Monopole Problem

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).

Inflation theory was developed in the late 1970s and early 1980s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Starobinsky, Guth, and Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation". It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.

The detailed particle physics mechanism responsible for inflation is unknown. A number of inflation model predictions have been confirmed by observation; for example temperature anisotropies observed by the COBE satellite in 1992 exhibit nearly scale-invariant spectra as predicted by the inflationary paradigm and WMAP results also show strong evidence for inflation. However, some scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton.

In 2002, three of the original architects of the theory were recognized for their major contributions; physicists Alan Guth of M.I.T., Andrei Linde of Stanford, and Paul Steinhardt of Princeton shared the Dirac Prize "for development of the concept of inflation in cosmology". In 2012, Guth and Linde were awarded the Breakthrough Prize in Fundamental Physics for their invention and development of inflationary cosmology.

Overview

Cosmic inflation is the hypothesis that the very early universe expanded exponentially fast. Distances between points doubled every 10^-37 seconds; the expansion lasted at least 10^-35 seconds, but its full duration is not certain. A distance of 1 cm expanded to a distance more than 20 times the distance from the Earth to the Moon. All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10^-29m which grew to a sphere with a radius around 0.9m.

The hypothesis was originally proposed to solve issues in cosmology. The originally proposal by Alan Guth in 1979 was motivated by predictions by particle physics theories that the universe should have high densities of magnetic monopoles, contrary to observations. An exponential expansion would dilute the monopoles to the extent they could no longer be detected. It was quickly realized that such exponential expansion would resolve two other problems, the flatness problem and horizon problem. The rapid expansion means a universe with any amount of curved spacetime will emerge from inflation very "flat", that is with much smaller curvature consistent with observations. The rapid expansion also means that parts of the universe in thermal equilibrium before inflation can end up after inflation very far apart, so far apart that no particles could ever have made the journey in the lifetime of the universe. This matches observations that points separated by more than a "horizon" distance have almost identical cosmic microwave background temperatures.

The underlying physics of inflation is not well understood.
According to the Friedmann equations that describe the dynamics of an expanding universe, a fluid with sufficiently negative pressure exerts gravitational repulsion in the cosmological context. A field in a positive-energy false vacuum state could represent such a fluid, and the resulting repulsion would set the universe into exponential expansion. Thus one simple theory is a new field, active only during inflation. The energy of this field produces the initial energy of the Big Bang.

Theory

An expanding universe generally has a cosmological horizon, which, by analogy with the more familiar horizon caused by the curvature of Earth's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in an accelerating universe never reaches the observer, because the space in between the observer and the object is expanding too rapidly.

The observable universe is one ''causal patch'' of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon, which is believed to be 46 billion light years in all directions from Earth. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view. Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: Its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They could not have learned it by getting signals, because they were not previously in communication with our past light cone.

Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communication. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous.

As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space.

The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter, dark matter and residual vacuum energy in the Universe have to add up to the critical density, and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.

Space expands

In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out Schwarzschild black hole—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially).

In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following metric:

:$ds^2=- (1- \Lambda r^2) \, c^2dt^2 + \, dr^2 + r^2 \, d\Omega^2.$

This exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum energy density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure ''p'' equal in magnitude to its energy density ''ρ''; the equation of state is ''p=−ρ''.

Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.

Few inhomogeneities remain

Because the accelerating expansion of space stretches out any initial variations in density or temperature to very large length scales, an essential feature of inflation is that it smooths out inhomogeneities and anisotropies, and reduces the curvature of space. This pushes the Universe into a very simple state in which it is completely dominated by the inflaton field and the only significant inhomogeneities are tiny quantum fluctuations. Inflation also dilutes exotic heavy particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the Universe was only hot enough to form such particles ''before'' a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the observable universe. Together, these effects are called the inflationary "no-hair theorem" by analogy with the no hair theorem for black holes.

The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for not testable disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, energy densities generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) declines as the inverse of the volume: when linear dimensions double, the energy density declines by a factor of eight; the radiation energy density declines even more rapidly as the Universe expands since the wavelength of each photon is stretched (redshifted), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see the solution of the energy density continuity equation for an ultra-relativistic fluid). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.

Reheating

Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from  K down to  K.

) This relatively low temperature is maintained during the inflationary phase. When inflation ends, the temperature returns to the pre-inflationary temperature; this is called ''reheating'' or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe. Because the nature of the inflaton field is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance.

Motivations

Inflation tries to resolve several problems in Big Bang cosmology that were discovered in the 1970s. Inflation was first proposed by Alan Guth in 1979 while investigating the problem of why no magnetic monopoles are seen today; he found that a positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space. It was quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does ''today'', the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.

Magnetic-monopole problem

Stable magnetic monopoles are a problem for Grand Unified Theories, which propose that at high temperatures (such as in the early universe), the electromagnetic force, strong, and weak nuclear forces are not actually fundamental forces but arise due to spontaneous symmetry breaking from a single gauge theory. These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field.

Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature, and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe. Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe.

A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: Monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude.

While solving the monopole problem motivated the original hypothesis, not every cosmologists was impressed. Martin Rees

HOME


Content is Copyleft
Website design, code, and AI is Copyrighted (c) 2014-2017 by Stephen Payne


Consider donating to Wikimedia



As an Amazon Associate I earn from qualifying purchases