question: If light sets the cosmic speed limit, how did the universe expand trillions of kilometers in every direction in only fractions of a second during the big bang?
comment: Simply put, massive amounts of matter didn't move faster than light in every direction. The matter stayed put in the space it was in, but space itself expanded and there is no speed limit on the expansion of space (as far as we know), only on the things that move through space. Think of it like a lemon poppy seed loaf sprinkled through with little poppy seeds. When it goes in the oven, it's a small lump of dough. Let the poppy seeds be matter sprinkled through the universe. The dough is space. During baking, the dough expands but the seeds stay the same. As the dough rises (space expands), the seeds (matter) get farther apart, but each seed is still surrounded by the exact same dough as before, it's just that there's much more dough. In the case of the universe, the dough is able to rise at a ridiculous rate of speed.
passages: The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away, and, in fact, the light emitted towards the Earth was actually moving "away" from the Earth when it was first emitted, in the sense that the metric distance to the Earth increased with cosmological time for the first few billion years of its travel time, and also indicating that the expansion of space between the Earth and the quasar at the early time was faster than the speed of light. None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.
   According to the equivalence principle of general relativity, the rules of special relativity are "locally" valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed "c"; in our diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance "ct" in a time "t", as the red worldline illustrates. While it always moves locally at "c", its time in transit (about 13 billion years) is not related to the distance traveled in any simple way since the universe expands as the light beam traverses space and time. In fact the distance traveled is inherently ambiguous because of the changing scale of the universe. Nevertheless, we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension that we've declared to be the spatial dimension). The former distance is about 4 billion light years, much smaller than "ct" because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar. The latter distance (shown by the orange line) is about 28 billion light years, much larger than "ct". If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.
   The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if proper distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally. (See Comoving and proper distances for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10 seconds after the Big Bang to around 10 seconds), when the universe may have rapidly expanded by a factor of around 10 to 10.
   While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "separation" is different from that used in an inertial frame. This can be seen when observing distant galaxies more than the Hubble radius away from us (approximately 4.5 gigaparsecs or 14.7 billion light-years); these galaxies have a recession speed that is faster than the speed of light. Light that is emitted today from galaxies beyond the cosmological event horizon, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past. Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.Tamara M. Davis and Charles H. Lineweaver, "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe". astro-ph/0310808 Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within education and communication of scientific concepts.
   Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann-Lemaître-Robertson-Walker metric and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above), because gravitational attraction binds matter together strongly enough that metric expansion cannot be observed at this time, on a smaller scale. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the universe given the matter density and average expansion rate.
   A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the FLRW geometry, the same geometry which describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed "c" with respect to the local motion of the exploding matter, a phenomenon analogous to frame dragging.
   Section::::Understanding the expansion of the universe.:Metric expansion and speed of light.
  
  At the end of the early universe's inflationary period, all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principle and Einstein's general theory of relativity and this is when the precise and regular form of the universe's expansion had its origin (that is, matter in the universe is separating because it was separating in the past due to the inflaton field).
   The Big Bang is not an explosion of matter moving outward to fill an empty universe. Instead, space itself expands with time everywhere and increases the physical distance between two comoving points. In other words, the Big Bang is not an explosion "in space", but rather an expansion "of space". Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our universe only on large scales—local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.
  
  Section::::Features of the model.:Horizons.
   Section::::Metric expansion of space.
  
  This puzzle has a bearing on the question of whether light from distant galaxies can ever reach us given the metric expansion of space. The universe is expanding, which leads to increasing distances to other galaxies, and galaxies that are far enough away from us will have an apparent relative motion greater than the speed of light. It might seem that light leaving such a distant galaxy could never reach us.
   Over time, the Universe and its contents have evolved; for example, the relative population of quasars and galaxies has changed and space itself has expanded. Due to this expansion, scientists on Earth can observe the light from a galaxy 30 billion light-years away even though that light has traveled for only 13 billion years; the very space between them has expanded. This expansion is consistent with the observation that the light from distant galaxies has been redshifted; the photons emitted have been stretched to longer wavelengths and lower frequency during their journey. Analyses of Type Ia supernovae indicate that the spatial expansion is accelerating.
   Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.
   BULLET::::- the Copernican Principle which demands that no place in the universe is preferred (that is, the universe has no "starting point").
  
  Scientists have tested carefully whether these assumptions are valid and borne out by observation. Observational cosmologists have discovered evidence — very strong in some cases — that supports these assumptions, and as a result, metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly, scientists have tested the properties of the universe and observation provides compelling confirmation. Sources of this confidence and confirmation include:
   The figures quoted above are distances "now" (in cosmological time), not distances "at the time the light was emitted". For example, the cosmic microwave background radiation that we see right now was emitted at the time of photon decoupling, estimated to have occurred about years after the Big Bang, which occurred around 13.8 billion years ago. This radiation was emitted by matter that has, in the intervening time, mostly condensed into galaxies, and those galaxies are now calculated to be about 46 billion light-years from us. To estimate the distance to that matter at the time the light was emitted, we may first note that according to the Friedmann–Lemaître–Robertson–Walker metric, which is used to model the expanding universe, if at the present time we receive light with a redshift of "z", then the scale factor at the time the light was originally emitted is given by
   One of the biggest puzzles in contemporary cosmology is why the expansion of the Universe is accelerating. About seventy percent of the Universe today consists of so-called dark energy that counteracts gravity's attractive force and causes this acceleration. Very little is known about what dark energy is. CHIME is in the process of making precise measurements of the acceleration of the Universe to improve the knowledge of how dark energy behaves. The experiment is designed to observe the period in the Universe's history during which the standard ΛCDM model predicts that dark energy began to dominate the energy density of the Universe and when decelerated expansion transitioned to acceleration.
   The metric expansion of space is of a kind completely different from the expansions and explosions seen in daily life. It also seems to be a property of the universe as a whole rather than a phenomenon that applies just to one part of the universe or can be observed from "outside" it.
   While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame. The definition of distance used here is the summation or integration of local comoving distances, all done at constant local proper time. For example, galaxies that are more than the Hubble radius, approximately 4.5 gigaparsecs or 14.7 billion light-years, away from us have a recession speed that is faster than the speed of light. Visibility of these objects depends on the exact expansion history of the universe. Light that is emitted today from galaxies beyond the cosmological event horizon, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past.
   Technically, the metric expansion of space is a feature of many solutions to the Einstein field equations of general relativity, and distance is measured using the Lorentz interval. This explains observations which indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us (see Hubble's law).
  
  Section::::Theoretical basis and first evidence.:Cosmological constant and the Friedmann equations.
   However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Comoving and proper distances#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.
   A final possibility is that dark energy is an illusion caused by some bias in measurements. For example, if we are located in an emptier-than-average region of space, the observed cosmic expansion rate could be mistaken for a variation in time, or acceleration. A different approach uses a cosmological extension of the equivalence principle to show how space might appear to be expanding more rapidly in the voids surrounding our local cluster. While weak, such effects considered cumulatively over billions of years could become significant, creating the illusion of cosmic acceleration, and making it appear as if we live in a Hubble bubble. Yet other possibilities are that the accelerated expansion of the universe is an illusion caused by the relative motion of us to the rest of the universe, or that the supernovae sample size used wasn't large enough.
   The accelerated expansion was discovered during 1998, by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration. The idea was that as type 1a supernovae have almost the same intrinsic brightness (a standard candle), and since objects that are further away appear dimmer, we can use the observed brightness of these supernovae to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred. The unexpected result was that objects in the universe are moving away from one another at an accelerated rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.
   Another revolutionary observation in 1998 seemed to complicate the situation further: two distant supernovae were found in separate studies to be fainter than expected in a steadily expanding universe; that is, they were not merely moving away from the earth but accelerating. Thus, the universe's expansion was calculated to have been accelerating since approximately 5 billion years ago. Given the gravitation braking effect that all the matter of the universe should have had on this expansion, a variation of Einstein's cosmological constant was reintroduced to represent an energy inherent in space, balancing the equations for a flat, accelerating universe. It also gave Einstein's cosmological constant new meaning, for by reintroducing it into the equation to represent dark energy, a flat universe expanding ever faster can be reproduced. 
   Similarly, the stretch method fits the particular supernovae magnitude light curves to a template light curve. This template, as opposed to being several light curves at different wavelengths (MLCS) is just a single light curve that has been stretched (or compressed) in time. By using this "Stretch Factor", the peak magnitude can be determined.
   American astronomer Edwin Hubble observed that the distances to faraway galaxies were strongly correlated with their redshifts. This was interpreted to mean that all distant galaxies and clusters are receding away from our vantage point with an apparent velocity proportional to their distance: that is, the farther they are, the faster they move away from us, regardless of direction. Assuming the Copernican principle (that the Earth is not the center of the universe), the only remaining interpretation is that all observable regions of the universe are receding from all others. Since we know that the distance between galaxies increases today, it must mean that in the past galaxies were closer together. The continuous expansion of the universe implies that the universe was denser and hotter in the past.
   In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion "through" space, but rather to the expansion of space itself. For example, galaxies far away from Earth appear to be moving away from the Earth with a speed proportional to their distances. Beyond a boundary called the Hubble sphere, the rate at which their distance from Earth increases becomes greater than the speed of light.
  
  Section::::Propagation of light.
   That space is undergoing metric expansion is shown by direct observational evidence of the Cosmological principle and the Copernican principle, which together with Hubble's law have no other explanation. Astronomical redshifts are extremely isotropic and homogeneous, supporting the Cosmological principle that the universe looks the same in all directions, along with much other evidence. If the redshifts were the result of an explosion from a center distant from us, they would not be so similar in different directions.
  
presuppositions: Expansion of the universe should move no faster than the speed of light. If light is the cosmic speed limit, then the universe couldn't have expanded faster than the speed of light.
corrections: Space expansion has no speed limit. The matter of the universe stayed put in the space it was in, but the space itself expanded, and there is no speed limit on the expansion of space.
raw_presuppositions: Expansion of the universe should move no faster than the speed of light. If light is the cosmic speed limit, then the universe couldn't have expanded faster than the speed of light.
raw_corrections: Space expansion has no speed limit. The matter of the universe stayed put in the space it was in, but the space itself expanded, and there is no speed limit on the expansion of space.