Cosmic inflation

Cosmic inflation is the idea, first proposed by Alan Guth in 1981, that the nascent universe passed through a phase of exponential expansion (the inflationary epoch) that was driven by a negative pressure vacuum energy density.

This expansion is similar to a de Sitter universe with a positive cosmological constant. As a direct consequence of this expansion, all of the observable universe originated in a small causally-connected region. Quantum fluctuations in this microscopic region, magnified to cosmic size, then became the seeds for the growth of structure in the universe (see galaxy formation and evolution). The particle responsible for inflation is generally called the inflaton.

The name of the theory was a semi-humorous reference to the economic inflation in the United States in the late 1970s.

Motivation

Inflation resolves several problems in the Big Bang cosmology that were pointed out in the 1970s. Among these are the observed flatness of the universe (the flatness problem), its extraordinary homogeneity on large (non-causally-connected) scales (the horizon problem), and its lack of any observed topological defects (the monopole problem), predicted by many Grand Unified Theories. Predictions of the standard model of inflation include geometrical flatness of the universe and near scale invariance of the primordial density fluctuations of the universe. These have been confirmed to great accuracy by precision measurements of the cosmic microwave background (such as those made by the WMAP satellite) and surveys of the distribution of galaxies observed by galaxy surveys (such as the Sloan Digital Sky Survey).

There are also consequences for high-energy particle physics near or at the GUT scale, as the simplest models of inflation have energies around the GUT scale, at 10¹⁵GeV. During the 1980s, there were many attempts to relate the field that generates the vacuum energy to specific fields that were predicted by Grand Unified Theories or to use observations of the universe to constrain those theories. These efforts were largely fruitless and the exact nature of the particle or field that generates the vacuum energy density for inflation (the "inflaton") remains a mystery: inflation is understood principally by its detailed predictions of the initial conditions for the hot early universe, and the particle physics is largely ad hoc modelling.

Inflation must be followed by a period of reheating to generate the hot radiation of the early universe. It is still largely a mystery what causes reheating, but one proposal is called parametric resonance, involving a resonant decay of the inflaton into other particles, as it oscillates during the termination of inflation.

Recent observation of the cosmic microwave background seem to favour inflation over competing models^*. One theoretical challenge for inflation arises from the need to fine tune the potentials for the fields which may give rise to inflation: while the inflaton must have a large vacuum energy it must have a low mass (and a large Compton wavelength). However high energy physics is thought to include many scalar fields (this is, for example, the situation in string theory) and a large number of possible solutions is also expected, especially in string theory (see String theory landscape).

Mechanisms

The development of inflationary models has proceeded over the last twenty-five years to accommodate theoretical difficulties and cosmological measurements. To this day, cosmologists and particle physicists continue to offer novel approaches to inflation but all the models have in common a period of exponential expansion as a solution to the Friedmann equations. Using basic assumptions about a universe in thermodynamic equilibrium almost invariably leads to an inflationary scheme. In fact, in the union of all possible cosmological scenarios for the early universe, those that lack epochs of inflation are well in the minority. What follows is a historical account of the development of the most popular inflationary models to date.

Old inflation

The original model of inflation,A. H. Guth, "The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems", Phys. Rev. D 23, 347 (1981). proposed by Alan Guth, had the universe in a false vacuum. The universe was in an exactly de Sitter phase. In this model, regions of non-inflating universe are created through the nucleation of bubbles of true vacuum, while the rest of the universe continues inflating. When two such bubbles collide, the vast energy of the bubble walls is converted into the particles seen at the early universe. This process is called reheating. Alan Guth has described the inflationary universe as the ultimate "free lunch": new universes, similar to our own, are continuously produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) both the first law of thermodynamics or energy conservation and the second law of thermodynamics or the arrow of time problem.

However, the original model of Guth fails because, in order to guarantee a sufficient amount of inflation to solve the standard problems, the bubble nucleation rate must be too low for bubble walls to collide and for the reheating process to actually work, because the space between bubbles - which is still in the inflating phase - expands so fast that the separation between bubbles grows faster than the bubbles themselves. The energy that is released in the decay of the false vacuum is deposited entirely in the kinetic energy of the bubble walls, and none is liberated by the collision needed for the hot big bang. This is called the "graceful exit problem" and Guth's original model is now called "old inflation."

Slow-roll inflation

Andrei LindeA. Linde, "A New Inflationary Universe Scenario: A Possible Solution Of The Horizon, Flatness, Homogeneity, Isotropy And Primordial Monopole Problems", Phys. Lett. B 108, 389 (1982). and, independently, Andreas Albrecht and Paul SteinhardtA. Albrecht and P. J. Steinhardt, "Cosmology For Grand Unified Theories With Radiatively Induced Symmetry Breaking," Phys. Rev. Lett. 48, 1220 (1982). proposed a "new inflation" or "slow-roll inflation" in which the inflaton is modelled by a scalar field slowly rolling down a nearly flat potential. In this model, the expansion of the universe is only approximately de Sitter, and the Hubble parameter is actually decreasing: the expansion is slowing. While the spectrum of fluctuations generated in the false vacuum de Sitter universe of old inflation is exactly scale-invariant, new inflation produces only a nearly scale invariant spectrum.J. M. Bardeen, P. J. Steinhardt and M. S. Turner, "Spontaneous Creation Of Almost Scale-Free Density Perturbations In An Inflationary Universe," Phys. Rev. D 28, 679 (1983). This means that information about the potential during inflation can be extracted, in principle, from the cosmic microwave background by measuring the spectral index. In "slow-roll inflation", inflation terminates when the inflaton potential reaches the end of its nearly-flat part, where its slope starts to increase (relative to the energy density) and the rolling speeds up. This is when reheating occurs in this scenario, as particles are created via ineractions with the inflaton, on the expense of the potential's energy density.

New inflation is generally eternal: that is, the process continues eternally. Although the scalar field is classically rolling down the potential, quantum fluctuations occasionally bring it back up the potential. These regions expand much faster than regions in which the inflaton has a lower potential energy. Thus, while inflation ends in some regions, the regions in which it continues are growing exponentially, and thus continue to dominate. This steady state, which was first described by Andrei Linde, in which inflation ends in some regions while quantum mechanical fluctuations keep it going in the majority of the universe, is called "eternal inflation". It is widely believed that eternal inflation, however, cannot be eternal in the past (although Andrei Linde disputes this) and so does not solve the problem of initial conditions for the universe. Another kind of inflation, called hybrid inflation, is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.

Brane cosmologies

See Brane cosmology for more information.

One popular idea that has been suggested in the context of string theory and quantum gravity is that the universe actually contains many more dimensions of space than the three we experience, but that the universe only inflated along the three normal dimensions of space. This theory, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa. It suggested that we have three large dimensions because of certain topological properties of colliding strings. However, considerable doubt has been cast on the practicability of these ideas.

The ekpyrotic, cyclic models and variable speed of light cosmology are considered competitors to inflation.

Observations

Observationally, it is hoped that improved measurements of the cosmic microwave background will tell us more about inflation. In particular, high precision measurements of the polarization of the background radiation will tell us if the energy scale of inflation predicted by the simplest models is correct, and measurements of the spectrum of primordial fluctuations will tell us if our naive models of inflation can produce the correct primordial fluctuations. A perfectly scale invariant spectrum is generally considered incompatible with the simplest models of inflation as is a running spectral index (a spectrum with curvature). These sorts of measurements are expected to be performed by the Planck satellite, Clover Project and other ground-based cosmic microwave background experiments. However, the first experimental confirmation of some predictions of cosmic inflation theories has been provided by data from the WMAP mission in March 2006. The WMAP polarization data seem to favor the simplest versions of inflation.

As of 2006, it is unclear what relationship if any the period of cosmic inflation has to do with observations of dark energy in the universe. Dark energy, particularly quintessence is broadly similar to inflation, but occurs at a much lower energy, 10^-12GeV, at least 27 orders of magnitude less than the scale of inflation.

References

External links

Was Cosmic Inflation The 'Bang' Of The Big Bang?, by Alan Guth, 1997
An Introduction to Cosmological Inflation by Andrew Liddle, 1999
update 2004 by Andrew Liddle
hep-ph/0309238 Laura Covi: Status of observational cosmology and inflation
hep-th/0311040 David H. Lyth: Which is the best inflation model?
The Growth of Inflation Symmetry, December 2004
Guth's logbook showing the original idea
WMAP Bolsters Case for Cosmic Inflation, March 2006
NASA March 2006 WMAP press release

Physical cosmology | Cosmic inflation

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