Field of study

Presently available cosmological data indicate that known forms of energy and matter comprise only 4% of the makeup of the Universe. The remaining 96% is unknown, called `dark', but its existence is needed to explain the evolution of the Universe. The dark matter, contributes 22% of the mean density. It is introduced to explain the observed dynamics of galaxies and clusters of galaxies. The dark energy comprises 74% of the density and is responsible for the observed accelerating expansion. These data mean that we know almost nothing about the dominant components of the Universe!
 
Understanding the nature and the abundance of the dark energy and dark matter within the standard model of cosmology has difficulties. These difficulties have led many physicists to seek anthropic explanations which, unfortunately, have little predictive power. An alternative model has been proposed by Steinhardt and Turok (ST).
 
It is based on the idea of a cyclic evolution of the Universe. The ST model has been inspired by string/M theories. In its simplest version it assumes that the spacetime can be modelled by the higher dimensional compactified Milne space. The attraction of the ST model is that it potentially provides a complete scenario of the evolution of the universe, one in which the dark energy and dark matter play a key role in both the past and the future. The ST model requires dark energy for its consistency, whereas in the standard model, it is introduced in a totally ad hoc manner.
 
The mathematical structure and self-consistency of the ST model has yet not been fully tested and understood. Such task presents a serious mathematical challenge. It is the subject of our research programme.
 
The cyclic evolution model has in each of its cycles a quantum phase including the cosmological singularity, CS. The CS plays key role because it joins each two consecutive classical phases. Understanding the nature of the CS has primary importance for the cyclic model. Each CS consists of contraction and expansion phases. A physically correct model of the CS, within the framework of string/M theory, should be able to describe propagation of a p-brane, i.e. an elementary object like a particle, string and membrane, from the pre-singularity to post-singularity epoch. This is the most elementary, and fundamental, criterion that should be satisfied. It presents a new criterion for testing the cyclic model. Hitherto, most research has focused on the evolution of scalar perturbations through the CS.
 
Successful quantization of the dynamics of p-brane will mean that the compactified Milne space is a promising candidate to model the evolution of the Universe at the cosmological singularity. Thus, it could be further used in advanced numerical calculations to explain the data of observational cosmology. Failure in quantization may mean that the CS should be modelled by a spacetime more sophisticated than the compactified Milne space.

Publications

1. P. Dzierzak, J. Jezierski, P. Malkiewicz and W. Piechocki , Quantum Big Bounce , (2008) arXiv:0810.3172v1 [gr-qc]
 
2. P. Malkiewicz and W. Piechocki, Excited states of a string in a time dependent orbifold, delivered to Classical and Quantum Gravity (2008) arXiv:0807.2990v2 [gr-qc]
 
3. P. Malkiewicz and W. Piechocki, Transition of an extended object across the cosmological singularity, Acta Phys. Pol. B (2007). abs
 
4. P. Malkiewicz and W. Piechocki, Propagation of a string across the cosmological singularity, AIP Conf. Proc. 957, 429-432 (2007).
 
5. P. Malkiewicz and W. Piechocki, Propagation of a string across the cosmic singularity, Class. Quant. Grav., 24 (2007) 915 [arXiv:gr-qc/0608059].
 
6. P. Malkiewicz and W. Piechocki, Probing the cosmic singularity with a particle, Class. Quant. Grav., 23 (2006) 7045 [arXiv:gr-qc/0606091].
 
7. P. Malkiewicz and W. Piechocki, The simple model of big-crunch/big-bang transition, Class. Quant. Grav., 23 (2006) 2963 [arXiv:gr-qc/0507077].
 
8. P. Malkiewicz and W. Piechocki, Quantum particle in the Milne space, Journ. Physics: Conference Series 33 (2006) 236.go
 
9. P. Malkiewicz and W. Piechocki, A toy model of the cosmic singularity, Intern. Journ. Geometric Methods Mod. Phys., Vol. 4 No 2 (2006) 305.go
 
10. P. Malkiewicz and M. Nieszporski, Darboux transformations for q-discretizations of 2D second order differential equations, Journal of Nonlinear Mathematical Physics Volume 12, Supplement 2 (2005), 231–239.go

Presentations given

"A model of cosmological singularity", Seminar for Ph.D. students in SINS, 03.06.2008, Warsaw
 
"The nature of cosmic singularity", Conference: Perspektywy Astrofizyki Czastek, 14-18.10.2007, Cracow
 
"Propagation of a string across the cosmic singularity", Seminar for Ph.D. students in SINS, 06.03.2007, Warsaw
 
"Simple model of big-crunch/big-bang transition", Seminar for Ph.D. students in SINS, 06.12.2005, Warsaw
 
"Particle Dynamics in the Milne Space", Pomeranian Workshop in Fundamental Cosmology, 01-06.09.2005, Pobierowo

Courses taken or planned

Orthogonal coordinate systems: theory and practice passed
 
Unbounded operators on Hilbert spaces passed
 
General relativity passed
 
Introduction to String Theory passed
 
I have also attended:
Summer School in Cosmology (Trieste, 2008),
New Trends in Particle Physics and Cosmology (Sheffield, 2008),
The First Quantum Geometry and Quantum Gravity School (Zakopane, 2007),
The Second International Summer School on Astroparticle Physics NIJMEGEN06 (Nijmegen, 2006) and
Pomeranian Workshop in Fundamental Cosmology (Pobierowo, 2005).

Seminars

Currently I attend the following seminars:
Seminar for Ph.D. students in SINS,
Cosmology Seminar in SINS,
Cosmology and Particle Physics Seminar in the Physics Department.
 
I also participate in the Cosmology Club held weekly in SINS.

Doctoral Thesis Preparation

I prepare my thesis under supervision of Professor Wlodzimierz Piechocki. I was admitted into the PhD program on 10.2006. The title of my thesis is "Modeling the evolution of the Universe with compactified Milne spacetime".
 
Currently, I focus on examination of classical dynamics of strings in a curved and singular spacetime (or membranes winding uniformly around compactified dimension of compactified Milne spacetime, which in a sense is equivalent). Next, I will perform quantum mechanical analysis of this dynamics.
 
The defense of my doctoral thesis is planned for the beginning of 2009.
 
[Grant promotorski przyjeto, poczatek realizacji 07.09.2007. W tym momencie realizuje III etap grantu.]