Lecture 18 Flashcards
what is a cosmological simulation
representation of the universe on a computer that:
- begins at a very early cosmic epoch with density perturbations taken from cmb
- tracks matter distribution forward in time, accounting for effects of gravity and cosmic expansion
- outputs maps of matter distribution at many times along the way until today
why do we use simulations
they are numerical experiments that can be used to conduct experiments and test hypotheses
by comparing them to known observations, we can determine which combinations of parameters best describes our universe
what is the universe in a box simulation
cube chunk of the universe, mass is represented by massive number of particles each representing a small piece of total mass, particles get pulled around by each others gravity
how does gravity in computer simulations work
each chunk of mass gets pulled by the gravity of every other chunk of mass
acceleration computed from newtons law
over a small time, velocity and position changes
repeat for new velocity
why do simulations soften gravity
to avoid R tending to 0 and the force tending to infinity
how do simulations soften gravity
they choose a softening length epsilon
force is not accurate when less than epsilon
so epsilon sets simulations resolution, but the resolution can be comparable to the size of a galaxy so its okay on large scales
how do simulations set the change in time for measuring velocity and position changes
need a balance between a large enough time it doesnt take ages to run but not too large so it is jumpy
ensure each particle doesnt move too far in a single timestamp - not further than epsilon
ends up being roughly millions of years
what is the dynamic range
length of the box \ epsilon
we want the whole universe so the desired dynamic range is incredibly bigger than what the best simulations can get today
what do we do in a simulation about the edge of a box
we assume periodic boundaries
the same box is replicated exactly in each direction
particle that move off one edge can appear on the other
what is making mock simulations
need to take a simulation and make it look like real data that we have measured
how to get light in a simulation from a telescope
the telescope gives a square shape cone out of the sky
need to stack simulation boxes to get right geometry
figure out where galaxies are and how bright they are
how do you constrain cosmology based on real surveys
run a huge number of simulations with different cosmologies and see which ones come closest to the data
you use machine learning to build emulators so you don’t have to run as many
fails/suceeds of us living in a simulation
fails if:
technological process doesn’t continue. either due to fundamental limits or self destruction
future humans lose interest in toy models of reality
succeeds ifL
some way to become aware of glitches or bugs
pros of us living in a simulation
limits:
quantum mechanics tells us there is a fundamental limit to measurements given by the uncertainty principle, resolution?
fundamental limit in discreteness of time given by Planck time. clock speed?
cannot see beyond observable universe. box size?
do we see such parameters that rE ARBITARARILY CHOSEN Like our own?
why do speed of light and gravity have the values they do?
why does dark energy have the value it does?
cons of us living in a simulation
just as we don’t understand limits doesnt mean there isn’t a physics explanation
complexity increases as we descent further into the cosmos, this is opposite to a simulation where it would be simple
