# Project Plan and Literature Review


**The big picture:**
Using neural networks/flow-based models to generate density fields with non-Gaussian features as an alternative to running N-body simulations.

We have aim to explore two models:

• a translational and rotational equivariant deterministic model (i.e. CNNs) embedded with the physical symmetries implied by the cosmological principles of homogeneity and isotropy. This model will hopefully allow us to transform a high redshift (z = 10) density field to a low redshift (z = 0) density field.

• A flow-based generative model that generates the low redshift density field (z = 0) stochastically from a white noise sample. Hopefully, the flow-based model will be invertible, allowing us to use our final density field to generate our initial white noise sample. The white noise sample will be unique to the z = 0 density field generated in different cosmologies.

We aim to combine these models using a sequence of (conditional) flows to precisely generate a variety of density fields in a range of cosmologies.

*Note: I am not sure if at this stage if testing alternative theories of gravity and extended cosmologies will be beyond the scope of the project*

We will be using summary statistics such as the power spectrum and overdensity histograms to validate our models.

*Q: in the end, will we compare the power spectra and histograms of density fields generated by our models with the same summary statistics applied to N-body simulations?*

We have been using Gaussian random fields as toy-models to construct a suitable data-processing pipeline and ML model architecture. Our final model must be robust to allow us to obtain non-Gaussian features due to the gravitational dynamics in different cosmological models.

This also provides a further advantage of being able to make verify that the properties of oue generated density fields agree with with well-known analytical results. For example, we have modelled the evolution of the cosmological growth factor between z = 10 and z = 0 and how this depends on the matter content of EdS universes.