the expected configuration of its first major data release (DR1). To do so, we 1) simulated a Euclid-like observation and generated mock shear catalogues from multiple realisations of the 3 × 2 pt fields on the sky; and 2) measured the 3 × 2 pt Pseudo-Cℓ power spectra for a given tomographic configuration and derived the constraints they place on the standard dark energy equation-of-state parameters, (w0, wa). For a simulation including Gaussian-distributed photometric redshift uncertainties and shape noise under a ΛCDM cosmology, we find that bins that are equipopulated with galaxies yield the best constraints on (w0, wa) for an analysis of the full 3 × 2 pt signal or the angular clustering component only. For the cosmic shear component, the optimum (w0, wa) constraints can be achieved by bins equally spaced in fiducial comoving distance. However, the advantage with respect to alternative binning choices is only of a few per cent in the size of the 1σ (w0, wa) contour and we conclude that the cosmic shear is relatively insensitive to the binning methodology. We find that the information gain extracted on (w0, wa) for any 3 × 2 pt component starts to become saturated beyond roughly seven or eight bins. Any marginal gains resulting from a greater number of bins are likely to be limited by additional uncertainties present in a real measurement and the increasing demand for accuracy of the covariance matrix. Finally, we considered a 5% contamination from catastrophic photometric redshift outliers and found that if these errors are not mitigated in the analysis, the bias induced in the 3 × 2 pt signal for ten equipopulated bins results in dark energy constraints that are inconsistent with the fiducial ΛCDM cosmology at ≳3σ.

Abstract:

Symbolic regression (SR) is the machine learning (ML) method for learning functions from data. After a brief overview of the SR landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown (and probably significant) probability of failing to find any given good function, and they suffer from ambiguity and poorly justified assumptions in their function-selection procedure. To address these, I propose an exhaustive search and model selection by the minimum description length (MDL) principle, which allows accuracy and complexity to be directly traded off by measuring each in units of information. I showcase the resulting publicly available Exhaustive Symbolic Regression (ESR) algorithm on three open problems in astrophysics: the expansion history of the universe, the effective behaviour of gravity in galaxies and the potential of the inflaton field. In each case, the algorithm identifies many functions superior to the literature standards. This general-purpose methodology should find widespread utility in science and beyond. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generated 100 000 mock realisations of dark matter density fields in both real and redshift space across multiple redshifts and cosmological models. We derived an analytical framework linking the non-Gaussianity of the power spectrum distribution to higher-order statistics of the density field, including the trispectrum and pentaspectrum. We explored the effect of redshift-space distortions, the geometry of the survey, the Fourier binning, the integral constraint, and the shot noise on the skewness of the distribution of the power spectrum measurements. Our results demonstrate that the likelihood of the estimated matter power spectrum significantly deviates from a Gaussian assumption on non-linear scales, particularly at low redshift. This departure is primarily driven by the pentaspectrum contribution, which dominates over the trispectrum at intermediate scales. We also examined the impact of the finiteness of the survey geometry in the context of the Euclid mission, and we find that both the shape of the survey and the integral constraint amplify the skewness.

Abstract:

The Cosmic Dawn Survey pre-launch catalogues cover an effective 10.13 deg 2 area with uniform deep Spitzer /IRAC data ( m ∼ 25 mag, 5 σ ), the largest area covered to these depths at IR wavelengths. We used these data to gain new insight into the growth of stellar mass across cosmic history by characterising the evolution of the galaxy stellar mass function through 0.2 < z ≤ 6.5. The total volume (0.62 Gpc 3 ) represents an order of magnitude increase compared to previous works that explored z > 3 and significantly reduces cosmic variance, thus yielding strong constraints on the abundance of galaxies above the characteristic stellar mass (ℳ ★ ) across this ten billion year period. The evolution of the galaxy stellar mass function is generally consistent with results from the literature but now provides firm estimates of the number density where only upper limits were previously available. Contrasting the galaxy stellar mass function with the dark matter halo mass function suggests that massive galaxies (ℳ ≳ 10 11 M ⊙ ) at z > 3.5 required integrated star-formation efficiencies of ℳ/(ℳ h f b )≳ 0.25–0.5, in excess of the commonly held view of a ‘universal peak efficiency’ from studies on the stellar-to-halo mass relation. Such increased efficiencies imply an evolving peak in the stellar-to-halo mass relation at z > 3.5 that can be maintained if feedback mechanisms from active galactic nuclei and stellar processes are ineffective at early times. In addition, a significant fraction of the most massive quiescent galaxies are observed to be in place by z ∼ 2.5–3. The apparent lack of change in their number density by z ∼ 0.2 is consistent with relatively little mass growth from mergers. Utilising the unique volume, we find evidence of an environmental dependence of the galaxy stellar mass function all the way through z ∼ 3.5 for the first time, though a more careful characterisation of the density field is ultimately required for confirmation.

Abstract:

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR, which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focused on the promising regions in order to be equally performant. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.