Cosmology forum has an educational function, among others, and that will work better if we try to agree on terminology. I'm proposing some usages here---others may wish to offer different ones---a mentor may eventually write a sticky thread of suggested terminology. At least we can get our semantic differences out in the open, if there are any. So here goes. Everybody is familiar with the three cases in cosmology, Omega > 1, = 1, and < 1. The words closed, flat, and open refer to these three cases. A closed universe is simply one where Omega > 1. Therefore a closed universe may or may not continue to expand indefinitely. The three main cases (Omega > 1, = 1, and < 1) do not refer to the universe's fate. They refer to the average curvature of space. Omega is about spatial curvature, not spacetime curvature, and consequently also about spatial extent: finite spatial volume versus infinite spatial volume. That's because of how Omega is defined. It is the ratio of the real energy density, throughout space at this moment, compared to the theoretical density which would be required to make space perfectly flat (at the current rate of expansion)---the so-called critical density. I emphasize this is about spatial curvature, not spacetime. You might want to ask how the critical density depends on the current expansion rate. Get somebody to explain in another thread. Omega > 1 translates into there being more matter or energy, a higher average density of energy, than would be needed for flatness, and an average positive curvature----analogous to the surface of a sphere. It translates to the case where space is roughly the 3D analog of a familiar 2D sphere. It wouldn't be perfectly spherical because matter isn't distributed perfectly uniformly. It would have bumps, dimples, warts etc. The 3D volume of a 3-sphere of radius R is 2 pi2 R3. The most recent batch of WMAP satellite data gave a lower bound for R, the radius of curvature, equal to about 100 billion lightyears. In other words if space has a finite size then it is currently at least that big. You can compute the current volume volume in cubic lightyears, if you wish. Omega = 1 translates into there being exactly the right amount of matter or energy, the right average density of energy (converting everything to energy terms for convenience) so that space can be flat. Flatness in 3D means roughly the same thing as in 2D. The angles of triangles add up to 180 degrees---other stuff like that, the geometric ratios you expect from middleschool. In theory a flat space could be tricked into being a periodic structure but people have looked for that and found no sign of it. Typically the flat case (Omega = 1) is treated as infinite spatial volume----like standard Euclidean 3D space extending indefinitely in all directions. But with the usual warts and dimples you expect. Spatial expansion just refers to a regular pattern of increasing distances called the Hubble law. To describe it I need stationary observers. Observers stationary with respect to CMB, or (as used to be said) with respect to the Hubble flow, are idealized observers adrift in intergalactic space who don't detect any movement relative to the cosmic microwave background. They have no big doppler hotspot in their CMB sky. On earth we have a big CMB hotspot in one direction (constellation Leo) so we know the sun and planets are moving about 380 km/s in that direction by a simple doppler calculation. And we see a big coldspot in the opposite direction, for the same reason. Stationary observers are a convenient tool. They can agree on a common idea of now. And on distances at the present moment. The instantaneous distance between two stationary observers is well-defined---think radar distance broken into small enough increments that negligible time is needed to make the measurements. A chain of simultaneous radar ranging done quickly so that nothing changes significantly while the measurements are performed. Hubble law is about the growth rate at some moment in time, of distances between stationary observers. A moment in time like now, for example. The current rate is 1/140 of a percent increase in distance every million years. Expressed as a km/s rate of increase it's proportional to the distance, so it is natural to write as a percentage. Or you can say v(t) = H(t)D(t), or v = HD, showing current recession speed as proportional to current distance by the current factor of the Hubble parameter. The km/s rate of increase of a distance should not be confused with the rate of something traveling to a destination. No matter how rapid the increase is, even if it is several times the speed of light, this doesn't mean the observer is getting anywhere or has some individual momentum or kinetic energy, or can catch up to flying photons. Travel speed and recession speed are different. For practical purposes, the observer is sitting still and his recession speed depends only on how far away the other observer is, who determines the distance between them. I guess the moral underlying all of this is that geometry is dynamic, not static. Geometry (including distances and the angles of triangles and soforth) is changeable and how it changes depends in part on the distribution of matter. We have no right to expect distances between widely separated objects to remain the same. We may think we are entitled to have distances behave in a static rigid way because we live on this little planet made of rock. Rock is structured by crystal bonds that don't change. All kinds of physical bonds stabilize distances. But in space at large, between galaxies, there are no bonds, so geometry morphs according to the law of gravity. Since gravity = geometry, you could call our law of gravity "the law of morphing geometry" (i.e. gen rel is the law governing geometry and how it changes in response to matter) What other common parlance terms do we need to define? If you have some suggestions, please post them. Or just general comments. There is also the scale factor, a function of time written a(t). It is a nice simple function whose growth is governed by a concise equation due to Friedmann (around 1925). The factor a(t) plugs into the standard metric used in cosmology, which tells you how the distances between stationary objects change with time. And if you have two times t=then and t=now-----then when some light was emitted and now when it is received here on earth by some telescope----the redshift z is determined by the formula z+1 = a(now)/a(then). That is, z+1 is the ratio by which distances have expanded while the light was in transit. And z+1 is also the ratio by which the wavelenths of the light have been increased while it was in transit. And z, by definition, is one less than this ratio. So if the wavelength comes in to us longer by a factor of 1.3, then z is 0.3. Subtracting one is just a convention, somethng traditionally done for historical reasons. Have we got other basic terms we need to define? Comments?