Cosmology with Geometry Nodes

By MohammadHossein Jamshidi, Ph.D student of Physics/Cosmology at Shahid Beheshti University, Iran.

I’m a Ph.D student of Physics/Cosmology at Shahid Beheshti University. I have also been an animation engineer in the game industry since 2012. You may find some of my works on my GitHub.

Here I share some of the ideas and techniques of using Blender during my research in cosmology. Although these are specifically used in cosmology, I am confident that similar ideas apply to other areas of science. All the files shown here are available for free on this GitHub repository.

Cosmology is the science of studying the physical world on gigantic scales, both in size and time; so large that a galaxy could be considered as a single point, and so long that a millennium could be taken as just one frame of time!

My interest in the world of cosmology lies in Cosmic Microwave Background (CMB) radiation, the light rays that reach us from the very early universe. The CMB has a temperature of about 2.7 Kelvin (around -270 degrees Celsius) and is nearly uniform across the sky; however, it has some tiny fluctuations (of size 10 to 10 K) across the sky which contain very fascinating information from the early definable times, and also the history of the universe. These light rays are quite the last things that we can observe in the sky, coming from the farthest distance that could ever be observed. They have recorded numerous events in the history of the universe, and now we are fortunate enough to be able to decode some of their interesting information.

Inspirations to use Geo Nodes for Cosmology

The early ideas to use Blender for Cosmology were enlightened in my mind from the creative and delightful works of Seanterelle on YouTube. I was impressed by his nice simulations with Geo Nodes that had eye-catching performance, and I tried to use Geometry Nodes for cosmological computations.

In 2024, for one of our projects on the CMB, we utilized Geometry Nodes as a tool for computation, visualization, and algorithm debugging. We needed a tool to visualize caps and stripes of different sizes on the CMB sky, to check how much of their areas overlap with the Galactic Mask (the areas where we can’t receive CMB light due to contamination by our Galaxy). By utilizing the Geo Nodes and some simple rigging, we were able to make such a visualizer.

One may access the results of that project in this paper. This visualization served as a starting point for us to use Geo Nodes in broader areas and more use cases.

Geometry Nodes compute things on mesh elements in parallel. If the mesh elements (faces or vertices, etc.) are considered “data storage slots” and “processing threads”, we can perfectly utilize Geo Nodes for doing “Single Instruction Multiple Data” (SIMD) computations. Although other tools, such as CUDA or Compute shaders might be faster, Geo Nodes provides also a free debugger and visualizer. It is especially perfect for small-scale projects; we can calculate and visualize instantly, and in most cases, we can reach the final numerical result in real-time.

Sometimes we just need a fast and reliable tool, especially for tests on our calculation procedure, to check whether its results are physically correct. Geo Nodes is a handy tool to test the correctness of a procedure/algorithm on a smaller scale. In the following sections, we’ll see some examples of real-life cosmology that we could utilize Geo Nodes not only for visualization and debugging, but also for computation.

As pointed out in the previous section, to work with Geometry Nodes for manipulating data, we need a 3D mesh to store the data on and perform processes with. Making proper meshes for our data is the first step towards utilizing Geo Nodes.

How are the sky maps stored?

From a computational perspective, it is decisive how to store the data appropriately. The way we store the data can drastically decrease the amount of calculations.

Cosmologists and geologists need to work with spherical maps/data, and they must store their data in a way that enables faster spherical calculations. There is a special kind of pixelation of the sphere called HEALPix (Hierarchical Equal Area isoLatitude Pixelation).

As suggested by its name, the pixels of this pixelation have the same area. This sphere can be partitioned into rings of pixels that are parallel to the equator. None of its pixel centers are located at the poles (dealing with poles is problematic most of the time). This pixelation is great for storing the data, and doing spherical math with it is very efficient.

To make a HEALPix sphere at different resolutions, you can find a step-by-step tutorial here.

Despite the benefits of HEALPix pixelation, working with the positioning and ordering(numbering/indices) of these pixels can sometimes be complicated. In the following, we’ll see how Geo Nodes saves us from tedious stuff in map analysis.

Once we create a HEALPix sphere with proper pixel ordering, we can use face attributes of the HEALPix mesh to store the CMB data and visualize it using Geo Nodes. A detailed tutorial for visualizing CMB maps is available here, though I briefly describe the steps here. First, we need to inject the map data (e.g., temperature of the CMB) into the mesh and store the data of each pixel on each face of the HEALPix sphere. Now we should take the min and max temperature, and put them in the range as colors.

Geometry Nodes’ data(attribute) projection is a very powerful tool that is beneficial in many real-life examples. In this section, I’ll bring a few.

In processing spherical data in cosmology, we need map transformations, and it is valuable mathematically and computationally to keep the HEALPix pixelation during these transformations. Here, we see how it is possible to rotate a map and preserve the pixelation. It may seem hard to perform such a task, but it would be very easy with the attribute projection tool in Geometry Nodes.

The idea is to rotate the HEALPix mesh (the one that contains the map on its faces) and project its data to another HEALPix sphere that is not rotated (transformed). This is actually the idea behind all the map transformations discussed in this section.

Implement-wise, in Geo Nodes, we need to:

• Make a virtual copy of the original sphere;
• Rotate it;
• Cast a ray from inside the sphere towards each pixel and see at which pixel it collides;
• Project the ray casted attribute on the original mesh.

Following these steps, one will have a nice rotated map, while the pixelation is kept intact.

Map rotation is not the only use case of the attribute projection; another case that we found useful is to distort a map while keeping the pixelation. The idea is very similar to the one for rotation, that of projecting a distorted map onto an undistorted sphere.

Different physical processes may lead to a distortion in the map. For instance, the Doppler effect is a physical phenomenon that causes the CMB map to be changed by several means, and one of them is aberration (a special kind of distortion). If we weren’t moving with respect to the light sources, the light rays coming to us would be received in the commonly expected directions. However, as our planet (and galaxy) moves in space (with respect to light sources), we receive the incoming light rays in changed directions. This phenomenon is called aberration. This happens to all the light rays (including CMB) coming to us, so every sky map will be distorted because of our motion with respect to the light sources.

The aberration effect can be easily simulated in Geometry Nodes. If we know at which speed we are moving and in which direction, we can compute the aberrated direction of the incoming light rays (we estimate it by the change in the frequency of the observed light rays). To simulate the aberration, we need to distort pixel borders (vertices of the HEALPix sphere).