Relativistic Spacetime Research Articles

Space-time analysis of the relationship between landslides occurrence, rainfall variability and ENSO in the Tropical Andean Mountain region in Colombia

According to studies by the Intergovernmental Panel on Climate Change (IPCC), tropical mountainous areas are experiencing increasingly unfavorable climatic conditions regarding geohazards due to a heightened occurrence of intense rainfall events. These climatic shifts contribute to heightened geological risks, notably an elevated frequency of landslides, exacerbating the challenges faced by these regions. There is an urgent need to understand and measure how rainfall variability affects geo-hydrological hazards, which remain difficult to determine and predict. The complex and non-linear space-time relationships and dynamics of rainfall, El Niño-Southern Oscillation (ENSO), and landslides in the Tropical Andean Mountain region in Colombia require an adequate analysis and understanding of their link in terms of its spatial and temporal component at different scales. By evaluation in annual, seasonal, and monthly scales, additional insights on the relationships using a wavelet spectral analysis and a space-time permutation scan statistics method using SaTScan™ are provided. In this study, a space-time and frequency analysis of landslides using a 42-year (1981–2022) rainfall and Multivariate ENSO Index v2.0 time series is presented. According to the results, landslides closely aligned with rainfall patterns, exhibiting a bimodal annual cycle. The ENSO added complexity, with La Niña years leading to more frequent landslides throughout the year and El Niño years showing concentrated occurrences in specific months. This study highlights the influence of rainfall patterns and antecedent rainfall on landslide occurrence, the impact of ENSO phases on rainfall and landslides, and the increasing trend of landslides in Colombia.

Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime

In this research paper, we determine the nature of conformal [Formula: see text]-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal [Formula: see text]-Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal [Formula: see text]-Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal [Formula: see text]-Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form [Formula: see text], which is the [Formula: see text]-dual of the vector field [Formula: see text] on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation.

Solitonic effect on relativistic string cloud spacetime attached with strange quark matter

<abstract><p>In this research paper, we discussed some geometric axioms of a relativistic string cloud spacetime attached with strange quark matter. We determined the conformal $ \eta $-Ricci soliton on a relativistic string cloud spacetime attached with strange quark matter with a $ \varphi(\mathcal{R}ic) $-vector field. In addition, we illustrated some physical significance of conformal pressure $ P $ in terms of conformal $ \eta $-Ricci soliton with the same vector field. Besides this, we deduced a generalized Liouville equation from the conformal $ \eta $-Ricci soliton. Furthermore, we examine the harmonic relevance of conformal $ \eta $-Ricci soliton on string cloud spacetime attached with strange quark matter with a potential function $ \psi $. Finally, we turned up a necessary and sufficient condition for the 1-form $ \eta $, which is the $ {g} $-dual of the vector field $ \gamma $ on a string cloud spacetime attached with strange quark matter to be a solution for the Schrödinger-Ricci equation.</p></abstract>

Process Skills and Attitude towards Science as the Contributing Factors in Cognitive Performance among Special Science Class Students: A Quantitative Study

This study dealt with the influence of process skills and attitude towards Science as contributing factors to cognitive performance among Special Science Class students in Lorenzo S. Sarmiento Sr. National High School. The primary goal of the study was to determine the level of process skills, attitude towards Science, and cognitive performance in terms of their respective indicators, the significant difference between process skills and cognitive performance, attitude towards Science and cognitive performance, and what domains of process skills and attitude towards Science substantially influenced cognitive performance. Also, this study utilized a quantitative, non-experimental design with 166 respondents among Special Science Class students in Lorenzo S. Sarmiento Sr. National High School. The average weighted mean, Pearson r, and multiple regression analysis were the statistical tools used in this study. The study concluded that the level of process skills was high, which meant that process skills among Special Science Class students were often manifested; the level of attitude towards Science was also high, except for the family model indicator, which was observed to sometimes manifest; and the level of cognitive performance was also high, which meant that it was often manifested by Special Science Class students. Moreover, there was a significant relationship and high correlation between process skills and cognitive performance, and the same was true of attitudes towards Science and cognitive performance. For regression analysis, in Science process skills, there were six domains that influenced cognitive performance: observing, measuring, and using numbers; making inferences; predicting; communicating; and using time-space relationships. In attitude towards Science, all domains were influenced by cognitive performance, namely, Science is fun, classroom teacher, self-directed efforts, and family model. However, there was only one indicator in Science process skills that did not influence cognitive performance, and this was the classifying. Furthermore, the overall level of process skills and attitude towards Science as contributing factors to cognitive performance among Special Science Class students in Lorenzo S. Sarmiento Sr. National High School was high. Thus, teachers should implement strong, diverse teaching methods that cater to various learning styles, and parents should help them in their Science-related work. With this, Special Science Classes could create a conducive environment that nurtures the development of Science process skills and fosters a positive attitude towards Science, ultimately enhancing students’ cognitive performance in the discipline.

A robophysical model of spacetime dynamics

Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity: how curvature guides the movement of matter. However, such schemes cannot accurately represent relativistic dynamics in the laboratory because of the dominance of dissipation and external gravitational fields. Here we demonstrate that an “active” object (a wheeled robot), which moves in a straight line on level ground and can alter its speed depending on the curvature of the deformable terrain it moves on, can exactly capture dynamics in curved relativistic spacetimes. Via the systematic study of the robot’s dynamics in the radial and orbital directions, we develop a mapping of the emergent trajectories of a wheeled vehicle on a spandex membrane to the motion in a curved spacetime. Our mapping demonstrates how the driven robot’s dynamics mix space and time in a metric, and shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow the programming of a desired spacetime, such as the Schwarzschild metric near a non-rotating blackhole. Our mapping and framework facilitate creation of a robophysical analog to a general relativistic system in the laboratory at low cost that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

A relativistic discrete spacetime formulation of 3+1 QED

This work provides a relativistic, digital quantum simulation scheme for both 2+1 and 3+1 dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step Δt=Δx. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.

Field trip – Outer Flysch Carpathians and Pieniny Klippen Belt (PKB)

We are glad that we can meet personally during the 2nd Symposium of the IGCP 710 Project, after the pandemic time, which disrupted our idea of regular, annual meetings. After the 1st virtual meeting during the autumn of 2021, we have now the chance to discuss face to face and go to the field together to touch „Tethyan” rocks for a better understanding of what happened hundreds/decades of millions years ago in our lovely ancient ocean. As you know, through your knowledge and experience, the Tethyan Ocean history, both in its western and eastern parts, is fascinating, but enigmatic from time to time, to say the least.Generally, the geological history of the Tethys Ocean is broadly established. Yet many details are still unknown and many major questions remain, related to geotectonics, palaeogeography, palaeoceanography and palaeobiogeography. Improved understanding of the Mesozoic-Cenozoic ocean/climate history is based on accurate reconstruction of the distribution of continents and ocean basins and on opening and closing of seaways along the Tethys. There is little or no agreement about the number or size of separate basins, nor on their space-time relationships. Moreover, there is no consensus on the number and location of former micro-continents and on their incorporation into the present-day Eurasian-Mountain Belt. Geologists studying individual parts of these belts have been educated within different geological systems and adhere to different geological paradigms. Correlation between Western and Eastern Tethys is difficult, not only because of the large distances involved, but also because they are separated by the area of the huge Himalayan collision within which much of the pre-Paleogene tectonostratigraphic information has been lost. The aim of this IGCP project is to bring together geologists from the western and eastern parts of the former Tethys (Morocco/Iberia–SE Asia) to establish a common framework and a common tectonostratigraphic concept (latest Paleozoic–Mesozoic with emphasis on Permian–Jurassic).On the one hand, UNESCO forms a special umbrella for the IGCP Projects, and on the other hand, it has been very active in supporting the ideas of “geoparks” and “geotourism” for years. For this reason, we decided to use an international magazine – Geotourism – to print our materials, both abstracts and a field trip guidebook. We hope it will be useful for both Tethyan friends and geotourism enthusiasts.Enjoy Krakow during the stationary part of the Symposium and the Polish-Slovak-Czech Carpathians during a 5-day field trip!!

Obstructions to the existence of trapped submanifolds in relativistic spacetimes

Obstructions to the existence of trapped submanifolds in spacetimes of arbitrary dimension are given. These obstructions are obtained under natural geometric assumptions, which can be applied to initial data set for Einstein equations, assuring the absence of trapped submanifolds in its development. We highlight that for several of our results the existence of symmetries in the spacetime is not necessary.

Space-time relationships between COVID-19 vaccinations and human mobility patterns in the United States

As COVID-19 vaccines were administered in early 2021, they helped to mitigate the spread of the COVID-19 virus and signaled an important shift in the pandemic. To better understand how ongoing COVID-19 vaccinations were related to human mobility across the U.S., we identified different mobility-vaccination profiles between January and May 2021 by county in the U.S., using K-means multivariate time-series clustering. The impacts of demographic, socioeconomic, and COVID-19-related variables on different profiles were examined. Results showed 5 different clusters of mobility-vaccination profiles were found for the U.S. One cluster represented counties in larger population centers and metropolitan areas (e.g., Los Angeles and New York) that had estimated 25% higher mobility and 75% higher vaccination rates than rural counties in the Mountain and South U.S. Census regions (e.g., counties in Arkansas and Mississippi), where people were mobile despite not getting vaccinated. Higher education and household income were found to impact counties’ mobility-vaccination profiles. Examination of trip purposes for selected counties returned higher trips to retail/recreation and workplaces for rural counties with relatively lower mobility-vaccination profiles. The results can serve as input for regional and local health officials regarding population responses to a pandemic relevant to economic recovery and future disease prevention.

Some Curvature Properties of Finsler Warped Product Metrics

The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing Riemannian curvature. Moreover, we obtain equivalent conditions for locally Minkowski Finsler warped product spaces. Finally, we explicitly construct two types of non-Riemannian examples.

FeynGrav 2.0

We present a new version of FeynGrav. The present version supports Feynman rules for matter with non-vanishing mass and SU(N) Yang-Mills model. We revisit the gauge fixing procedure for gravity and derive interaction rules valid for an arbitrary gauge fixing parameter. We provide a few simple examples of calculations to illustrate package usage. Program summaryProgram Title: FeynGravCPC Library link to program files:https://doi.org/10.17632/rwnrbbdkkv.1Developer's repository link:github.com/BorisNLatosh/FeynGravLicensing provisions: GPLv3Programming language: Wolfram Mathematica 10 and higherExternal routines/libraries: FeynCalc [1,2]Nature of problem: FeynGrav is a software package that simplifies calculations involving the Feynman rules for gravity. These rules are complex and consist of numerous terms, but FeynGrav makes it possible to work with a specific set of rules within the FeynCalc environment. The package includes interaction rules for regular matter with different spin values, as well as for the SU(N) Yang-Mills model in curved spacetime and general relativity. FeynGrav provides scripts to generate the relevant interaction rules and libraries of pre-generated expressions, making it a powerful tool for researchers in the field of theoretical physics.Solution method: I propose a framework that provides a straightforward way to obtain expressions for the corresponding Feynman rules by efficiently utilizing perturbative expansions. In particular, within the perturbative approach to quantum gravity, certain quantities admit finite perturbative expansions, while others have infinite perturbative expansions. I derive formulas that allow the generation of terms with infinite expansions for any given order of perturbation theory. In all actions describing gravitational interactions, all derivatives can be placed on terms with finite perturbative expansions via integration by parts. In this way, the proposed framework gives a simple algorithm for deriving Feynman rules.Additional comments including restrictions and unusual features: Scripts responsible for generating interaction rules are placed in the “Rules” folder. They can be used separately and only require FeynCalc to run. The “Libs” folder contains the “FeynGravLibrariesGenerator.wl” script and the libraries it generates. “FeynGrav.wl” is the main package file that imports data from the libraries and uses it to work with the interaction rules. The file “FeynGrav_Examples.nb” contains examples of calculations.

Dynamic adaptive spatio–temporal graph network for COVID‐19 forecasting

AbstractAppropriately characterising the mixed space–time relations of the contagion process caused by hybrid space and time factors remains the primary challenge in COVID‐19 forecasting. However, in previous deep learning models for epidemic forecasting, spatial and temporal variations are captured separately. A unified model is developed to cover all spatio–temporal relations. However, this measure is insufficient for modelling the complex spatio–temporal relations of infectious disease transmission. A dynamic adaptive spatio–temporal graph network (DASTGN) is proposed based on attention mechanisms to improve prediction accuracy. In DASTGN, complex spatio–temporal relations are depicted by adaptively fusing the mixed space–time effects and dynamic space–time dependency structure. This dual‐scale model considers the time‐specific, space‐specific, and direct effects of the propagation process at the fine‐grained level. Furthermore, the model characterises impacts from various space–time neighbour blocks under time‐varying interventions at the coarse‐grained level. The performance comparisons on the three COVID‐19 datasets reveal that DASTGN achieves state‐of‐the‐art results with a maximum improvement of 17.092% in the root mean‐square error and 11.563% in the mean absolute error. Experimental results indicate that the mechanisms of designing DASTGN can effectively detect some spreading characteristics of COVID‐19. The spatio–temporal weight matrices learned in each proposed module reveal diffusion patterns in various scenarios. In conclusion, DASTGN has successfully captured the dynamic spatio–temporal variations of COVID‐19, and considering multiple dynamic space–time relationships is essential in epidemic forecasting.

Statistical modeling of the space–time relation between wind and significant wave height

Abstract. Many marine activities, such as designing ocean structures and planning marine operations, require the characterization of sea-state climate. This study investigates the statistical relationship between wind and sea states, considering its spatiotemporal behavior. A transfer function is established between wind fields over the North Atlantic (predictors) and the significant wave height (predictand) at three locations: southwest of the French coast (Gironde), the English Channel, and the Gulf of Maine. The developed method considers both wind seas and swells by including local and global predictors. Using a fully data-driven approach, the global predictors' spatiotemporal structure is defined to account for the non-local and non-instantaneous relationship between wind and waves. Weather types are constructed using a regression-guided clustering method, and the resulting clusters correspond to different wave systems (swells and wind seas). Then, in each weather type, a penalized linear regression model is fitted between the predictor and the predictand. The validation analysis proves the models skill in predicting the significant wave height, with a root mean square error of approximately 0.3 m in the three considered locations. Additionally, the study discusses the physical insights underlying the proposed method.

Ricci solitons on general relativistic spacetimes

The main aim of this manuscript is to characterize the general relativistic spacetimes with Ricci and gradient Ricci solitons. It is proven that if the metric of a general relativistic spacetime (M 4, ξ) admitting a special unit timelike vector field ξ is an almost Ricci soliton (g, ξ, λ), then (M 4, ξ) is a perfect fluid spacetime, and almost Ricci soliton (g, ξ, λ) on (M 4, ξ) becomes shrinking Ricci soliton. We prove that a general relativistic perfect fluid spacetime equipped with a special unit timelike vector field together with a Ricci soliton is an Einstein spacetime. In this sequel, we also prove that the Ricci soliton is shrinking, soliton vector field is Killing and the scalar curvature of the perfect fluid spacetime is constant. It is proven that a general relativistic perfect fluid spacetime together with a Ricci soliton is a generalized Robertson-Walker (GRW) spacetime. The existence of gradient Ricci solitons on general relativistic spacetimes are established. We also construct a non-trivial example of general relativistic spacetime equipped with a special unit timelike vector field, and verify some of our theorems.

A Nonoverlapping Vision Field Multi-Camera Network for Tracking Human Build Targets

This research presents a procedure for tracking human build targets in a multi-camera network with nonoverlapping vision fields. The proposed approach consists of three main steps: single-camera target detection, single-camera target tracking, and multi-camera target association and continuous tracking. The multi-camera target association includes target characteristic extraction and the establishment of topological relations. Target characteristics are extracted based on the HSV (Hue, Saturation, and Value) values of each human build movement target, and the space-time topological relations of the multi-camera network are established using the obtained target associations. This procedure enables the continuous tracking of human build movement targets in large scenes, overcoming the limitations of monitoring within the narrow field of view of a single camera.

Solitonic Aspect of Relativistic Magneto-Fluid Spacetime with Some Specific Vector Fields

The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient Ricci–Yamabe soliton (GRY-soliton). We exhibit that a magneto-fluid spacetime filled with a magneto-fluid density ρ, magnetic field strength H, and magnetic permeability μ obeys the Einstein field equation without the cosmic constant being a generalized quasi-Einstein spacetime manifold (GQE). In such a spacetime, we obtain an EoS with a constant scalar curvature R in terms of the magnetic field strength H and magnetic permeability μ. Next, we achieve some cauterization of the magneto-fluid spacetime in terms of Ricci–Yamabe solitons with a time-like torse-forming vector field ξ and a φ(Ric) vector field. We establish the existence of a black hole in the relativistic magneto-fluid spacetime by demonstrating that it admits a shrinking Ricci–Yamabe soliton and satisfies the time-like energy convergence criteria. In addition, we examine the magneto-fluid spacetime with a gradient Ricci–Yamabe soliton and deduce some conditions for an equation of state (EoS) ω=−15 with a Killing vector field. Furthermore, we demonstrate that the EoS ω=−15 of the magneto-fluid spacetime under some constraints represents a star model and a static, spherically symmetric perfect fluid spacetime. Finally, we prove that a gradient Ricci–Yamabe soliton with the conditions μ=0 or H=2; μ≠0, H>2 and obeying the equation of state ω=−15 is conceded in a magneto-fluid spacetime, and a naked singularity with a Cauchy horizon subsequently emerges, respectively.

Small satellite formations and constellations for observing sub-daily mass changes in the Earth system

SUMMARY Satellite gravity missions so far are medium size satellites consisting of one or a pair of satellites flying in near-polar or sun-synchronous orbital planes. Due to the limited observation geometry and the related space–time sampling, high-frequency non-tidal mass variation signals from atmosphere and ocean cannot be observed and cause temporal aliasing. For current single-pair satellite gravimetry missions as GRACE and GRACE Follow-On (GRACE-FO) temporal aliasing is the limiting factor and represents the major error source in the gravity field time-series. Adding a second inclined satellite pair to a GRACE-like polar pair (Bender constellation) currently is the most promising solution to increase the spatio-temporal resolution and to significantly reduce the temporal aliasing error. This shall be implemented with the MAGIC mission in future. With the ongoing developments in miniaturization of satellites and gravity-relevant instruments (accelerometers and intersatellite ranging), in future constellations of multiple small satellite pairs may solve this problem even beyond the capabilities of a Bender constellation. Therefore, in this study the capabilities of such constellations flying in specific formations are investigated in order to enable a retrieval of the temporal gravity field on short time scales. We assess the performance of up to 18 satellite pairs. The satellite configurations cover satellite pairs in polar and inclined orbits flying in pair-wise or pearl-string formation with varying mean anomalies and right ascensions of the ascending node (RAAN). As future potential miniaturized instruments optomechanical accelerometers with similar performance as those flying on GRACE-FO are a candidate, while for the intersatellite ranging instrument still some technological development is required. Therefore, in this study a microwave ranging system equivalent to the GRACE and GRACE-FO instruments performance is taken as baseline assuming that such instruments can be miniaturized in future as well. In numerical closed-loop simulations, up to nine different satellite configurations with up to 18 satellite pairs are evaluated based on the retrieval of the non-tidal temporal gravity field on a monthly basis. From the simulation results it is concluded that the best-performing satellite constellation of 18 polar satellite pairs already is outperformed by a typical Bender-like constellation of 1 polar and 1 inclined pair. In general, we identify that increasing the number of satellite pairs leads to an improved gravity field retrieval, either at low spherical harmonic degree and order (d/o) by the shift in RAAN or at high d/o by the shift in mean anomaly. By a two-step simulation approach, co-estimating also (sub-)daily gravity fields for selected configurations with a large number of satellite pairs distributed equally over the globe, it is possible to retrieve stand-alone gravity fields at 24, 12 and 6 hr temporal resolution. Ultimately it is concluded that a network of miniaturized satellites with instrument performances similar to GRACE-FO and flying in a well-defined constellation has the potential to observe (sub-)daily mass variations and therefore could drastically reduce the problem of temporal aliasing due to high frequency mass variations in the Earth system.

An elementary-step kinetic model for ethyl acetate synthesis by direct addition of acetic acid to ethylene on a silicotungstic acid catalyst

An elementary-step kinetic model for ethyl acetate synthesis by direct addition of acetic acid to ethylene over a silica supported silicotungstic acid catalyst is developed. A reaction network comprising 5 reactions, i.e. 3 direct additions, an esterification and a condensation, between 6 major components (ethylene, acetic acid, water, ethyl acetate, ethanol and diethyl ether) is accounted for. The reactions are described by means of Langmuir-Hinshelwood-Hougen-Watson and Eley-Rideal type rate expressions, including the adsorptions of all components, except diethyl ether, on the active sites of the catalyst. The model can quantitatively capture the effects of space time, temperature, pressure and feed composition, on conversions and also qualitatively reproduces the observed selectivities. However, it is necessary to include two physicochemical phenomena, i.e. i) silicotungstic acid solvation by water for the adequate description of the pressure effect on kinetics and ii) the proton-ethanol cluster formation to improve the fit between the experimental and model predicted values. Estimates for activation energies, adsorption enthalpies, solvation and cluster formation enthalpies and entropies are obtained through regression. At a temperature of 442 K, pressure equal to 1.2 MPa, an ethylene:acetic acid:water:dinitrogen feed molar ratio of 78.2:6.5:5.3:10.0 and relative space time amounting to 0.5, ethyl acetate is for 84 % produced by direct addition of acetic acid to ethylene, while the esterification between acetic acid and ethanol contributes for 16 %. Hence, besides reproducing conversions and selectivities, the kinetic model provides insights on fundamental level, which are essential for the optimization and innovation of production plants utilizing direct addition technology.

Compact star with coupled dark energy in Karmarkar connected relativistic space–time

Compact star with coupled dark energy in Karmarkar connected relativistic space–time

Is the Universe Infinite? Characterising a Hierarchy of Reasoning in Student Conceptions of Cosmology Concepts Using Open-Ended Surveys

Cosmology presents students with ideas that stimulate their curiosity and brings together various concepts from STEM that call on a variety of reasoning types across multiple representational modes, involving subtleties of spacetime relations, a variety of models and evidence requiring multiple lines of high precision observations. This study investigated high school students’ levels and types of reasoning that frame their conceptions in different cosmology topics. An open-ended knowledge survey, the Cosmology Knowledge Survey (CosmoKS), was developed and implemented online to 286 high school students (aged 16–18 years) from Australia and Sweden. A modified version of the Structure of the Observed Learning Outcome (SOLO) taxonomy with four levels (pre-structural, uni-structural, multi-structural and relational) was used as a guide to analyse students’ open-ended and structured responses. This provided insights into the level and complexity of reasoning underpinning a variety of conceptions across the four dimensions of cosmology education: size and scale, spacetime location, composition of the universe and evolution of the universe. The study identified underlying patterns in student reasoning and conceptions in cosmology, summarised as (i) navigating spatial and temporal relations, (ii) counterintuitive concepts and (iii) language and everyday experience, especially intuition. The analysis led to the characterisation of a hierarchy of reasoning that helps identify sources of alternative conceptions and provided the basis for the development of a concept inventory and progression with broad implications.