Analytic Aesthetics

Peer reviewe

<em>Euclid</em> preparation: XLVII. Improving cosmological constraints using a new multi-tracer method with the spectroscopic and photometric samples

\ua9 2024 The Authors. Future data provided by the Euclid mission will allow us to better understand the cosmic history of the Universe. A metric of its performance is the figure-of-merit (FoM) of dark energy, usually estimated with Fisher forecasts. The expected FoM has previously been estimated taking into account the two main probes of Euclid, namely the three-dimensional clustering of the spectroscopic galaxy sample, and the so-called 3 72pt signal from the photometric sample (i.e., the weak lensing signal, the galaxy clustering, and their cross-correlation). So far, these two probes have been treated as independent. In this paper, we introduce a new observable given by the ratio of the (angular) two-point correlation function of galaxies from the two surveys. For identical (normalised) selection functions, this observable is unaffected by sampling noise, and its variance is solely controlled by Poisson noise. We present forecasts for Euclid where this multi-tracer method is applied and is particularly relevant because the two surveys will cover the same area of the sky. This method allows for the exploitation of the combination of the spectroscopic and photometric samples. When the correlation between this new observable and the other probes is not taken into account, a significant gain is obtained in the FoM, as well as in the constraints on other cosmological parameters. The benefit is more pronounced for a commonly investigated modified gravity model, namely the γ parametrisation of the growth factor. However, the correlation between the different probes is found to be significant and hence the actual gain is uncertain. We present various strategies for circumventing this issue and still extract useful information from the new observable

Robert Grosseteste on transcendentals

In 1996 Jan Aertesen stated that the core of Medieval Philosophy – starting from the Summa de Bono (c. 1225) by Philip the Chancellor – is the doctrine of the transcendentals. This chapter will verify if Grosseteste belonged to the tradition of transcendental thought. After a brief discussion of Aertsen’s thesis, it will focus on some elements of the transcendental theory before and during Grosseteste’s time. In particular it will trace the elements of this doctrine in the twelfth century then those in the first treatises on transcendentals in the thirteenth century. We will then outline five features of the transcendental theory before we discuss Grosseteste’s elaboration of those five characteristics. That is the list of the transcendentals, the introduction of ‘truth’ among them in the thirteenth century, the analogical nature of transcendental names, the primacy of ‘good’ among them and finally considerations about the differences among the transcendentals. This chapter concludes that even though Grosseteste did not develop a systematic account of transcendentals, he did however possess the core ideas of it courtesy of his Neoplatonic sources