Cosmology is the study of the Universe on the largest scales. As such it deals with structures and dynamics that are quite different from those of terrestrial physics or, indeed, of most other branches of astronomy. It is a subject in which the finite speed of light plays a major role, conflating distance with time: in observing distant galaxies we see them not as they are now, but as they were when the light left them; and that is typically long enough ago to encompass significant evolution in the Universe's contents and dynamics. On cosmological scales the dynamics are dominated by gravitation and, possibly, dark energy. The current theory of gravitation is Einstein's General Theory of Relativity (GR), a non-linear and hugely complex theory entailing subtle and largely unfamiliar mathematical and physical concepts; the nature of dark energy remains speculative as of this writing. It is thus a non-trivial matter to assemble a coherent physical model of the Universe at large, requiring careful definitions of such seemingly mundane things as distance and time. We begin the effort in this introduction with a brief description of the Universe and its contents, and an assessment of our ability to understand the Universe on large scales in both space and time.

Galaxies and friends

Figure 1 illustrates the Universe as we naively think of it: a vast, crowded collection of galaxies. But this is deceptive, for such a picture collapses three dimensions into two and amplifies brightnesses, and thus under-represents the distances between galaxies and overstates both the density of matter and the degree of illumination of the Universe at large. The Universe in actuality is quite thinly populated and only faintly illuminated.

The visible contents of the Universe at large are almost entirely in the form of galaxies, mostly as large, luminous galaxies such as ours. Large galaxies, such as our Milky Way Galaxy, contain billions of stars and much diffuse matter.

Solutions to the Friedmann Equations are models of the Universe's expansion and constitute a four-parameter family of expansion functions a (t); it is the cosmologists’ job to determine which of them is correct, or at least plausible. We approach this problem from two directions: estimations of the densities of sources of gravitation from observations, for use in solving the Friedmann Equations; and comparisons of predictions of trial solutions with observed structure and kinematics of the Universe's contents.

We begin by solving the Friedmann Equations for single-component models, and demonstrating the comparison of their predictions with observations of the real Universe. The best-fitting model at present is the Concordance Cosmological Model (CCM), containing radiation, matter, and dark energy; and discussed in detail in Chapter 15.

Space-time curvature is established by the density of gravitating matter and energy, and is reflected in the metric tensor components. The equations relating the resulting metric tensor to matter/energy density are the Einstein Field Equations (EFE) of gravitation; generically, G(g) = T(ρ, ε) where T characterizes the density of sources of gravitation and G is a curvature tensor containing metric tensor components and their derivatives.

The Newtonian equivalent of the EFE is Poisson's Equation, ∇2Φ = 4πGρ, Where Φ is the gravitational potential and ρ is matter density. This equation may be logically deduced from Newton's laws of motion and of gravitation, but Einstein's Field Equations are less secure: the relation between space-time curvature and mass/energy cannot be unambiguously deduced from fundamental principles, but must be inferred – guessed at, if you like – from broad principles and analogies that leave room open for many specific possibilities. It was arguably Einstein's greatest contribution that he came up with what appears to be the right answer: his field equations have stood the test of time (so far) and are the basis for relativistic cosmology (among other things).

Of the two halves of the EFE the curvature side is the more problematic, so we begin the discussion with the tensor representing matter and energy, which can – to a large extent – be logically deduced from familiar physics.

Sources of gravitation

Energy-momentum tensor

Possible sources of gravitation include all forms of mass/energy, including such things as kinetic energy, pressure (which carries dimensions of energy density), stress, electromagnetic field energies, etc.; in addition to ‘normal’ matter and radiation. One consequence is that the tensor describing the densities of sources of gravitation is known by many names: mass-energy tensor, energy-momentum tensor, stress-energy tensor, etc. We will stick to the most commonly used name, the energy-momentum tensor, and denote it by T.

It is not hard to guess that this tensor must be of rank 2 if it is to include directional components such as momenta, stress, and electromagnetic field potentials. The proper and most general definition of T is a variational one: T is the quantity needed for a stationary matter/radiation action.

Principles of contracting have evolved over the eons, from simple tribal bartering to formal contracting, which has been in place, and enforced, since ancient Egypt times. Plato recognised basic rules for the cancellation of agreements and Roman law placed contracts into various classes. However, mass communications and connections between potential contracting parties have expanded contracting in a manner not envisaged. Although the fundamental principles of contract law will continue to apply in the digital world, new and unusual circumstances arise which must be addressed and managed by commercial parties and legal systems. Online commerce, local and global, has become commonplace in the past two decades. Numerous traders have embraced the new opportunities by creating global meeting places and auction houses such as eBay and Amazon. The sale of software, cars, travel, books, music and videos are just some of the many commercial transactions carried out in cyberspace. Trillions of dollars’ worth of goods and services transactions occur online annually. Online contracts are typically entered into without paper, without the use of a pen and without the use of the spoken word. This chapter explores how such contracts may be entered into and how conditions may be incorporated into them. This chapter also addresses the changes to the Electronic Transactions Acts as a result of the adoption of the UN’s Convention on the Use of Electronic Communications in International Contracts (New York, 2005).

That radiation is a source of gravitation is a consequence of the special relativistic equivalence of matter and energy. Radiation is commonly overlooked in this regard because its energy density in the current Universe is typically very small. The densest form of radiation in our vicinity, for instance, is solar irradiance at F ≈ 1350 W/m2 (at the Earth's distance from the Sun), corresponding to an energy density of ε ≈ F/c ≈ 4.5 × 10−6 J/m3 or an equivalent mass density of ρ = ε/c2 ≈ 5 × 10−23 kg/m3. This is thinner than the ‘vacuum’ between planets, or between stars in our part of the Galaxy. Under most non-cosmological circumstances there is thus no need to include radiation in computing gravitational forces in the current Universe. But in the very early Universe radiation was the dominant form of gravitation and forms the basis of expansion models prior to t ~ 104 years, or about one millionth of its current age.

For cosmological purposes it is useful to describe ‘radiation’ as highly relativistic particles, for which the EOS parameter is w = 1/3 and ε = ε0a−4. In the very early Universe this was true of many elementary particles; in the current Universe it applies only to photons and to light neutrinos. Current photon sources are many and varied, producing measurable radiation energy densities at wavelengths from gamma to radio waves. Of these types of radiation two are the largest contributors to the overall radiation density: optical/IR radiation, mostly from stars and stellar systems, with εopt ≈ 10−15 J/m3; and microwaves with εmicro ≈ 6 × 10−14 W/m3. Almost all this microwave energy is in the form of a nearly uniform and isotropic radiation field called the Cosmological Microwave Background Radiation (CMB), which is thus the dominant form of radiation in the current Universe. The current CMB energy density is nearly two orders of magnitude greater than the combined densities of all other forms of radiation, but is still more than four orders of magnitude less than the energy density of (non-relativistic) matter.

The digital revolution has necessitated a re-examination of intellectual property issues by intellectual property holders, users and law makers. The nature of the digital age enables data to be easily copied, published and disseminated. Placing data, images, logos and text on websites, for example, is child’s play. This means that trade mark holders have a new frontier to battle. Misuse of their trade mark rights, deliberate or incidental, commercial or personal, arises in relation to cybersquatting and domain names, hyperlinking (particularly deep linking), framing in web pages and the use of meta-tags.

This chapter addresses issues relating to the impact of electronic commerce on the specific intellectual property rights of trade marks, patents and circuit layouts. It is intended to be only a brief overview of the law in these areas.

The nature of trade marks

A trade mark is ‘a sign used, or intended to be used, to distinguish goods or services dealt with or provided in the course of trade by a person from goods or services so dealt with or provided by any other person’. A trade mark is used in the course of trade to show a connection between a particular business and the goods or services it supplies. Trade marks indicate a standard of quality associated with a product or service and protect consumers from confusion and deception. Trade marks are protected under common law and under the Trade Marks Act 1995 (Cth).

A prime example of the uptake of technology and the resulting order from the disorder has arisen through the availability of music and video files. In the 1990s the compression of files and increasing speed of the internet permitted the downloading of music files such as individual songs. In the 21st century the compression and speed have increased so dramatically that entire music albums, television shows and movies (of any length) are downloaded with ease. Internet users relish the technology. In the words of the High Court of Australia:

The downloading of music, video and other files online is prolific, if not epidemic. The transfer of copyright material – material that would have cost several billion dollars in total to buy – is a source of considerable concern for the music industry, in particular. The fact that a substantial number of such files are subject to copyright, and that the right to copy is one of the many exclusive rights provided by the Copyright Act, is typically disregarded by internet users. Notwithstanding the popularity of micropayment through the iTunes store, the Google Play store and the Microsoft store, to name a few, peer-to-peer (P2P) transfers have facilitated the majority of the downloads. There have been numerous cases brought before the courts aimed at stopping or at least discouraging these downloads. Yet sites providing access, most of them indirectly, on a P2P basis continue to flourish. This is a question of supply attempting to meet demand notwithstanding legal and perhaps moral concerns.