## Based on the results of each simulation, the compaction in the final structure, which contained more than 20 model particles denoting stellar matter, was identified as galaxies.

*Astrophysicists have developed a neural network that predicts cosmological parameters from the properties of individual galaxies. Knowing the set of astrophysical properties of an individual galaxy makes it possible to limit the global cosmological parameter of matter density in the Universe with a relative spread of about 10 percent. At the same time, this result does not depend on the specific mass, size, and type of galaxy.*

## What is Cosmology?

Cosmology describes the universe as a whole, in terms of global fundamental properties and average values that determine the behavior of our world. Despite the fact that our world can be considered completely homogeneous and integral only on the largest scales (on the order of the size of superclusters of galaxies), cosmological parameters also affect the properties of smaller objects.

To date, it is not entirely clear how long this influence persists – to what extent small astrophysical systems continue to store information about cosmological quantities and whether this information disappears at all on any scale.

## A new approach: Using a Neural Network

Scientists decided to find out what cosmological parameters and with what accuracy can be determined based on astrophysical observations at the scale of a single galaxy. To do this, physicists used a set of 1000 hydrodynamic simulations, each of which was presented in two versions: using two independent software packages.

Each simulation described the evolution of 33.5 million matter-simulating particles in the accompanying cosmological volume with a modern linear size of about 37 megaparsecs (a typical distance between neighboring galaxies is about a megaparsec) in the redshift range from z=127 to z=0, that is, up to the modern state.

The simulations varied the cosmological parameters of the current average density of matter and the root-mean-square fluctuation of this density averaged over the volume. The density parameter of baryonic matter (that is, ordinary, non-dark matter) remained fixed at the same time.

Based on the results of each simulation, the compaction in the final structure, which contained more than 20 model particles denoting stellar matter, was identified as galaxies.

For each of the galaxies, physicists determined 14 basic astrophysical parameters that describe the mass of various components of the galaxy (the central black hole, gas, stars, and the total, taking into account dark matter), the orbital velocity, and its characteristic spread within the galactic halo, the chemical composition of stars and gas, and the velocity star formation, characteristic dimensions and proper motion of the galaxy (translational and rotational).

In one of the two software packages, the brightness of each galaxy was additionally determined in three ranges. At the same time, the authors avoided dividing into any subgroups and subsequently did not distinguish satellite galaxies from central.

## Dividing the results

The researchers randomly divided the simulations into three subsets: a training set of 850 simulations, a validation set of 100, and a test set of the remaining 50. In the first two sets of simulations, physicists trained the neural network to predict the mean and standard deviation of global cosmological parameters from a set of astrophysical parameters in a separate galaxy, and on the third one, they tested the operation of the algorithm by comparing the estimated parameters with the actual values.

To quantify the results, scientists each time calculated the relative spread of the parameter (the ratio of the standard deviation to the mathematical expectation) and accuracy (the difference between the actual value and the mathematical expectation).

To get rid of the distortions that are associated with the choice of a particular galaxy (since the forecast may turn out to be successful by pure chance), the authors averaged this value over all galaxies formed within the same simulation.

As a result, the neural network has learned to predict the matter density parameter from the set of astrophysical parameters of an individual galaxy located within the redshift z<3, with an average relative spread of 10–15 percent and an average accuracy (deviation from the actual value in the simulation) of about 0.034–0.042 in the range of values of the parameter itself is 0.1–0.5.

At the same time, linear correlations between the matter density parameter and individual astrophysical properties turned out to be rather weak: the absolute value of the linear correlation coefficient did not exceed 0.31 when using the first software package and 0.55 when using the second one, and the correlation with the mass of individual components, star formation rate, and chemical composition of galaxies was almost zero in both cases.

The most noticeable effect of the change in the matter density was observed in the dependence between the maximum orbital velocity in the galactic halo and the stellar mass of the galaxy, however, these two parameters alone from the rest were not enough to adequately predict the density. According to the authors, this excludes the construction of a simple linear model.

At the same time, it was not possible to determine the parameter of the root-mean-square fluctuation of the density of matter – a typical statistical forecast error covered almost the entire range of available parameter values and made the result uninformative.

## Conclusions

According to the researchers, this is due to the fact that the last parameter affects only the amplitudes of the initial density fluctuations in the simulated volume – at the simulation output, this can be converted into the fraction of the most massive galaxies among the rest, which cannot be tracked by observing one galaxy.

The authors emphasize that, in fact, the cosmological parameters impose restrictions on the astrophysical parameters of galaxies not separately, but they single out the permissible range of their variation in a multidimensional parametric space. Therefore, in order to learn how to reliably check cosmology with this method, they need more thorough theoretical analysis and further computer simulations with neural networks.

In addition, to avoid incorrect conclusions, it is necessary to vary a wider set of parameters in simulations and monitor effects that mimic the effect of changing the cosmological density of matter, although they have a different physical nature.

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**Sources:**

• Villaescusa-Navarro, F., Ding, J., Genel, S., Tonnesen, S., La Torre, V., Spergel, D. N., Teyssier, R., Li, Y., Heneka, C., Lemos, P., Anglés-Alcázar, D., Nagai, D., & Vogelsberger, M. (2022, January 6). *Cosmology with one galaxy?* arXiv.org.

• Wood, C. (n.d.). *Any Single Galaxy Reveals the Composition of an Entire Universe*. Quanta Magazine.