🚧Work in progress!🚧
^^ go back to parent lecture ^^
To interpret the images from large surveys one need sofisticated theretical counterpart in the form of numerical simuatlions. There, the final aim is to self-consistently model all matter components, with the least amount of assumptions. How to do so? Well, for this we need to take a step back to understand what legacy undeniable informaiton we know about the large scale. In year 1964 CMB a radiometer at Bell Telephone Laboratories first measured an all-direction homogeneus radiation, that is theoretically explained as a residual from Big Bang recombination. This radiation however contains small variations depending on the angle, and its fluctations are directly linked. So to run a simulation what people do is to create a program that stores a number of particles that attracts each other through Newtonian gravity.
How many particles?
Suppose you want to simulate a (2Gpc)3 volume with a resolution of a galaxy (~1011 Mo),
being the average density of the Universe ~50Msun/kpc^3, you'd need
((2000000kpc^3)*(50Msun/kpc^3)/(10^11Msun)), that is
~15003 particles.
If you need 10 double floating points per particle (mass and 3D velocity, position, and acceleration),
you'd need +270GB of RAM to run it.
What about the cosmology?
Well, the cosmological ingredients that enters in the typical cosmolgical simulations
are the
energy density
component of the universe.
which in short tells you how much contribution an element is contributing
to the overall curvature of the Universe at the present time.
For instance, both from lensing and from the CMB we know that the dark matter
nowadays contributes as ~0.27, while, by measuring the visible matter we know
the visible matter accounts for ~0.045.
I said nowadays, but how could these things be different in the past?
well, mainly because the Universe can expand (or in theory also contract)
and the curvature itself has a density term (so called ΩK):
so in the past the contribution of the dark matter and visible energy was higher
since the Universe was samller.
In the recent 20 years, by measuring the distance of nearby
supernovae we know the Universe is also accelerating in its expansion.
This acceleration is mapped as a so-called cosmological constant that is a constant
negative-pressured term in the Einstein equation of general relativity, and its contirbution
nowadays is approximately ~0.72, or since observations show that
on large scales our universe is flat, simulations always fix ΩΛ = 1 - Ωmatter.
You may wonder, to compute force acceleration has complexity of O(N2) of 15003. This it true, but there are various approximations you can do to keep a good precision and a complexity of O(NlogN). What proved to be succesful is a code created by Dr. Volker Springel: Gadget first released in 2000. Gadget evoled a lot and there are various versions and spin-offs with various strength and weakness. The winning strategy to integrate gravitational interactinos that lasted for 25+ years however is still the same: organise particles in a octree, and treat long range forces with the so called Particle-Mesh technique and Barnes & Hut for short range interactions.
To be more practical, here are a cosmological simulations (volume and resolutio not relevant here) evolved with TreePM Gadget-like code. See how at the beginning of the video we see a hmogeneus cube as all matter at the beginning are almost equally spaced. In reality, particles position and velocity deviate slightly from what you expect from a identical latex of particles. These small deviations are computed from the initial power spectrum of matter as measured from the distribution of the CMB. As the time evolve, and as the redshift lowers, the particles start clumping together thanks to gravity: they form filaments and haloes, and as haloes merge they form clusters with subhaloes. If that simulation had gas and star formation, one would get that each halo cluster is a galaxy clusters hosting sub haloes as galaxy members.