The Universe Before the Big Bang: Cosmology and String Theory
The past century has been characterized by ever-increasing progress in our knowledge of nature and our understanding of its physical laws. The experimental investigation of the properties of matter, starting from the development of atomic physics at the end of the nineteenth century, has allowed us to look inside the atom, inside its nucleus, and even inside the constituent particles of the nucleus, pushing the frontier towards ever-decreasing distances and ever-increasing energies. At the opposite scale, astronomical and astrophysical observations have allowed us to go beyond the frontiers of our solar system and our galaxy, and we have even broken free from every kind of optically active system, pushing the frontier towards ever-increasing distance scales and thereby exploring older and older epochs.
At the same time, the development of progressively more sophisticated theoretical and mathematical models such as relativity, quantum mechanics, and ﬁeld theory, has allowed us to build up a coherent framework to accommodate and understand this vast amount of experimental data. The two paths laid down by the development of nuclear physics and astrophysics, apparently divergent (in distance scale) but effectively convergent towards ever-increasing energies, then successfully merged, yielding, during the 1970s, the so-called standard cosmological model. It is certainly not an overstatement to say that this model represents one of the pillars of twentieth-century physics.
The standard cosmological model, which will be described in detail in the following chapters, provides us with a complete and satisfactory description of the current Universe. Furthermore, this model can be extrapolated backward in time to recover the temporal evolution of the Universe – explaining for instance the origin of light elements (so-called nucleosynthesis), starting from an initial state characterized by a primordial hot “mixture” of elementary particles. Moreover, the natural completion of the standard model, known as the inﬂationary model, explains how the large scale structures that we currently observe (galaxies, clusters of galaxies) may emerge from tiny primordial ﬂuctuations in the matter density.
According to the standard model and its “inﬂationary” extensions, the Universe is a system which has continously expanded from a huge initial explosion, commonly known as the Big Bang.
The relics of this explosion (in particular, the cosmic microwave background, electromagnetic radiation characterized by a thermal, black-body spectrum) was ﬁrst observed in 1965 by Arno Penzias and Robert Wilson, who were awarded the Nobel Prize for this discovery. Despite the fact that such results are relatively recent, the concept of the expanding Universe has already become part of popular culture. Indeed, expressions like “explosive Universe”, “Big Bang”, and “initial singularity” are now common language. There is widespread awareness that the Universe is “expanding”. A number of excellent popular science books, written by world-renowned scientists, describe the history of the Universe from the Big Bang to the present time.1 But what exactly do we mean by the Big Bang? As the term suggests, a Big Bang is certainly a big explosion.
More precisely, a rather violent and fast production of radiation and matter particles characterized by extremely high density and temperature. The cooling produced by the expansion (according to the standard laws of thermodynamics) has “ﬁrmed up” such particles into matter lumps, that have eventually combined into the large scale structures of the Universe we observe today. We can say that these aspects of cosmological evolution are well understood and widely accepted, barring some still debated issues concerning, for instance, the problem of baryogenesis (i.e., the mechanism by which only matter particles are produced from the relics of the primordial explosion, while large lumps of antimatter seem to be completely absent today on large scales).
The term “Big Bang”, however, is often used (even in a scientiﬁc context) in a broader sense, as synonymous with the birth and origin of the Universe as a whole. In other words, this term is used also to indicate the single event from which everything (including space and time themselves) directly originated, emerging from an initial singular state, i.e., a state characterized by inﬁnitely high values of energy, density and temperature.
This second interpretation is certainly suggestive, and even scientiﬁcally motivated within the standard cosmological model. Nonetheless, it has been challenged by recent developments in theoretical physics that took place at the end of the twentieth century.
Indeed, recent theoretical progress suggest that the behavior of matter at very high energies could be radically different from what we usually observe in the ordinary macroscopic world. In particular, when the energy and the corresponding strength of the various forces are very close to a critical value – to be deﬁned later in the book – it may no longer be legitimate to describe matter in terms of point-like particles (as suggested by the well established laws of low-energy physics). Matter could in fact take more “exotic” forms, either thread-like (called strings) or membrane-like, thus occupying spatial patches that progressively increase with energy. Furthermore, an even more astonishing consequence of this scenario – to be discussed in Chap. 10 – is that, as the energy and strength of the forces increase, the effective number of dimensions of space also rises. In other words, the dimensionality of space-time is not rigidly ﬁxed, but becomes a dynamical variable.
These new theoretical ideas therefore suggest novel descriptions of the initial state of the Universe. Close to the Big Bang, i.e., in a regime of very high energy concentration, the state of the Universe was quite different not only from its current state, but probably also from the one predicted by the standard cosmological model. Besides being extremely hot and dense, and highly curved, the Universe was probably also a higher-dimensional structure, inhabited by exotic objects like strings and membranes, and dynamically governed by forces and symmetry laws that have left today only extremely weak (and possibly indirect) traces.
Within this scenario, more ﬂexible and richer than the standard one, it becomes possible to build cosmological models without any initial singularity, where cosmological evolution can be traced arbitrarily far back in time, even to inﬁnity. Such models allow the Universe to exist, and develop through a long “prehistory”, even before the actual Big Bang, now identiﬁed as the explosion which gives rise to the matter and to the forms of energy that we now observe. The Big Bang is still present but, although it remains a milestone in the evolution of the cosmos, no longer represents the origin of space, time, and the Universe itself. It thus becomes possible, within this framework, to explain how the Big Bang takes place, by studying mechanisms able to concentrate enough energy in a given space-time point to trigger the observed explosion.
All these aspects of modern cosmological models will be presented and illustrated – albeit in an incomplete fashion, if only due to lack of space – in the following chapters. But let us start by explaining how the hypothesis that the Big Bang was the origin of “everything”, while having solid scientiﬁc roots, can nevertheless be challenged by recent developments in theoretical physics.
To this end, it is worth recalling one of the greatest lessons that the natural sciences have learned from Galileo, Newton, and the other founding fathers of modern physics: celestial bodies do not have any “mystic” essence or “metaphysical” property, but move and evolve in time according to the same laws that govern the dynamics of more mundane material objects. The whole Uni- verse is itself an ordinary physical system obeying those laws that science seeks to discover and to piece together using reproducible experiments. The Universe that we observe today, in particular, can be fully (and satisfactorily) described on large scales by the laws of classical physics, including general relativity, the relativistic theory of gravitation developed by Albert Einstein at the beginning of the twentieth century. This theory both includes and generalizes Newton’s gravitational theory, and has successfully passed all experimental tests performed since its conception.
As will be discussed in the next chapter, the theory of general relativity predicts a warping of space and time which is directly proportional to the energy density distributed in the matter sources. By applying this theory to our expanding Universe one then obtains a cosmological model in which the curvature of the Universe itself evolves with time, following the corresponding evolution of the energy density and temperature.
As the expansion proceeds, matter becomes progressively more rareﬁed and colder, according to standard thermodynamics. Thus, as a consequence of general relativity, the curvature of the Universe becomes gradually smaller. It is intuitively obvious, in particular, that an inﬁnite expansion would tend to render the Universe completely empty, and its geometry – i.e., the space-time, to use relativistic jargon – would tend to become ﬂat. In a similar fashion, one can use general relativity to establish that, in the past, when the Universe was smaller and more compact, it was also hotter, denser and thus much more warped than it is today. Going progressively backward in time the density, the temperature, and the curvature of the Universe increase without bound until they reach – in a long, but ﬁnite time interval – an inﬁnitely dense, hot and curved “singular” state.
The idea that such a singular state (identiﬁed with the Big Bang, and conventionally placed at the time coordinate t = 0) may represent the birth of the Universe is based upon the fact that the dynamical equations of general relativity lose their validity at the onset of a singularity, and cannot be extended beyond a singular point (in this case, backward in time beyond t = 0). In other words, the solutions of those dynamical equations describe an “incomplete” space-time which is not inﬁnitely extended in time, being characterized by an impassable “boundary” located at a ﬁnite temporal distance from any physical observer. It is thus general relativity itself which, in a cosmological scenario, unavoidably leads to the notion of an initial singularity, enforcing the idea that the Big Bang was the beginning of space-time and the moment of birth of our Universe.
If we were to adhere strictly to general relativistic predictions, we should then conclude that the main topic of this book – the Universe before the Big Bang – is something meaningless. Before jumping to this conclusion, however, there is a question we should ask ourselves. Is the incompleteness of space-time predicted by general relativity a true physical property of our Universe, or is it only a mathematical property of some equations, that are really inadequate to describe space and time near the Big Bang?
This is certainly a legitimate question in physics, where the occurrence of a singularity often does not correspond to any real entity, but is just a signal that some physical laws have been extrapolated beyond their realm of validity.
Let us consider the following, very simple and well-known ex- ample. The laws of classical electromagnetic theory establish that, inside the atom, the positively charged nucleus exerts an attractive force on the negatively charged electron, and that this mutual force increases as the distance between the two charged particles decreases (according to the well-known Coulomb law). In particular, when the distance between the nucleus and the electron tends to zero, the force becomes inﬁnite. On the other hand, a revolving electron should progressively radiate away its energy, thus progressively shrinking its orbit closer and closer to the nucleus. We should then conclude that, according to the classical electromagnetic laws, all electrons would eventually fall into the nucleus, atoms would collapse into singular point-like states, and ordinary matter would not exist in the form we know it. Such a situation does not occur, however, simply because at short enough distances the laws of classical physics break down and the laws of quantum mechanics come into play, preventing the collapse of the electron into the nucleus.
We may also refer to another example, less obvious, but equally well known to physicists. The energy density of thermal radiation, computed by applying the laws of classical physics, obeys the so-called Rayleigh–Jeans spectrum. This predicts an un- bounded growth of the energy density with the frequency of the thermal radiation. But once again this energy singularity disappears if we take into account the need to use quantum mechanics to describe the behavior of matter and radiation at high enough frequencies (i.e., at high enough energies). One then ﬁnds, by applying the required quantum mechanical principles, that the thermal energy density ﬁrst increases with frequency, reaches a maximum at a ﬁnite frequency value, and eventually decreases as the frequency goes to inﬁnity, following the so-called Planck spectrum (named after Max Planck, who was one of the founders of quantum mechanics).
There are also other circumstances, however, where the occurrence of a singularity in the equations describing a physical system may point to some abrupt change in the state of the system, requiring the introduction of different variables and different degrees of freedom for an appropriate description. In this case it is also instructive to consider a simple example, drawn from particle physics.
Let us ﬁrst recall that at sufﬁciently low energies (i.e., well below the typical energy of strings) all known ordinary matter – including also those forms of matter produced artiﬁcially in the various accelerators around the world – can be reproduced by a proper combination of a relatively small number of fundamental building blocks, the so-called elementary particles. Some of these particles (actually, only a very small fraction of their total number) are stable: this means that, were they set up in a fully isolated environment, they would persist in their original state, retaining their physical properties unchanged for an inﬁnitely long time.
Other particles, however, are unstable: even without any external inﬂuence, these particles decay, that is, they disappear, leaving in their place two or more different (and lighter) particles. Their mean decay time, called the lifetime, depends upon the forces producing this intrinsic instability.
Consider, for instance, an atom. It consists of electrons (which are stable particles), protons (which are also stable, as far as we know) and neutrons, which are stable, but only within the atomic nucleus. In an empty environment (i.e., in vacuum) a neutron decays, with a typical lifetime of the order of ﬁfteen minutes, producing three new stable particles: a proton, an electron, and a neutrino. Now for each of these “newly born” particles, the de- cay process can be regarded as a kind of “Big Bang” in the realm of subnuclear physics: an abrupt explosive process marking the appearance of these particles and the beginning of their life, on a microscopic scale. This does not imply, however, that these particles emerged from “nothing”. Before they appeared, there was a corresponding physical system in a different initial state, representing a neutron which, under the inﬂuence of some nuclear forces (called weak interactions and ﬁrst described theoretically by Enrico Fermi), has transformed into a new state represented by three different particles.
There is no doubt that the physical description of the system undergoes a sudden and abrupt change when the neutron decay occurs. Nonetheless, the decay itself does not represent any impassable boundary. In a similar fashion, the cosmological explosion that we identify as the Big Bang certainly marks the beginning of the present state of the Universe, i.e., of the Universe in the form that we currently observe. However, if we relax the a priori assumption that the Big Bang must also mark the origin of space and time, the question as to whether our Universe existed before such an explosive event, and in which state, may become perfectly meaningful.
An equally legitimate question, however, could also naturally arise at this point: Why should we address the issue about a possible state of the Universe before the Big Bang, thus casting doubts on the hypothesis – suggested and supported by general relativity – that the Big Bang is effectively the true beginning of everything?
The answer to this is quite simple. General relativity, as previously stressed, is a classical theory. It has been successfully tested at densities, temperatures and curvatures much higher than those we may observe in our ordinary macroscopic world, but deﬁnitely much lower than the ones coming into play in the primordial Uni- verse. The use of general relativity near the Big Bang implies trusting the validity of this theory not only beyond any experimental evidence, but also in a regime where there are well-founded reasons for doubting the legitimacy of classical theories.
In fact, in the regime of extremely high energies, where the above-mentioned strings and membranes may become relevant, the properties of the gravitational interaction are expected to be significantly different from those predicted by general relativity. New ﬁelds and new kinds of short-range interactions may come into play, as inevitable consequences of the laws of quantum physics.
On the other hand – as we shall see in the following chapters – it is the standard cosmological model itself that leads us to the unavoidable conclusion that quantum mechanics, together with the physical laws appropriate to describe matter on microscopic scales, are key elements in the dynamics of the primordial Universe.
Taking the expansion of the Universe seriously, and going backward in time, we do indeed reach epochs during which the entire structure of the Universe and its energy (currently spread over billions of galaxies) was compressed into a spatial region of about one hundredth of a millimeter in length. The energy density of the Universe at that time was inconceivably high compared to what we usually observe on macroscopic scales. We can compute, using general relativity, that the energy density for such a small compact region was about 1080 times greater than the typical density in an atomic nucleus (which is already very high). Such a value, dubbed the Planckian limiting density, is the threshold value cor-responding to the onset of a regime where the geometry of space and time itself (together with matter) must obey the laws of quantum mechanics. General relativity, however, does not know about quantum mechanics: it can thus bring us to the doorstep of the Big Bang, so to speak, but it cannot proceed further without entering a regime in which its predictions are no longer reliable.
Therefore, in order to correctly describe the Universe when approaching the Planckian regime, a classical theory like general relativity is not sufﬁcient. Instead one must have a theory able to provide a consistent description of gravitation even within a quantum framework. Since such a theory was not available when the standard model was developed, speculative attempts were made to extrapolate the predictions of general relativity right to its limits, that is, to describe the birth of the Universe from an inﬁnitely hot, dense, and curved state: the initial singularity, beyond which nothing existed.
This methodology wherein the results of a known theory are extrapolated into an as yet unexplored range is a natural procedure after all, and it is common practice in the scientiﬁc context, as a ﬁrst step towards more sophisticated theories and more complete models. However, as far as cosmology is concerned, pushing this procedure to its extreme leads us to identify the limits of our cur- rent knowledge with a natural barrier, as though nature had set up a deﬁnitive, impassable gate at the Big Bang position. Such a situation is reminiscent of the attitude the ancient peoples had towards the Columns of Hercules: since no-one had crossed the strait of Gibraltar, and no-one knew the world beyond it, it was common opinion (and it seemed plausible) that the world would end at that point.
This basic lack of knowledge, however, is continuously being ﬁlled by the recent developments of theoretical physics, which have provided us with a very powerful tool: string theory. In principle, this theory (and its possible, though as yet not fully deﬁned completion, M-theory) allows a coherent merger of quantum mechanics and gravitation, and thefore provides a potentially consistent framework to describe the geometry of space-time in the regime of extremely high energy densities and curvatures. It has thus become possible to study the evolution of the Universe near the Big Bang, and even beyond it, by means of a robust and consistent theory, valid at all energies. It is as though, in the above analogy with ancient times, someone had built a more solid and reliable ship that would allow some brave explorers to sail the seas beyond the Columns of Hercules. In this way, it has been found that the extension of space-time is not necessarily con- strained by an initial singularity, and questions about the possible state of the Universe before the Big Bang are fully legitimate and well posed.
Anticipating the demand of the curious reader, and as an intro- duction to the content of the following chapters, let us immediately give some idea of what the Universe would look like according to the indications provided by string theory, if we could look back in time to the epoch of the Big Bang, and even beyond the Big Bang itself. Such remote epochs cannot be traced using objects like stars and galaxies, which formed only very recently on the time-scale of cosmic evolution. These structures were not yet formed at the onset of the Big Bang, and neither did they exist before it. Instead, we need to exploit some geometrical properties of the Universe that are always valid, like space-time curvature. Let us therefore ask about the past evolution of space-time curvature, and represent its behavior graphically as a function of time.
According to the so-called standard cosmological model (which will be introduced in next post, and which is the model providing the grounds for the hypothesis of the Big Bang as the singular beginning of “everything”) the Universe expands and the curvature decreases in time in a continuous and decelerating fashion. Hence, going backward in time, we reach epochs characterized by progressively increasing curvature. This monotonic growth proceeds continually until the inﬁnite curvature state is reached (corresponding to a singularity, and conventionally ﬁxed at the initial time t = 0). Beyond that point, no classical description is possible (see Fig. 1.1).
However, as already pointed out, a singularity can often be interpreted in a scientiﬁc context as a signal that we are applying some physical laws outside their realm of validity. Concerning this point, it is interesting to quote the opinion of Alan Guth, one of the fathers of modern inﬂationary cosmology. In his recent book he makes the following remarks about the initial singularity:
It is often said – in both popular-level books and in textbooks – that this singularity marks the beginning of time itself. Perhaps it’s so, but any honest cosmologist would admit that our knowledge here is very shaky. The extrapolation to arbitrarily high temperatures takes us far beyond the physics that we understand, so there is no good reason to trust it. The true history of the universe, going back to “t = 0”, remains a mystery that we are probably still far from unraveling.
In other words, according to Guth, there is little hope of describing the initial phase of the Universe within the standard cosmological model. Indeed, as we have already pointed out, in the presence of arbitrarily high curvature, energy and density, the Einstein theory of gravitation ceases to be valid, and the associated description of the space-time geometry becomes meaningless.
Beside the singularity problem, however, there are also other issues concerning the standard cosmological model that hint at the need for a modiﬁcation near the initial time, even before reaching the quantum gravity regime. Such a modiﬁcation requires in particular that, at some point during its primordial evolution, the Universe should undergo a phase of highly rapid expansion, dubbed inﬂation. We are giving here just a glimpse of what will be illustrated in more detail in Chap. 5. For the purposes of our fast-track, time-reversed journey, it will be enough to point out that during an inﬂationary phase of conventional type the evolution of the Universe is expected to be determined by the energy density of a “strange” particle – dubbed the inﬂation – that generates a scalar- type ﬁeld strength.
Going further backward in time, the potential energy of this ﬁeld progressively increases, and eventually becomes so strong as to be able to “freeze out” the space-time curvature. Then, as shown in Fig. 1.2, the curvature of the Universe stops increasing and levels off to an almost constant value. During this initial inﬂationary phase, the geometry of the Universe thus approaches that of the de Sitter space-time (named after the cosmologist who found the solution describing a spacetime with constant curvature). The primordial Universe, in that case, closely resembles a tiny, four- dimensional hypersphere with constant radius.
However, there is also a problem in this case: a phase in which the Universe expands while the curvature stays ﬁxed at a constant value cannot be extended backward in time without limit. In fact, for a physical (stable) particle, moving according to the laws of general relativity within this type of geometry, it would take a long, but certainly ﬁnite amount of time to reach us starting from the moment when the radius of the Universe was zero. In order to obtain a “complete” model of space-time, the initial Universe should exist in a contracting phase, at least according to the de Sitter solution to the equations of general relativity. However, as has been shown by some cosmologists (in particular, Arvind Borde, and Alexander Vilenkin), within the framework of an inﬂationary model based upon the potential energy of some scalar ﬁeld, a transition between a contracting and an expanding phase is not allowed, at least according to general relativity and the physical laws that we currently believe to be valid.
Hence, the inﬂationary scenario at constant curvature is also unable to provide a complete model for the evolution of our cosmos. As Guth himself points out in his book:
Nonetheless, since inﬂation appears to be eternal only into the future, but not the past, an important question remains open: How did it all start? Although eternal inﬂation pushes this question into the past, and well beyond the range of observational tests, the question does not disappear.
Apart from the possibility of experimental tests (which will be discussed later in the book) it seems undeniable, as outlined by Guth, that a constant curvature, expanding phase cannot be arbitrarily extended backward in time, and does not lead to a complete description of the origin of our Universe. A possible solution to this problem relies upon the possibility that a Universe with the appropriate, expanding de Sitter geometry might spontaneously emerge from the vacuum at some very early epoch (but not inﬁnitely distant in time), through a typical quantum mechanical effect.
Leaving aside this possibility for the moment and limiting our options to a classical context, it is clear that if the curvature cannot remain indeﬁnitely constant, then we are only left with two alternatives in order to extend our cosmological description back in time. The ﬁrst possibility is that at some point the curvature starts to increase again. In this case, however, the singularity would persist, with the only difference that the position of the Big Bang would be moved backwards in time with respect to the standard cosmological model. The second possibility is that, going backwards in time, the curvature starts to decrease, becoming smaller and smaller as we go back in time. This second case is exactly the model of the Universe suggested by string theory, represented in Fig. 1.3, which will be discussed in detail in the following chapters.
In fact, as will be shown in Chap. 3, string theory suggests that the plot of the cosmological curvature scale versus time could have a specular reﬂection symmetry with respect to the time co- ordinate t = 0. It also suggests models in which there is no singularity in the space-time curvature, and time can be arbitrarily extended to inﬁnity, in both the backward and the forward directions. Within these models – dubbed string cosmology models, as opposed to standard cosmology or conventional inﬂationary models – the curvature starts from arbitrarily small values, increases up to a maximum value (dictated by string theory), and eventually decreases until it joins the behavior typical of standard cosmology and the current epoch.
The typical trend for the cosmological space-time curvature, in this context, is thus described by a bell-shaped curve, eventually joining the curve that represents the standard-model curvature.
Indeed, at recent times standard cosmology works well, so string cosmology should not predict signiﬁcant differences. However, as shown in Fig. 1.3, the string cosmology curve matches the standard one at higher curvatures (and hence earlier) than the curve corresponding to the inﬂationary de Sitter model. This occurs because the highest value of curvature reached in a string cosmology con- text (viz., the top of the bell curve drawn in Fig. 1.3) is in general higher than the value reached during de Sitter inﬂation. This feature may have some key phenomenological consequences, as will be discussed in the following chapters.
The moment at which the curvature reaches its (high, though ﬁnite) maximum value at the top of the bell replaces the singularity and corresponds to the position of the Big Bang in the standard cosmological scenario. It is then natural to refer to the cosmological phase characterized by increasing curvature (the left-hand side of the bell in the graph) as the pre-Big-Bang phase, describing the initial evolution of the Universe starting from an initial “vacuum” state. In the same way, the right-hand side of the bell corresponds to the post-Big-Bang phase, characterized by decreasing curvature and representing the typical evolution of the current Universe, in agreement with standard cosmological predictions.
According to this class of string cosmology models, the Uni- verse at the epoch of the Big Bang was not a newly born baby, but a rather aged creature, midway through an evolution of probably in- ﬁnite duration. Furthermore, the Big Bang itself is not viewed as a singular point, but as a transition – certainly violent and explosive, but of ﬁnite duration and intensity – between two phases characterized by different physical and geometrical properties. What hap- pens, therefore, is that a traditional representation of our cosmos is somehow overturned, whence a comparison with the well-known Copernican revolution may seem natural. With Copernicus, the Earth lost its role as the center of the Universe, or focal point of the physical space. Similarly, within string cosmology, the Big Bang may lose its role as the beginning of the Universe, or focal point of physical time. A sort of Copernican revolution – in time, rather than in space – even though the Big Bang, in contrast to the Earth for Copernicus, does not completely lose its privileged role in the cosmic scene.
At this point, we are beginning to outline a potentially interesting cosmological scenario. However, before we proceed further, we cannot avoid asking the following question, which is of fundamental importance if we hope to keep working in a scientiﬁc con- text: What is the observational evidence that could either prove or disprove this scenario for the primordial evolution of the Universe?
The answer to this question is quite similar to the one an archaeologist would give to anyone asking him about the evidence supporting the existence of ancient civilizations. He would argue that, by studying old remains and available relics, one can attempt to trace back to original sources and reconstruct the past. In the same way, a cosmologist may be viewed as an archaeologist who studies the relics of the various cosmic epochs, in order to piece together the evolution of the Universe.
For a further clariﬁcation of this point let us go back to an example concerning unstable particles, and consider again the process of neutron decay introduced previously. In a sense, the particles left by the decay represent the relics of the decay process: analyzing such decay products, a physicist is able to trace back to and reconstruct the properties of the initial state. In particular, by studying the proton, the electron, and the neutrino that have emerged from the decay, and using his knowledge of the theory of weak interactions, he may deduce the prior existence of a neutron and compute, for instance, the neutron mass, even without having directly observed the initial particle.
In a similar fashion, the evolution of the Universe and the transitions between the various cosmological epochs are generally characterized by intense emission of a very large amount of radiation, of all kinds and in all allowed frequency bands. Part of such radiation has subsequently been transformed, by exploiting the relativistic equivalence between mass and other forms of energy. However, there is also a fraction of this radiation which reaches us today, retaining its original features. So by studying its properties, it is then possible to gain direct information about the past evolution of our Universe.
It is worth mentioning that, also in the context of the standard cosmological scenario, the hypothesis of a primordial explosion has been experimentally conﬁrmed by the observation of relic electro- magnetic radiation, the so-called cosmic black-body background, discovered by Penzias and Wilson. In the same way, as will be discussed in Chap. 6 and thereafter, other types of relic cosmic radiation – gravitational, dilatonic, or axionic backgrounds – could experimentally corroborate or rule out various scenarios describing the Universe before the Big Bang.
Finally, to complete this short introduction, let us just mention a few other topics that will be covered in subsequent chapters. A ﬁrst and quite essential issue pertains to the motivations for introducing the cosmological phase already dubbed the pre-Big-Bang phase. Our aim, in particular, will be to explain how such a phase appears to emerge naturally within string theory, and not in the context of Einstein’s gravitational theory.
Another point concerns the kinematical aspects of the primordial cosmological evolution. Despite their differences with respect to conventional inﬂationary models, string cosmology models are also initially characterized by a very fast, accelerated expansion. It follows that they are inﬂationary models too, in every respect, and may thus provide solutions for the shortcomings of the standard cosmological scenario.
But the point which is likely to be the key issue concerns the phenomenological consequences of these models, and the problems concerning their observation and their possible use as tests of string theory itself. We will therefore attempt to present a detailed description of the physical effects marking the differences between string models and more conventional cosmological models, paying particular attention to the possibility of either direct or indirect experimental observations of such differences.
To this end, it is interesting to observe that the phenomeno-logical consequences of a cosmic phase preceding the Big Bang can be divided into three classes: type I, II or III. Type I includes observations that will be carried out in the near future (20–30 years from now); type II consists of observations relative to the immediate future (some years from now); and type III refers to observations (whether performed or not) that are already accessible to current technology. It was the very existence of experimentally testable consequences, emerging with growing evidence from the development of string cosmology models, that has encouraged and motivated many researchers to pursue the study of string cosmology and its various possibilities.
In order to provide the reader with a better introduction to the problems of cosmic evolution, and to the primordial epoch close to the birth of the Universe, it seems adequate to start with a concise overview of the standard cosmological model and its underlying theoretical background (the theory of general relativity). The next chapter will be devoted to this purpose.
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