Evolutionary cosmology is in many ways analogous to a religion, it seeks to explain observable physical reality by guessing at the structure of things beyond observation. In the case of evolutionary cosmology the observable physical reality is the standard model of theoretical physics that now has the workings of the observable universe fairly well pinned down. In order to explain the level of complexity and functionality seen in the observable universe it is however necessary to speculate on larger and even more complex structures, and it is these larger and even more complex structures that evolutionary cosmology provides insight into. Albert Einstein famously said that the universe is a big place and there is plenty of room for God. This was a bit of a misleading statement, but had Einstein been aware of the ideas of evolutionary cosmology back in the early 20th century he would have had a lot more room for the placement of God.
The part of physical reality that we are most familiar with is the rather mundane cold hard world made up of PNE mater. Protons, neutrons and electrons in the form of stabile elements put together in the materials around us. Added to that is the visible light spectrum of electromagnetic radiation that we can see with our eyes, infra red electromagnetic radiation that we can feel as heat on our skin as well as the higher energy electromagnetic radiation that we limit our exposure to in order to prevent sun burn. Electric fields in the form of static electricity and magnetic fields from permanent magnets are also often observable in a normal earthly existence. Electric currents are not directly observable unless the current is so high (more than about 300A) that the mechanical pull of the magnetic field can be felt over close distances. Electric currents in conductors, electric motors, incandescent lighting, fluorescent lighting and light emitting diode lighting are now also common parts of life on earth, but these phenomenon tend to be a bit on the edge of traditional observation and understanding.
The standard model of theoretical physics provides a framework for predicting the behavior of physical reality, and this goes well beyond the PNE mater that we are most familiar with. The standard model also encompasses the high energy physics of fusion in stars and a wide variety of other particles and phenomenon that are involved with the mechanics of mater, energy, gravity, time and space itself. Not all of the mechanisms of space and time are directly observable, but enough has been observed to paint a fairly clear picture of how our physical reality functions.
The ultimate test of the validity of the standard model of theoretical physics is in it's predictive ability. Any human model is just an approximation of what actually exists, but aggressive refinement of the standard model over the past hundred and fifty years has resulted in a situation where we think we have it pinned down pretty good. The fact that PNE mater, electricity and magnetism as well as the high energy workings of stars is now well enough understood that different lines of analysis yield compatible results indicates that the standard model is in fact a good representation of what actually exists.
Where the standard model breaks down though is in explaining why physical reality exists in the way that it does. All we get to see is a tiny little window on the universe limited by the speed of light. We cannot see any farther than the approximately fourteen billion light years "illuminated" since the big bang formation of our universe. The standard model predicts that the universe is actually hundreds of millions of times larger than this fourteen billion light year bubble we call home. The universe is also spherical in the fourth dimension, meaning that there is no edge to it. This is fairly well pinned down as reality, but the big question remains as to what existed before the big bang and what caused the specific level of complexity that we observe in our universe.
It seems quite clear that we are not alone, that is our universe is not the only universe in existence. The big bang must have come from somewhere, and that somewhere is another universe. The breakthrough idea is linking the discontinuity at the beginning of our universe with the discontinuities of supernova explosions of large stars. It is widely believed that supernova explosions of large starts spawn new "baby" universes. A big bang creation of a universe comes out of a supernova explosion in the "parent" universe.
The basic idea of evolutionary cosmology is that the characteristics of a universe are both hereditary and undergo mutation. Those characteristics of a universe are the numbers that describe physical reality, the speed of light, the gravitational constant and about a dozen other constants that describe the interaction of mass, energy, time and space. The physical properties of a universe are dictated by the values of these constants. It just happens that what we see in our observable universe can only exist if all of those numbers are exactly what they are known to be. Slight changes in any of those constants and the whole thing just does not work.
The basic mechanism of evolutionary cosmology is that more supernova explosions spawn more baby universes. Since supernova explosions can only take place when large stars exist it is star formation that leads to the creation of new universes. Through an evolutionary process where the characteristics of a universe are passed on to the new baby universes with some level of mutation high levels of star formation are selected for. Universes with large numbers of stars spawn more baby universes, and therefore pass on their particular set of characteristic numbers to a larger number of new universes.
The other very interesting thing about star formation is that it is the building block of life. Life does not come about without an energy source and a certain level of physical complexity. It seems clear that we exist because our universe has precisely the characteristics that it does. So not only is this universe with a large number of stars the result of an evolutionary process, but our own existence is the result of an evolutionary process of many generations of universes.
Evolutionary cosmology seems to very neatly explain how our universe came to be, but there remain many areas of unknown. Which came first the supernova or the star? This is sort of a which came first the chicken or the egg question. Obviously the evolutionary process started with something much simpler, but just what was that much simpler something and how did it come to be? Ultimate origin questions ultimately are unanswerable because no matter how far back origins are traced the question always remains: What came before that?
The other really big area of speculation has to do with just how it is possible for large numbers of universes to coexist. The standard explanation is in a large number of dimensions of space, but this is sort of a whishy washy answer. Clearly the fact that our universe is spherical with no edge points to the existence of some fourth spacial dimension, but the existence of just one more spacial dimension than we observe is a lot different than a practically infinite number of additional dimensions to house a practically infinite number of universes. What is clear is that our local perspective is so limited that we just can't comprehend the level of complexity in space and time required for what we see to exist the way that it does.
Ultimately it is in this unknown level of additional complexity to space and time that there is room for God or whatever other hallucinations we chose to cook up. There very well may be connections between universes or other mysterious workings not yet catalogued. Ultimately it is probably good for humanity to have room to speculate. A solid understanding of our physical reality can be boring and depressing because it tends to seem limiting.