Inflationary universe cosmology

(astronomy) A theory of the evolution of the early universe which asserts that at some early time the observable universe underwent a period of exponential expansion, during which the scale of the universe increased by at least 28 orders of magnitude.

A theory of the evolution of the early universe, motivated by considerations from elementary particle physics as well as certain paradoxes of standard big bang cosmology, which asserts that at some early time the observable universe underwent a period of exponential, or otherwise superluminal, expansion. During this inflationary epoch the scale of the universe increased by at least 28 orders of magnitude.

“Old” inflationary model

The suggestion of an inflationary period during the early universe, in connection with a specific model, was first made in 1980 by A. Guth. Guth reasoned that if grand unified symmetries are broken at some large energy scale, then a phase transition could occur in the early universe as the temperature cooled below the critical temperature where symmetry breaking occurs. According to the standard big bang model of expansion, the time at which this would occur would be about 10⁻³⁵ s after the initial expansion had begun. See also Grand unification theories; Phase transitions; Symmetry breaking; Symmetry laws (physics).

As Guth demonstrated, the effects of such a phase transition in the early universe could be profound. In order to calculate the dynamics of a phase transition it is necessary to follow the behavior of the relevant order parameter for the transition. This is done by determining the free energy of a system as a function of the order parameter, and following the changes in this energy as the temperature changes. The illustration shows a typical example of what might be expected for the case of symmetry breaking in grand unification theories. At some high temperature T the minimum of the relevant function is at zero value of the order parameter, the vacuum expectation value of a certain field. Thus the ground state of the system, which occurs when this energy is a minimum, will be the symmetric ground state. As the temperature is decreased, however, at a certain critical temperature T_c, a new minimum of the energy appears at a nonzero value of the order parameter. This is the symmetry-breaking ground state of the system. See also Free energy.

In the illustration it is seen that there is a barrier between the two minima. This means that classically the system cannot make a transition between the two states. However, it is a well-known property of quantum mechanics that the system can, with a certain very small probability, tunnel through the barrier and arrive in the new phase. Such a transition is called a first-order phase transition. Because the probability of such a tunneling process is small the system can remain for a long time in the symmetric phase before the transition occurs. This phenomenon is called supercooling. When the transition finally begins, “bubbles” of new phase locally appear throughout the original phase. As more and more bubbles form, and the original bubbles grow, eventually they combine and coalesce until all of the system is in the new phase. See also Quantum mechanics.

Free energy as a function of the order parameter for the case of a first-order transition.

The metastable symmetric phase has a higher energy than the new lower energy symmetry breaking phase. Until the transition occurs, this means that the symmetric phase has associated with it a large constant energy density, independent of temperature. When this constant energy density is placed on the right hand side of Einstein's equations, where the energy density of matter appears, it is found that the resultant Hubble parameter describing expansion is a constant. Mathematically this implies that the scale size of the universe increases exponentially during this supercooling phase. This rapid expansion is what is referred to as inflation. See also Hubble constant; Relativity.

Successes of inflation

Guth pointed out that a period of exponential expansion at some very early time could solve a number of outstanding paradoxes associated with standard big bang cosmology.

Present observations seem to imply that either the present era is a unique time in the big bang expansion, or else the initial conditions of expansion had to be fine-tuned to an incredible degree. Measurements of the observed expansion rate combined with measurements of the observed mass density of the universe yield a value for the density parameter Ω which rapidly approaches zero for an open universe, infinity for a closed universe, and is exactly equal to one for a flat universe. All measurements of Ω yield values between about 0.1 and 2. However, theory suggests that once the value of Ω deviates even slightly from one, it very quickly approaches its asymptotic value far away from one for open or closed universes. Thus, it is difficult to understand why, after 10¹⁰ years of expansion, the value of Ω is now so close to one.

Inflation naturally explains why Ω should exactly equal one in the observable universe today. During inflation Ω(t) is driven arbitrarily close to one within the inflated region. If there are some 28 orders of magnitude of exponential expansion, then Ω(t) need not have been finely tuned to be close to one.

An equally puzzling problem which inflationary cosmology circumvents has to do with the observed large-scale uniformity of the universe. In particular, the 3-K microwave radiation background is known to be uniform in temperature to about one part in 10,000. However, in the standard big bang model the sources of this radiation observed coming from opposite directions in the sky were separated by more than 90 times the horizon distance (the distance a light ray could have travelled since the big bang explosion) at the time of emission. Since these regions could not possibly have been in physical contact, it is difficult to see why the temperature at the time of emission was so uniform in all directions. See also Cosmic background radiation.

Inflation solves the horizon problem very simply. If the observed universe expanded by 28 orders of magnitude, then it originated from a region 10²⁸ times smaller than the comparable region in the standard big-bang model. This makes it quite possible that at early times the entire observed universe was contained in a single horizon volume.

Unfortunately, the original inflationary scenario was fundamentally flawed. The phase transition began by the formation of bubbles of one phase nucleating amidst the initial metastable phase of matter. While these bubbles grow at the speed of light once they form, the space in between the bubbles is expanding exponentially. Thus, it is extremely difficult for bubbles to eventually occupy all of space, as is required for the completion of the transition.

“New” inflationary cosmology

In 1981, it was suggested that if the energy function (potential) of the illustration were slightly changed then it might be possible to maintain the successful phenomenology of the old inflationary model while avoiding its problems. In particular a special form of the potential was considered which is extremely flat at the origin. Such functions have essentially no barrier separating the metastable from the stable phase at low temperature. When the universe cooled down below the critical temperature, the order parameter could continuously increase from zero instead of tunnelling discretely to a large nonzero value. As long as the potential is sufficiently flat near the origin, however, it can take a long time before the order parameter approaches its value at the true minimum of the potential (a so-called slow-rollover transition). During this time the region of interest can again be expanding exponentially. Thus, in some sense a single bubble can undergo inflation in this scenario.

New inflation, too, is not without its problems. In order to have such a slow-rollover transition, the parameters of particle physics models must be finely tuned to some degree. No clear candidate model for new inflation has emerged from particle physics.

Another potential problem for any inflationary scenario concerns initial conditions. As discussed above, if an inflationary phase precedes the standard big bang expansion, then it is possible to resolve problems of the standard big bang model related to the unphysical fine tunings that seem necessary at time zero in order for the big bang to evolve into its presently observed form. However, if the initial preinflationary conditions are unphysical, then inflation may not have really solved any fundamental problems.

In 1983, Linde proposed a version of inflation, which he called chaotic inflation, that may in principle address this issue. He argued that the early universe may have been arbitrarily inhomogeneous. In some regions, inflation may have successfully taken place, even without the spontaneous symmetry breaking associated with a grand unified theory, and in other regions it may not have. He then suggested that the regions in which inflation did take place are in fact most probable. In addition, he pointed out that life would form only in those regions that became sufficiently isotropic so that, if many different regions of the universe now exist, it is not surprising that humans live in one that has undergone inflation. The issue of initial conditions for inflation remains the subject of much research, but may require an understanding of quantum gravity for its eventual resolution. See also Chaos; Quantum gravitation.

Primordial fluctuations

It has been demonstrated that new inflationary cosmology naturally allows a derivation from first principles of the spectrum of primordial energy density fluctuations responsible for galaxy formation. The spectrum that emerges from inflationary models is a so-called scale-invariant spectrum of perturbations. The first observation of anisotropies in the microwave background was announced in 1992, based on the analysis of data from the differential microwave radiometer experiment aboard the Cosmic Background Explorer (COBE) satellite. A quadrupole anisotropy in the background was observed at a level of about 5 × 10⁻⁶, just in the range that might be expected for primordial fluctuations from inflation that might also result in the observed distribution of galaxies. Moreover, the correlation of temperature deviations observed across the sky on scales greater than about 10° is remarkably consistent with the scale-invariant spectrum predicted by inflationary models. While neither of these observations conclusively proves the existence of an inflationary phase in the early universe, the fact that they are clearly consistent with such a possibility, and at present with no other scenario, gives great confidence that inflationary models may provide the correct description of the universe in the era preceding the present observed isotropic expansion.

Open inflation and a cosmological constant

Since 1995 it has been increasingly clear, based on measurements of the total clustered mass in the universe in galaxies and clusters of galaxies, that there is not sufficient matter to result in a flat universe today. There are two possibilities. The first possibility is that the universe is not flat but open. While this would deal a severe blow to standard inflationary models, a number of groups have proposed inflationary models, called open inflation models, which are tuned so that there is sufficient inflation to solve the horizon problem but not enough to result in a flat universe. The second possibility is that matter accounts for only part of the total energy density of the universe, with the remainder being associated with some new form of energy, possibly energy stored in the ground state of empty space, called a cosmological constant. This energy is in fact identical to the energy which is stored during the inflationary phase itself. If this is true, then we live in an inflationary universe today. Preliminary measurements of the expansion rate of the universe as a function of cosmic time, by observing the recession velocities of certain types of exploding stars, called type 1a supernovae in very distant galaxies, in fact argue that this is precisely the case. Other current data favors the second possibility, including ground-based measurements of the cosmic microwave background anisotropies on small scales, the distribution of which suggests a flat universe rather than an open one. See also Big bang theory; Cosmology; Supernova; Universe.