An improved method to test the Distance--Duality relation

Many researchers have performed cosmological-model-independent tests for the distance duality (DD) relation. Theoretical work has been conducted based on the results of these tests. However, we find that almost all of these tests were perhaps not cosmological-model-independent after all, because the distance moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent on a given cosmological model and Hubble constant. In this Letter, we overcome these defects and by creating a new cosmological-model-independent test for the DD relation. We use the original data from the Union2 SNe Ia compilation and the angular diameter distances from two galaxy cluster samples compiled by De Filippis et al. and Bonamente et al. to test the DD relation. Our results suggest that the DD relation is compatible with observations, and the spherical model is slightly better than the elliptical model at describing the intrinsic shape of galaxy clusters if the DD relation is valid. However, these results are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ

Direct reconstruction of dynamical dark energy from observational Hubble parameter data

Reconstructing the evolution history of the dark energy equation of state parameter $w(z)$ directly from observational data is highly valuable in cosmology, since it contains substantial clues in understanding the nature of the accelerated expansion of the Universe. Many works have focused on reconstructing $w(z)$ using Type Ia supernova data, however, only a few studies pay attention to Hubble parameter data. In the present work, we explore the merit of Hubble parameter data and make an attempt to reconstruct $w(z)$ from them through the principle component analysis approach. We find that current Hubble parameter data perform well in reconstructing $w(z)$; though, when compared to supernova data, the data are scant and their quality is worse. Both $\Lambda$CDM and evolving $w(z)$ models can be constrained within $10\%$ at redshifts $z \lesssim 1.5$ and even $5\%$ at redshifts 0.1 $\lesssim$ z $\lesssim$ 1 by using simulated $H(z)$ data of observational quality.Comment: 25 pages, 11 figure

Capitalisation of research and development investment and enterprise value: a study on the threshold effect based on level of financialisation

This study uses a mathematical model to explore how enterprises’ financialisation levels affect the role of research and development (R&D) investment capitalisation in enterprise value. We construct a mathematical model involving the financialisation level, capitalised R&D investment, and enterprise value. The sample comprises A-share listed companies that disclosed the capitalisation of R&D investment in the Shanghai and Shenzhen stock markets from 2014 to 2020. The results suggest that R&D investment capitalisation positively impacts enterprise value, especially in the current phase. With financialisation level as the threshold variable, R&D investment capitalisation has a double threshold effect on enterprise value in the current and next phases. Additionally, corporate financial investment behaviour has a timely impact on capitalised R&D investment but does not significantly impact enterprise value in a future phase. Enterprises evidently choose financial investment to enhance enterprise value by increasing capitalised R&D investment. These results can help enterprises formulate financial asset investment strategies and promote their development from virtual to real. The government should standardise enterprises’ financial investment behaviour, prevent excessive financialisation, and promote high-quality development of the real economy

Longitudinal optical conductivities for tilted Weyl fermions in arbitrary dimensionality

The unified form of longitudinal optical conductivities (LOCs) for tilted Weyl fermions in arbitrary spatial dimensionality is analytically calculated and expressed in terms of the joint density of state. The results are valid for both undoped and doped cases, both parallel and perpendicular components with respect to the tilting direction, and all the tilted phases. In addition, they automatically reproduce the analytical results of previous works for one-dimensional, two-dimensional, and three-dimensional tilted Weyl systems. Our work provides not only a once-for-all method prior to the one-by-one calculation of LOCs but also deep insights into the impacts of spatial dimensionality in the tilted Weyl fermions.Comment: 4 pages, no figure