"Growing up in Karnal, India, some of my precious memories are sleeping under the stars in summers and being awed by the majesty of the night sky. My mother pointed out the milky way and some of the constellations; I suspect some times we gazed forever, without blinking for minutes. Something about the night sky causes us all, young and old, to ponder over the very basic questions. We are inspired and motivated." Kalpana Chawla, 1st Indian born woman astronaut.

Motivation

The cosmology of the twentieth century has described the observable universe emerging from the big-bang, an incredibly hot and dense state 13,700 million years ago. However, it has only indicated us the existence of that state leaving their properties wrapped in an aura of mystery, because they escape the domain of established physics. The question for the logically consistent description of that state and hence the question about the origins of the universe is a perfectly legitimate and scientific one. Hand in hand with the beginning of the twenty-first century this question begins to get some concrete answers that may be verified in the near future, perhaps even with the Planck mission of the ESA.

Quantum cosmology is a fascinating challenge. Nothing in this branch seems clear. There are no solid results, nor there are any unique models. The field of quantum cosmology currently explodes in a range of models and brilliant, surprising, disturbing and interesting ideas, which, besides of not having any empirical support, lack of a verified theoretical foundation.

The Planck satellite, to be launched in October 31, 2008, will provide the most accurate map to date of the cosmic microwave background, and could give us evidence about the validity of some of the models of quantum cosmology. However, verification must come with the theoretical foundation through a quantum theory of gravitation. Such a theory is still not established, although there are indications that some of the existing proposals could go on the right track. The start of operation of the Large Hadron Collider in the summer of 2008 will be a milestone in the testing of high-energy physics and we may be perhaps at the beginning of a new era of verified results of the physics beyond the standard model.

It seems to be a deep and disconcerting feature of this universe that in order to understand the largest and biggest, we seem to be required to take a detailed look to the nearest and smallest. Specially the physics of the last hundred years has shown us that the universe hides its innermost mysteries with so much zeal, that it requires a very subtle and lucid study to be forged generation after generation, with dedication of those working on the field and with the enthusiasm and support from the others.

And this also justifies this modest page. It was a pleasure to prepare this page summarizing here some of my personal notes - those of an amateur - about this field. I am happy if I was able to awaken some interest.

Introduction

Quantum cosmology is the branch of cosmology that describes the origins of the universe. One of the Hawking-Penrose singularity theorems in general relativity states that every cosmological solution that fulfills certain energy conditions has a singularity in its past. In the realm of standard cosmology our universe is assumed to have started with a singularity, the "big-bang", about 13,700 million years ago. However, the theory of general relativity breaks down when describing singularities like black holes or the big-bang. Actually, it turns out to be the inadequate theory to describe to the evolution of the universe at a time before the Planck time. Before the Planck time the quantum effects of the gravitational field become important due to the high energies and small distances involved.

Thus, in order to formulate quantum cosmological models a theory of quantum gravity is necessary that unifies general relativity with quantum mechanics. Different proposals for theories from quantum gravity exist, like string theory or loop quantum gravity, among others. These theories give rise to different models from quantum cosmology. Currently none of these models has any experimental support, although the verification of certain properties of them could be within reach of the technology in the next years. The current evaluation of the models is only possible on the basis of theoretical arguments, like for example their relation to inflation. Inflation is one of the basic pillars of standard cosmology. This phase begins after the Planck time or perhaps already before the Planck time and gives rise to (i) the observed homogeneity (ii) the flatness of space, (iii) the origins of the first inhomogeneities. However, a convincing explanation on the origins of inflation is still missing and hidden in a new high-energy physics. Quantum cosmology should provide a suitable explanation for the origins of inflation.

In this series of articles I will try to provide an overview of the current most simple quantum cosmological models. This will be a summary of my personal notes after reading some papers. You probably know already that quantum gravity is a very dificult subject. However, I believe that it is possible to understand the basic phenomenological features of the current quantum cosmological models without relying on full quantum gravity theories. This is actually the reason that motivated my interest and study of these models. I will classify the models in four groups: (i) canonical quantum cosmology (ii) loop quantum cosmology (iii) pre-big-bang cosmology and brane cosmology

Never confuse the big bang with the big ben