The Friedmann equations describe the dynamics of the scale factor in a
FRW model-universe.
The equations can almost be derived with Newtonian
mechanics but the exact derivation must start with Einstein's field equations
and the FRW-metric. This is the aim of the present written report, written for
the course General Relativity, Cosmology And Classical Gauge Theories.
When the Friedmann equations have been derived, a brief discussion of the
solutions will be given. Next a simple class of anisotropic models (with
chaotic behaviour) will be discussed. The application of the classical
Friedmann equations is limited to the regime where quantum fluctuations of
the metric are negligible. The possibility of a quantization of the Friedmann
equation leading to the wave function of the Universe will be touched
upon.
report (ps.gz 379 kb)
The origin of life is a wonderful example of a complex phenomena that requires insight into many scientific fields: biology, chemistry, physics, astronomy, geophysics and even philosophy. Many theories have been suggested and forgotten but the general picture is beginning to emerge. Simple organic molecules came to the young Earth along with water by a great number of comets. In the prebiotic reducing atmosphere organic molecules including sugars and amino acids were formed. Resolved in water together with nucleic acids and trapped inside membranes of fat the more complex proteins and RNA developed by chance. The crucial step of replication may have emerged separately for both types of molecules or simultaneously in a single cell containing enzymes of both types. This is an attempt to "cover the whole subject" discussing some subjects which at least the author finds important in explaining the evolution of matter from non-living atoms to the first living cells.
(ps, 1Mb),
(html)
References on WWW:
Molecular Astrophysics, Leiden
Worldwide Molecular Astrophysics Resources
The 118 reported interstellar and circumstellar molecules
Why does the values of the natural constants allow intelligent life forms to emerge? and how much does our existence actually depend on each of the many constants. Could the universe be different? What would be the expected "default values"? The subject of this project is somewhat controversial because the Natural Constants (NC) cannot be changed. They have the same values at any point in space and at any time. Why? what prevents this? what is the 'memory media' in which the exact values and dimensions are stored?
(ps, 179kb) Restricted access...
George Gamow (1904-1968) was a Russian/American scientist with a number of reasons to be admired. He made pioneering work in nuclear science and cosmology by explaining the radioactive decay of atoms and use the theory on the explosive beginning of the universe. He predicted the Cosmic Microwave Background Radiation and he has been called the "Father of the Big Bang". As an amateur biologist he suggested 'a triplet code of four symbols' in DNA governing the evolution of life. Gamow was an excellent popular writer too. In his famous "Mr. Tompkins in Wonderland" he explained special relativity, quantum mechanics and other scientific theories for everybody including children! In several other books he proved that science can be fun. Gamow also wrote an informal autobiography "My World Line" which unfortunately was not completed before he died.
( ps, 2.068kb).
Why are most galaxies ellipticals while others, like our own galaxy, have spiral arms? To understand the different structures we find in galaxies, we must know how galaxies are formed. We must understand galaxy formation in general before we can reveal the structure and formation of the Milky Way. Our present knowledge about galaxy formation consists of many pieces of theoretical and observational results. Density perturbations in the CDM spectrum amplifies fluctuations in the CMB radiation to the seeds needed for protogalactic clouds. These clouds collapse and fragment into smaller clouds with masses comparable with globular clusters and dwarf galaxies. Star formation turn the gas into gravitationally bound systems of stars. We will take a look at the morphology of galaxies before we discuss DM and the physics of galaxy formation. In the end we will return to the Milky Way.
( ps, 103kb).
Inflation is todays best solution to the problems of the standard hot big bang cosmology. This is described by the Friedman-Robertson-Walker (FRW) line element, a solution to Einstein's field equations. We live in a flat universe with a very high degree of isotropy. This cannot be explained within the standard model. Inflation is a mechanism which solves these and other problems related to topological vacuum defects. There are many indications that the universe began its expansion because of a peculiar energy state with negative pressure due to the decay of a scalar field in vacuum. Is the vacuum energy density still the most dominating factor? What is the modern view of vacuum? How can a scalar field create an exponentially expanding de Sitter space-time? How can this space-time result in a big bang-universe with only a short period of inflation and a non-zero matter content?
( ps, 258kb).
In this paper I will investigate the geometry around Black Holes, and how this affects freely falling relativistic particles along geodesics which is certainly not straight lines as in normal flat spacetime. Stellar black holes are the relicts of collapsed massive stars which provides extreme mass-energy-densities. Nothing can escape from the black hole, not even light. This is because of the extreme curvature of space. The detailed description of black holes is included in The Einstein Field Equations. Historically one of the first exact solutions to these equations was that of Schwarzschild 1916 describing a spherical symmetric point mass, later identified as a black hole. I will concentrate on the Schwarzschild-solution, describing a non-rotating black hole and the Kerr solution, describing black holes with angular momentum. The aim of this work is to use some of the fundamental results to get a view of the geometry around a black hole. Curvature is one of the most remarkable geometrical properties, but some other basic concepts has to be introduced, these are: world lines, geodesics and metric tensors.
WWW-exhibition: (
html). Paper:
PostScript (581kb), html.