what is "curved space"?
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This is a bit of a "layman's" answer but here goes:\nSpace, not just the world we all live in, but all the space in the universe is "affected" by MASS (massive objects) in a way that most people do not realize.  Most  people think that gravity has something to do with a "magnetic" force of some kind that causes objects to be attracted to other objects.  The weird truth of it is that "gravity" is a side-effect of the "geometry" of space-time.\n\nWhat does that mean?  What Einstein figured out is that SPACE is actually "warped" or "curved" by mass (or massive objects) like the Sun or planets, or black holes - that sort of thing.  Now while you cannot really SEE this, \nyou can see the "effect" of it.   When an asteroid passes closely by a massive object, it may be affected by the objects gravity and drawn toward it.  But this has nothing to do with magnetism - it is actually the effect of the asteroid following the "curvature of space" (since the massive object - like the Sun - has warped space).  \n\nTo think of a common, simple example: imagine a BOWLING BALL sitting on a large rubber sheet (or your mattress).... you will notice that the massive ball makes an big depression in the sheet, or "dip" in your mattress.  Now imagine rolling a marble across this sheet, or your mattress.  If it is close enough to the bowling ball, it will be "captured by the gravity" (really warped space) and spiral inward toward the bowling ball.  So "Curved Space" is the "warping of space" caused by "massive objects", and what we see as gravity is really just objects responding to the natural curvature of space.  \n\nMany people then ask why an apple falls straight to the ground on earth.  The general idea is that space is "more steeply curved" when close to massive objects (as we are standing on earth) and since we are already ALWAYS in motion (you knew that - with rotation and all), when you "let go" of a ball, it follows the path of least resistance in curved space, which is right DOWN to the ground (now that is a "steep curve").\n-Gregory J. Mallon, La Plata, MD
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A warp cushion, the space of where a worm hole used to be leaves a different time around it and inside it.\nThe bubble like on Lost in Space is possible. Time holds space not Space holds Time otherwise we wouldn't be here now.
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"What are curvature perturbations?"\n"What is curvature perturbation?"\n\nYou don't define your terms very well.\n\nCurvature - do you mean space time curvature tensor?\nPerturbation is a disturbance, but is sometimes meant as the event or as the cause of the event.\n\nSo is curvature perturbing something or is something perturbing curvature?
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Take a sheet of paper and imagine it is space. Mark two dots on two different parts of the sheet. If u were a traveller going from one dot to another, you'd normally travel in a straight line. BUT, if u bend the sheet such that the dots touch each other, u can actually travel from one dot to another in no time at all. This new path in three dimensional space will be a wormhole while the curved sheet represents curved space.
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I know of one application in an abstruse area of physics: The sinh( ) of a scalar field occurs in gravitational theories where, for whatever reason, one emplys a metric disformally related to the 'physical' metric tensor.\n\nAlso, the shape of a freely hanging level chain is cosh( ) of displacement along the line joining ends
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The reason that gravity can be described as a bending of space space is that it acts on everything equally. Electric charges and magnets don't--they attract some items, repel others, and have no effect on yet other things. I don't think that there is any way space could be bent that would be consistent with the behavior of these forces.
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Nothing, in a logical sense of the word.\n\n\nThis is similar to the question, "OK, the universe is expanding, what is it expanding into?" Both questions are based on analogies which are designed to help us think about complex situations. They tend to be ones where we think of the universe as being something like the surface of an inflating beach ball which is being blown up. Our image of the "beach ball universe" includes space to expand into.\n\nThis is a limitation of the analogy, not the actual universe. The details of General Relativity describe the "shape" of the universe and how gravity effects different parts. GR works on the scale of galaxies and galaxy clusters. For smaller scales, dropping a pencil off your desk for instance, Newton's Gravity is fine. (GR turns into Newton's Law of Gravity at small scales.)\n\nOur brains are simply not designed to imagine curved space with all three spatial dimensions. To get around this the analogies use two-dimensional universes. But the analogies can't be taken too far. In this case, the only way to really understand deeply the structure of the universe is by understanding the mathematics. There is no exact mental picture.\n\nSo, the question has no answer, and in fact, logically speaking, makes no sense. (That isn't to say it is not a sensible question, it is a sensible question.)\n\nThe usual example of such a question is: "What is north of the north pole." Once one gets to the pole there is no more North. Everything is south. So asking what is north of the north pole is (logically) a nonsensical question.
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Speaking from the vantage point of one with some training in physics...  You are entirely correct.  Astronomers even take advantage of this effect by looking at extremely distant objects to see what the very early universe was like.\nVery intelligent question!  Good observation.\n\nAdditional: Some of the other answers are raising a valid point.  (Good job, Silverskorpious and Johhny!)  Space and time are not rigid and flat, but curved and pliable.  However, the phonomenon still works since any amount of time passing bewteen the emission and perception of light still places the event firmly in the past by the time it's observed.
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There isn't one.\n\nThis is similar to the question, "OK, the universe is expanding, what is it expanding into?"\n\nBoth questions are based on analogies which are designed to help us think about complex situations. They tend to be ones where we think of the universe as being something like the surface of an inflating beach ball which is being blown up. Our image of the "beach ball universe" includes space to expand into.\n\nThis is a limitation of the analogy, not the actual universe. The details of General Relativity describe the "shape" of the universe and how gravity effects different parts. GR works on the scale of galaxies and galaxy clusters. For smaller scales, dropping a pencil off your desk for instance, Newton's Gravity is fine. (GR turns into Newton's Law of Gravity at small scales.)\n\nOur brains are simply not designed to imagine curved space with all three spatial dimensions. To get around this the analogies use two-dimensional universes. But the analogies can't be taken too far. In this case, the only way to really understand deeply the structure of the universe is by understanding the mathematics. There is no exact mental picture.\n\nSo, the question has no answer, and in fact, logically speaking, makes no sense. (That isn't to say it is not a sensible question, it is a sensible question.)\n\nThe usual example of such a question is: "What is north of the north pole." Once one gets to the pole there is no more North. Everything is south. So asking what is north of the north pole is (logically) a nonsensical question.
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space probably does not end.  space-time may be something like the two-dimensional surface of a sphere.  it has no center and no edge.  nothing inside or outside the sphere exists for the two-dimensional surface, and nothing exists outside space-time in this model.
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The 3d space of the universe has been theorized as the 3 dimensional surface of a 4 dimensional sphere.  An analogy is our planet, where we live on the 2-dimensional surface of a 3-dimensional sphere.  When you travel on the surface of the earth, there is no border or edge to fall off or cross into another dimension.  In the same way, the 3-d space of the universe has no border or edge.  If you travel far enough in a "straight" line you will end up right where you started.\n\nThis means if the universe is expanding then there still is no receding border.
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Is our universe in another universe?\n  \nBefore we can address that question, we must first define universe.  \n\nThe word universe denotes all space and everything (matter, energy) contained within it.  The prefix uni means one.  The root verse means word, carnate message, meaningful substance, matter.  Questions regarding our universe persist today.  Does it have a beginning and end, or does it go on forever and ever?  Is it linear or curved?  If it has limits of length or curvature, then what lies beyond the Universe?  If something lies beyond the Universe, then can’t we accurately call that the Universe?\n\nSome lay people and some scientists conceive of the universe as infinite space.  Others define the universe as finite, or limited (perhaps curved), space.  Still others incorporate the elements of matter and/or energy into their definition of the universe, as opposed to the space beyond matter and energy.\n\nGiven these concepts of our universe, some scientists conclude that the “totality of space could be infinite. Shrink an infinite space by an arbitrary amount, and it is still infinite. (Scientific American March 2005).”  \n\nAs to the notion that we live in an ever expanding universe, moving away from every other universe on the fabric of space-time, some scientists are careful to point out that “\nAndromeda, our nearest large galactic neighbor, is actually moving toward us, not away. Such exceptions arise because Hubble's law describes only the average behavior of galaxies (Scientific American March 2005).”\n\nIn accordance with your supposition that our universe is in another universe, “it has been hypothesized by some scientists that the universe may be part of a system of many other universes, known as the multiverse (http://en.wikipedia.org/wiki/Universe).” Modern astrophysicists talk about multiple "pocket" universes that branch off from one another.  Stephen Hawking points out that parallel pocket universes can have no effect on a real observer inside a single pocket, so, according to Hawking, they are theoretical baggage that should be eliminated from cosmology, the study of the origins of the universe.\n\nSome string theories define the universe as a three-dimensional space in an invisible space having more dimensions. This is, in essence, a universe within a universe.  Our zone, a “braneworld” could periodically bounce into another parallel braneworld.  This may create what would appear as a Big Bang from one perspective or a Big Bounce of alternating expanding and contracting universe from another perspective.  Such a cataclysmic event is thought to occur 300 billion years from now, resulting in the rearranging and creation of a new universe.\n\nIs our universe inside another universe?  Well, apparently the Men in Black had it right.  Our universe seems to be inside of something else, another universe, called the multiverse.\n\nSteve\n:-D
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No. It is space itself that is expanding. The problem people have in thinking about this stuff is that it is tricky to think about curved space-time. But that is the level at which things must be thought to really understand what is going on.\n\nSo an analogy might be in order. Imagine you are at the north pole (the Big Bang). Time will be represented by the latitude down from the north pole and space will be represented by latitude lines. In this (very simplified!) model, space is one dimensional (a circle of latitude) and as time goes on (as we move down in latitude), space expands until we reach the equator and then contracts again until there is a Big Crunch at the south pole.\n\nSo now ask the question 'where is space expanding into?'. The answer is either meaningless or at best, answered by saying 'into the future'.\n\nThis analogy is actually very good except for a couple of points: The actual universe may not have a maximum spacial size (the equator) but may continue to expand forever; also, the size of space (the latitude lines) may actually be infinite in extent. The model has a finite universe with both a beginning and an end. The real universe may be infinite and have no Big Crunch.\n\nOne very good aspect of the model is that it clarifies a problem a lot of people have. There is no 'before the Big Bang' just as there is no 'north of the north pole'.
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General Theory of Relativity:\n\nA mass in space creates an indention much like a bowling ball on a trampoline.  Its this indention that is the cause of gravity.  If a marble were to roll across the trampoline into that indention, it would take a curve path and eventually fall into the bowling ball.  This is what happens when you fall to the Earth: your body is in a sense sliding on the curvature of space-time.
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lets start with the question: how do you measure curvature?\n\nthe surface of an extremely large sphere is less curved compared to the surface of a small ball. how much a surface is curved is defined by how quickly the surface shape changes.\n\nnow the radius of the two spheres above give an accurate measure of how curved the surfaces are. larger the radius, small the "curviness". the radius is called the "radius of curvature"\n\nnow for a perfect plane, the radius of curvature is infinity.\n\nThe earth is approximately an extremely large sphere. pour a looot of water on it and the water spreads out evenly over the earths surface, so the surface of water is an even larger sphere, so large that when you observe a very small area. the very small here is relative, relative to the entire surface area of the earth. So if you accurately meaure the surface properties, over a few hundred kilometers, the curvature might be barely perceptible, and becomes significant once you meaure over a quarter of the earths surface.\n\nwould be nice if it stopped getting more complex. but then there is the effect of gravity pull of the moon, the sun and some planets. all of these pull the surface of water towards them, so the water is no longer evenly spread over the surface of earth, but is ovoid. even this feature cannot be detected over small regions. the effect of gravity of other heavenly bodies on the earthly water bodies is called tides.\nhttp://en.wikipedia.org/wiki/Tide\n\nNow if you were talking about the surface of water inside a container, that is a different story altogether. the surface exhibits a curvature of the exact opposite nature. the level is slightly higher at the edges. this effect is more noticeable if the container is narrow. this is caused by two effects simultaneoulsy, surface tension and capillarity. \nhttp://en.wikipedia.org/wiki/Surface_tension\nhttp://en.wikipedia.org/wiki/Capillarity
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Curved. It is the last of the land that the vision can see lining with the sky. Since earth is spherical, the horizon has to be curved.
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Euclidean geometry is the study of geometry as defined by the axioms of Euclid. You can find those axioms here: http://en.wikipedia.org/wiki/Euclidean_Geometry .\nIt was noted by Klein that Euclidean geometry was actually just the study of one particular group of symmetries. His Erlangen program of 1872 revolutionized geometry by encouraging the stuidy of non-Euclidean geometries by simply studying the geometries produced by any arbitrary group.\nGauss and Riemann realized that while Euclidean geometry did not deal with a fundamental unit of length, the study of geometry on curved surfaces did introduce fundamental units of length (this was later applied in general relativity). The geometry on these surfaces, such as the sphere where parallel lines can meet at either 2 points or none, definitely did not satisfy Euclid's axioms, so they were also non-Euclidean. The Riemann sphere's relation to the complex plane made this geometry very useful. The projective plane is a non-Euclidean geometry that has found many applications as well. \nBasically, non-Euclidean geometry pops up whenever a surface (or an arbitrary smooth manifold) has non-zero Gaussian curvature. Things can get pretty wild in more than 2 dimensions. You can read about more non-Euclidean geometries oand their applications on this page: http://en.wikipedia.org/wiki/Non-euclidean_geometries