Double power series method for approximating cosmological perturbations

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a non-cosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on sub-horizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well known growing and decaying M\'esz\'aros solutions, these oscillating modes provide a complete set of sub-horizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.Comment: 22 pages, 10 figures, 2 tables. Mathematica notebook available from Github at https://github.com/AndrewWren/Double-power-series.gi

Word embeddings for retrieving tabular data from research publications

Scientists face challenges when finding datasets related to their research problems due to the limitations of current dataset search engines. Existing tools for searching research datasets rely on publication content or metadata, do not considering the data contained in the publication in the form of tables. Moreover, scientists require more elaborate inputs and functionalities to retrieve different parts of an article, such as data presented in tables, based on their search purposes. Therefore, this paper proposes a novel approach to retrieve relevant tabular datasets from publications. The input of our system is a research problem stated as an abstract from a scientific paper, and the output is a set of relevant tables from publications that are related to the research problem. This approach aims to provide a better solution for scientists to find useful datasets that support them in addressing their research problems. To validate this approach, experiments were conducted using word embedding from different language models to calculate the semantic similarity between abstracts and tables. The results showed that contextual models significantly outperformed non-contextual models, especially when pre-trained with scientific data. Furthermore, the importance of context was found to be crucial for improving the results.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work is part of the project TED2021-130890B-C21, funded by MCIN/AEI/10.1 3039501100011033 and by the European Union NextGenerationEU/PRTR. Alberto Berenguer has a contract for predoctoral training with the Generalitat Valenciana and the European Social Fund, funded by the grant ACIF/2021/507

On the proper kinetic quadrupole CMB removal and the quadrupole anomalies

It has been pointed out recently that the quadrupole-octopole alignment in the CMB data is significantly affected by the so-called kinetic Doppler quadrupole (DQ), which is the temperature quadrupole induced by our proper motion. Assuming our velocity is the dominant contribution to the CMB dipole we have v/c = beta = (1.231 +/- 0.003) * 10^{-3}, which leads to a non-negligible DQ of order beta^2. Here we stress that one should properly take into account that CMB data are usually not presented in true thermodynamic temperature, which induces a frequency dependent boost correction. The DQ must therefore be multiplied by a frequency-averaged factor, which we explicitly compute for several CMB maps finding that it varies between 1.67 and 2.47. This is often neglected in the literature and turns out to cause a small but non-negligible difference in the significance levels of some quadrupole-related statistics. For instance the alignment significance in the SMICA 2013 map goes from 2.3sigma to 3.3sigma, with the frequency dependent DQ, instead of 2.9sigma ignoring the frequency dependence in the DQ. Moreover as a result of a proper DQ removal, the agreement across different map-making techniques is improved.Comment: v2: improvements to the text; 2 figures and several references added; results unchanged. [14 pages, 3 tables, 2 figures

On asymptotic behaviour in truncated conformal space approach

The Truncated conformal space approach (TCSA) is a numerical technique for finding finite size spectrum of Hamiltonians in quantum field theory described as perturbations of conformal field theories. The truncation errors of the method have been systematically studied near the UV fixed point (when the characteristic energy related to the coupling is less than the truncation cutoff) where a good theoretical understanding has been achieved. However numerically the method demonstrated a good agreement with other methods for much larger values of the coupling when the RG flow approaches a new fixed point in the infrared. In the present paper we investigate this regime for a number of boundary RG flows testing the leading exponent and truncation errors. We also study the flows beyond the first fixed point which have been observed numerically but yet lack a theoretical understanding. We show that while in some models such flows approximate reversed physical RG flows, in other models the spectrum approaches a stable regime that does not correspond to any local boundary condition. Furthermore we find that in general the flows beyond the first fixed point are very sensitive to modifications of the truncation scheme.Comment: v2: presentation restructured, general considerations are put forward into section 2, section on bulk flows removed, quality of all pictures and referencing improved; 40 pages, 22 figures, 11 tables; to appear in JHE