7/29/2019 perimeter institute 2013 projects

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* Dark Matter, String Theory and the Thermal History of the Universe

David Marsh

One of the earliest successes of the big bang model of the universe was the prediction of the correct

light element abundances created from a thermal bath at high temperature, so called Big BangNucleosynthesis, or BBN (see Weinberg: The First Three Minutes).

In many theories of supersymmetric Dark Matter (DM), the DM itself is also created in a thermal

bath similar to BBN. However, we know very little about the universe at temperatures above the

BBN temperature. One leading theory, inlfation, invokes a particular non-thermal epoch of rapid

acceleration of the universe's expansion. A key problem in modern cosmology, known as reheating,

concerns how inflation ends and produces the thermal bath for BBN. In some string theory scenarios,

there should be an extended intermediate epoch and this can lead to DM production via different,

non-thermal, means as the modes of excitation of the extra dimensions of string theory settle down

and decay.

Thermal and non-thermal DM have very distinct astrophysical and cosmological implications. For

example, a leading, non-supersymmetric candidate for DM that is typical in string theory models is

the axion, and it is produced non-thermally in (almost) all cases. Very light thermal DM is ruled out

for being too "hot", while very light non-thermal DM like axions is not. Thermal and non-thermal

DM have varying effects on structure formation in the universe, and predict very different scenarios

for direct detection of DM on earth. There is the distinct possibility that axions are for this reason

preferred by the models of galaxy formation, and are detectable in future cosmological observations

of galaxy weak lensing. Non-thermal supersymmetric DM, on the other hand, can have larger cross-

sections for detection on earth.

The aim of this project is to outline the different thermal histories of the universe from the end of

inflation up to BBN in string-motivated scenarios and see what types and mixes of DM are preferred

by them. We will then go on to explore cosmological and terrestrial observations that may

distinguish between these scenarios in the near future. Alternatively, if the student wishes, we can

instead explore in more detail the extra dimensional dynamics of string theory in the inflationary and

post inflationary epochs leading up to reheating.

7/29/2019 perimeter institute 2013 projects

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Probing causal sets through diffusion

Astrid Eichhorn

There are many notions of dimensionality in mathematics, some of which are of interest to

physics: For instance, several quantum gravity approaches have yielded a non-trivial spectral

dimension: This is the dimension that characterises a random walk of a test particle on the

quantum spacetime. For large scales, it agrees with four, meaning that the quantum spacetime

looks classical. On small scales, several quantum gravity approaches have found a value of

about two, which is due to large quantum effects.

Causal sets is an approach to quantum gravity, which combines the notion of a discrete

spacetime with Lorentz invariance. So far, random walks on causal sets have not been

considered. The goal of this project is to set up simulations of random walks on causal sets,

from which the spectral dimension could be determined.

The project requires the ability to write a (simple) code for these simulations. Knowledge of

General Relativity and Quantum Field Theory is helpful to understand the background of this

project.

7/29/2019 perimeter institute 2013 projects

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The ground state of the Ising model and its entanglement entropy

Lukaszc Cincio

The ability of obtaining the ground state of quantum many-body Hamiltonian and

extracting its properties using various numerical techniques plays a fundamental role in

many aspects of condensed matter physics. The project involves studying a one-

dimensional quantum Ising model using exact diagonalization (up to 30 spins) and

tensor network techniques (arbitrary size and infinite) such as Matrix Product States.

The outcome of the simulation can be verified by an exact, analytical solution. If time

permits, the project can be extended to more advanced numerical tools, like Multi-scale

Entanglement Renormalization Ansatz and other models.