The Physics of Energy, page 88
Note that despite the large gulf between the length scales involved in quantum gravity and direct experiment, measurements of some cosmological features may give indirect evidence for aspects of quantum gravity. In particular, upcoming measurements of polarization in the cosmic microwave background (§21.2.1) could suggest the existence of gravitational waves that have their origin in quantum fluctuations in the very early universe. Such indirect evidence, however, does not show any promise of elucidating any detailed aspects of a quantum theory of gravity.
The most successful approach to quantum gravity at this time is string theory. String theory has not yet been completely formulated from first principles, and a complete background-independent description of the theory may require the development of new mathematics. Nonetheless, string theory provides a collection of compatible descriptions of quantum gravity in specific limits that appear to tie together into a single unified framework. Furthermore, in more constrained situations with additional space-time dimensions and symmetries (particularly supersymmetry, a hypothetical symmetry relating bosons and fermions), any gravity theory that satisfies known quantum consistency conditions has a description through string theory at high energies. It is not yet known, however, whether and/or how string theory can describe the specific physics observed in our four-dimensional universe including the Standard Model of particle physics and a small positive cosmological constant, or if there are other consistent theories of quantum gravity that may describe our universe.
Energy, Gravity, and Cosmology Defining energy in the context of general relativity and a space-time with cosmological structure and quantum dynamics presents significant challenges. When classical gravity is coupled to classical matter and radiation that inhabits a finite volume, with fixed boundary conditions for the metric at infinity approaching that of a flat space-time, the approach mentioned above of using the curvature of the system at large distances from the source can give a consistent way to define energy for theories with gravity. In a universe where the scale of space-time is inflating according to eq. (21.35), however, describing energy becomes more difficult. The basic problem is that, unlike in flat space, the background space-time metric (21.33) is not invariant under time translation. Since the cosmological constant contributes an energy density Λ, the total amount of dark energy in a given region of space increases as . Thus, even without worrying about issues of quantum gravity, there is no obvious way to define a conserved energy.4
If the Standard Model of particle physics, or any other quantum field theory, is described as a quantum theory in a fixed space-time background with a positive cosmological constant Λ, the Hamiltonian of the theory is time-dependent and energy is not conserved. In the spirit of the discussion of closed systems, one should include the contribution to energy from gravity, but the absence of a complete quantum theory of gravity makes it difficult to precisely formulate the concept of energy for quantum theories when gravity is included. In particular, at present we do not have an adequate theoretical framework with which to define energy as a meaningful conserved quantity from the cosmological point of view in the very early universe.
In most practical situations, quantum gravitational effects are irrelevant, and space-time can be described with great accuracy by classical general relativity, with matter and radiation treated as quantum systems evolving in a fixed, classical space-time background. Thus this theoretical difficulty is for most practical purposes irrelevant. In our current inflating universe, although dark energy represents some 68% of the total energy in the universe, most of this energy is distributed in the vast empty space between galaxies. The total amount of dark energy in the volume of a sphere with radius equal to Earth’s orbital radius, for example, corresponds to a mass of a small fraction of a kilogram. Thus, for any considerations involving terrestrial energy systems, the lack of a precise definition of energy on cosmological scales or the absence of a mathematically consistent theory of quantum gravity is irrelevant. To provide a satisfactory history of the extremely early universe, however, these theoretical problems would have to be addressed.
21.2A Brief History of Energy in the Universe
Over the centuries since the development of the telescope, humankind has gradually looked deeper into the cosmos and determined the present structure and the history of the visible universe. Over the past 50 years, astrophysicists have been able to piece together a reasonably coherent picture of the history of the universe back to times shortly after the big bang. Modern cosmologists have taken this history back even earlier, perhaps to the era before the big bang, although these ideas remain quite speculative. In this section we follow the evolution of the universe from the perspective of its energy content, beginning with an inventory of the energy distribution in the visible universe as currently understood.
21.2.1 Energy Inventory Today
The precision study of cosmology dates from the 1964 discovery by Americans Arno Penzias and Robert Wilson that the universe is filled with an almost uniform distribution of microwave radiation that has been traveling through space since shortly after the big bang. This cosmic microwave background radiation (CMB) is now understood to be a remnant of the thermal radiation that accompanied the big bang. The study of the CMB continues with ever increasing precision. The Wilkinson Microwave Anisotropy Probe, (WMAP) launched in 2001, provided precise measurements of the large-scale structure of the universe. The Planck satellite launched in 2009 refined the WMAP measurements. These measurements, coupled with astrophysical observations of distant galaxies and stars, have led to a consistent picture of the present distribution of mass-energy in the universe.
The measurements by the Planck satellite indicate that roughly 69% of the energy density of the universe is in the form of dark energy. Of the remaining 31% of the mass-energy in the universe, the greatest part – roughly 26% of the total – is composed of another invisible ingredient: dark matter. Unlike dark energy, which is uniformly distributed throughout space, dark matter is an invisible form of matter that is clumped in and around large aggregates of visible matter such as galaxies and galactic clusters. The existence of dark matter was first suggested in the 1930s to explain the pattern of galactic motions within clusters, and evidence for the presence of dark matter in galaxies was later given by the observation that the rotation rates of stars around the centers of galaxies are inconsistent with the amount of mass associated with visible stars. Since then, a host of further evidence for dark matter has accumulated from various astrophysical measurements, including measurement of gravitational lensing effects, in which the path of light from distant objects is bent by the distribution of mass-energy (see Figure 21.4). Just as the trajectories of objects like the Moon, satellites, and meteors are determined by the curvature in space-time due to Earth’s mass, the paths of photons passing by regions with extensive dark matter are affected by the curvature of space-time and can be measured by sensitive instruments.
Figure 21.3 Mass-energy distribution in the universe at present
Figure 21.4 A galaxy cluster with both visible and dark matter can act as a gravitational lens, distorting the path of light rays from a distant galaxy and creating multiple images as seen from Earth. Image: NASA/ESA.
Energy Inventory of the Current Universe
At the present time the energy density of the universe is dominated by dark energy that contributes some 68% of the energy in the universe, uniformly distributed at a density of roughly 10–9 J/m3. An unknown form of matter known as dark matter gives another 27% of the energy in the universe. Standard baryonic matter composed of familiar atoms makes up less than 5% of the energy density in the observed universe.
Dark matter is believed to be similar in nature to visible matter, except that it is composed of as yet unknown particles. Dark matter appears to interact minimally with the visible forms of matter such as electrons, neutrons, and protons except through gravity, and it does not emit or absorb electromagnetic radiation (hence the name “dark matter”). Some speculations concerning the nature of dark matter invoke a weakly interacting massive particle (WIMP), one source of which might be the symmetry known as supersymmetry mentioned in §21.1.5. Other ideas include an elusive, lighter particle known as the axion, which is predicted in some extensions of the Standard Model. Experiments are currently underway to directly or indirectly detect dark matter particles and test these various hypotheses.
The remainder of the mass-energy in the universe, only about 4.9%, is composed of matter in the familiar form – atoms composed of quarks (e.g. forming protons and neutrons) and leptons (e.g. electrons) that interact by electromagnetic, strong, and weak forces. This component of the mass-energy of the universe is often referred to as baryonic matter. Much of the baryonic matter in the universe today is hydrogen and helium that has been present since the very early universe. In addition, there are substantial amounts of oxygen, carbon, neon, and other light elements up to and including iron, which were formed in stellar fusion processes that we discuss in more detail in the next chapter. There are also small quantities of elements heavier than iron and relatively minute quantities of very heavy elements such as uranium that were produced in stellar death processes such as supernovae.
Only a relatively small fraction, roughly 1/6, of the baryonic matter in the universe is clumped into stars within the more than 100 billion galaxies in the observable universe. Most of the rest is in the form of hot (105–107 K) intergalactic gas within the huge clusters of galaxies that are the largest known structures in the universe. A small fraction of the baryonic matter remains to be accounted for.
Many galaxies (including our own) are believed to contain extremely massive black holes at their cores – regions of space-time into which so much matter has fallen together that even light cannot escape. The total contribution to the energy budget of these massive black holes, along with stellar-mass black holes that are believed to populate typical galaxies, is estimated to be quite small compared to the energy contribution of baryonic matter. A large population of small black holes that may have been produced in the early universe has also been hypothesized, however, as an alternative possibility for dark matter.
21.2.2 Before the Big Bang
The generally accepted history of our universe started with a big bang, when a dense, hot gas starting in an extremely compressed state began to expand outward. As it expanded, the material in the universe cooled, and gave rise to the current configuration of galaxies and other astrophysical objects in the universe. There are a number of reasons to believe, however, that the big bang was not the first instant at which the development of our universe proceeded according to understandable physical laws. Evidence from WMAP and the Planck satellite shows a correlation between the microwave background radiation spectra coming from different directions that suggests that a period of cosmological inflation preceded the big bang. In this section we summarize briefly the motivation for and implications of inflation, though we emphasize that this idea is still somewhat speculative. An even more speculative, but highly provocative proposal that dark energy may be associated with a structure and history for our universe much richer than that visible since the big bang is described in Box 21.2.
Box 21.2 Eternal Inflation in the Multiverse
One of the greatest puzzles in modern physics is why the dark energy density – the cosmological constant –in our universe is so small. We cannot directly compute this number, due to our ignorance of physics at very short distances and high energy scales, but we know no a priori reason why this number should be as small asits measured value of ~ in the natural units for quantum gravity (see Footnote 7). For a typical physical theory, as we understand it, the dark energy arises as a sum of terms, each of which independently is more than 100 orders of magnitude larger than the measured value, so the smallness of this quantity implies an apparently miraculous near-cancellation that is not understood in terms of any known physical principle or mechanism.
Until the turn of the last century, the cosmological constant was either ignored or believed to be constrained by some unknown dynamics to be zero. Years before the cosmological constant was found experimentally to be nonzero, the American physicist Steven Weinberg made an intriguing and profound observation: if the cosmological constant wasmuch bigger than (in Planck units), the expansion of the universe would have happened so quickly that the galaxies and other structures seen in our universe could not have formed. Weinberg went on to speculate that the smallness of the cosmological constant might be a consequence of the anthropic principle, which holds that “…the world is the way it is, at least in part, because otherwise there would be no one to ask why it is theway it is” [128]. To employ anthropic reasoning in a sensible scientific context, there must exist a large ensemble of universes – a multiverse – or an enormous universe containing different vast patches, in each of which the cosmological constant takes a different value. Only in those patches or universes where the cosmological constant is within the limits proposed by Weinberg do galaxies – and observers like us – evolve.
When the American physicist Saul Perlmutter and collaborators determined that the cosmological constant is small, but nonzero, and when no more conventional explanation for its value was forthcoming, cosmologists began to examine Weinberg’s anthropic explanation more closely. In the context of cosmological inflation in a multiverse, a region of space-time with a positive cosmological constant will expand exponentially. Within such a region, quantum tunneling can lead to the formation of a patch of another solution with lower energy. If this region also has a positive cosmological constant it also will expand exponentially, and so on. Each of these patches is causally disconnected from the others – a separate universe within the multiverse. (The figure shows an artist’s attempt to represent the multiverse. Image: ©Eric Prevost.) Some years ago, theorists working in string theory (§21.1.5) recognized that this theory admits many solutions that can give rise to different kinds of physics in widely separated regions of space-time. These solutions are roughly analogous to a permanent magnet that, once heated, can cool with magnetic polarization in a variety of different directions. The number of possible solutions to string theory is so huge that if the value of the cosmological constant is distributed smoothly over the range from zero to one in Planck units, there would be very many in which it takes a value similar to what we observe. Thus inflationary cosmology, which allows for formation of new patches of the universe, and string theory, which can endow each patch with its own value for the cosmological constant, together provide a self-consistent context for an anthropic explanation for the value of the cosmological constant observed in our universe.
On the face of it, this hypothesis seems fantastic, and it remains highly controversial. Resolving the problem of tuning a single number to be very small by invoking an inconceivably vast number of unobservable independent regions of the universe (essentially “parallel universes”) seems like an extreme measure. Some scientists reject anthropic reasoning out of hand. Others worry whether it has any predictive value. Nevertheless, cosmological inflation is a relatively well-established fact and string theory is the best candidate for a theory of quantum gravity. Together these ideas lead to the picture of eternal inflation in the multiverse – a world vast beyond comprehension, containing local patches with more different kinds of physics than there are atoms in our own observable universe.
The correlations that are seen in the distribution of microwave background radiation observed arriving from all directions suggest that the traditional big bang scenario is incomplete. The sources of this radiation are sufficiently distant from one another that they have never been in causal contact since the big bang. Nevertheless, the temperature that characterizes the CMB (see §22.2.2) is uniform over the sky to about one part in 100 000, implying that the sources of the radiation had already achieved thermal equilibrium when the radiation was emitted.
Figure 21.5 A cosmic microwave background radiation map of the whole sky from the Planck satellite. The colors correspond to temperature variations that are only about one part in 100 000 about the average value of 2.726 K. Image: ESA/Planck.
The currently favored and simplest explanation for the correlations is that these regions were once in causal contact, and that the universe underwent a period of exponential expansion known as cosmological inflation immediately preceding the big bang. The idea of cosmological inflation was first formulated by the American physicist Alan Guth in 1981. In cosmological inflation models, the universe had a large cosmological constant just before the big bang and expanded by a factor of roughly or more through eq. (21.35). This expansion is sufficient to explain why the temperature of the CMB is virtually the same in all directions. Cosmological inflation also resolves a number of other puzzles about the early universe, such as the absence of relics – exotic objects such as monopoles and cosmic strings, which are suggested in many formulations of physics beyond the Standard Model. Though these objects would have been produced in the early universe, cosmological inflation would have diluted their densities exponentially, explaining their apparent absence at the present time. Cosmological inflation also offers an explanation of structure formation in the universe, providing a mechanism by which quantum fluctuations from short distance scales expanded rapidly and became frozen into small density fluctuations that led to the development of structure in the early universe.
