What is Flat universe: Definition and 43 Discussions

The shape of the universe, in physical cosmology, is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as of a continuous object.
The spatial curvature is related to general relativity, which describes how spacetime is curved and bent by mass and energy. The spatial topology cannot be determined from its curvature, due to the fact that there exist (mathematically) locally indistinguishable spaces with different topologies.Cosmologists distinguish between the observable universe and the entire universe, the former being a ball-shaped portion of the latter that can, in principle, be accessible by astronomical observations. Assuming the cosmological principle, the observable universe is similar from all contemporary vantage points, which allows cosmologists to discuss properties of the entire universe with only information from studying their observable universe.
Several potential topological or geometric attributes of the universe interest may be discussed. Some of these are:
Boundedness (whether the universe is finite or infinite)
Flat (zero curvature), hyperbolic (negative curvature), or spherical (positive curvature)
Connectivity: how the universe is put together, i.e., simply connected space or multiply connected space.There are certain logical connections among these properties. For example, a universe with positive curvature is necessarily finite. Although it is usually assumed in the literature that a flat or negatively curved universe is infinite, this need not be the case if the topology is not the trivial one: for example, a three-torus is flat but finite.The exact shape is still a matter of debate in physical cosmology, but experimental data from various independent sources (WMAP, BOOMERanG, and Planck for example) confirm that the universe is flat with only a 0.4% margin of error. On the other hand, any non-zero curvature is possible for a sufficiently large curved universe (analogously to how a small portion of a sphere can look flat). Theorists have been trying to construct a formal mathematical model of the shape of the universe. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the four-dimensional spacetime of the universe. The model most theorists currently use is the Friedmann–Lemaître–Robertson–Walker (FLRW) model. Arguments have been put forward that the observational data best fit with the conclusion that the shape of the global universe is infinite and flat, but the data are also consistent with other possible shapes, such as the so-called Poincaré dodecahedral space and the Sokolov–Starobinskii space (quotient of the upper half-space model of hyperbolic space by a 2-dimensional lattice).

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  1. X

    I Cosmic Flatness Deduced from CMB

    The Wilkinson Microwave Anisotropy Probe (WMAP) measured temperature differences across the sky in the cosmic microwave background (CMB). See --->(Wikipedia: https://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe#Main_result) From these observations researchers concluded that the...
  2. M

    B Flat Universe Definition

    When we say the universe is "flat," do we mean: 1) If you could hypothetically "zoom" out to the edge of the universe it would appear roughly as a flat like a sheet of paper with local fluctuations / bumps to indicate the presence of matter. 2) If we draw 2 parallel lines from 1 location they...
  3. nomadreid

    I What use is the AdS/CFT correspondence in a flat universe?

    All the accounts which I have read (and which are accessible to my limited knowledge of General Relativity and its mathematics) on the holographic principle says vaguely that the AdS/CFT correspondence is very enlightening, but with the caveat that, well, we don't happen to live in an AdS space...
  4. Arman777

    Proving an Equation for a Single Component Flat Universe

    I am trying to prove that for a single component flat universe $$\frac{dz}{dt_0} = H_0(1 + z) - H_0(1 + z)^{\frac{3 + 3w}{2}}$$ For a single component flat universe, ##q = \frac{2}{3 + 3w}## ##a(t) = (t/t_0)^q## ##t_0 = qH_0^{-1}## ##1 + z = (t_0/t_e)^q## Now here is my approach...
  5. A

    I Expansion of flat universe

    From friedmann equation And For a flat universe with k=0 and ρ=ρc ,da/dt becomes undefined and d2a/dt2 becomes 0 But for the present time we know that our universe is flat and expanding with a acceleration (q -ve) , Therefore is it here something I am missing??
  6. M

    I Saddle and flat universe edges?

    Hi, I have become very interested in cosmology recently and I had a question about the possible shapes of the Universe. I understand the critical density plays a role in the shape. This is what I know (or think I know). At the critical density of energy and matter, the universe is flat. If it...
  7. Cerenkov

    B Help with understanding a Friedmann flat universe

    Hello. I've been doing some reading about Friedmann's three types of GR solution that yield closed, open and flat universes. I think I can grasp the closed solution best. As far as I understand it a closed universe is finite in both time and space. It begins, grows and then collapses in upon...
  8. grauitate

    I Can a gravitational wave (GW) propagate in a flat universe?

    As the universe expands and is per definition gravitationally decoupled on long distances and the overall metric therefore is "flat" and apparently no gravitational background exists, the question in some discussion arose: Can GWs propagate in in a gravitational empty space at all? If not, and...
  9. Willfrid Somogyi

    I Flat vs Open Universe: CMBR & Type Ia Supernovae

    So CMBR points to a flat universe, and this seems to be the generally accepted model. But in a flat universe is expansion not supposed to slow exponentially, stopping after an infinite time? How does this fit with the observation that distant type Ia supernovae show the universe's expansion to...
  10. H

    I Does the Universe's Expansion lead to Critical Mass < 1?

    We understand that for the Universe to be flat, the critical mass of everything that has mass must total an omega of 1.0. At first, with our lack of knowledge regarding dark energy, we thought that the universe that we detected (ordinary matter and dark matter) did not even add up to a third of...
  11. Z

    Flat Universe as Torus: Legit Research & Solutions?

    A lot of cranks on the net make a lot of the torus - of course magnetic fields are toroidal - but not space time right? Or could it be - a torus is flat (zero gaussian curvature) which is how we observe the universe to be as far as we have measured it's curvature on large scales - and it would...
  12. H

    What does it mean by a flat universe?

    My understanding: When we draw a triangle on a flat piece of paper and measure the angles using a protractor, the sum of the angles is ##180^\circ##. So we conclude that the universe is locally flat. Suppose we draw a very big triangle that spans across galaxies (say, using lasers and mirrors)...
  13. wabbit

    Why is the Universe (nearly) flat?

    My understanding is that the degree of flatness observed for the spatial universe is quite extraordinary, to the extent of begging for an explanation. If this is correct, then my question is, what are the (most) plausible mechanisms being considered as an explanation for either an exact, or...
  14. Kiyal

    Can someone explain what it is meant by a 'Flat Universe'?

    I have been reading and looking at videos regarding cosmic inflation and it said that the universe is flat. I am no expert and have no mathematical background - I love reading about space and learning new things about it. It just really irritates me when things go right over my head and this...
  15. Islam Hassan

    Big Rip Compatible with Flat Universe?

    Is there a fundamental incompatibilty between a flat universe and the possibility of a Big Rip-type scenario of the evolution of the universe? Does a Big Rip necessarily imply a hyperbolic universe? What relationship is there -if any- between the shape of the universe and the equation of...
  16. V

    Flat universe and big bang theory

    Hello everybody! This is my first post! I was wondering about the fact that we have measure our universe to be flat very accurately. This means that it is also infinite and if it is infinite now it was infinite from the beginning! This means that at bb the time collapses but not the space...
  17. N

    How do inflation, and the zero energy flat universe tie into one another?

    New to cosmology and somewhat confused. I get all the ideas indvidually, that inflation is the exponential growth in the beginning of the universe, than that gravity and matter cancel each other out to make the zero energy universe, and that a flat universe is the only one that is zero energy...
  18. S

    Flat Universe, dark energy and accelerating expansion

    The CMB data suggests that the Universe is flat with in 0.4%. CMB data also shows that the expansion of the Universe is accelerating (from the sum of angles of triangle formed by distant hot spots- Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess). The pushing out dark energy is about 74% of...
  19. T

    Omega being less than one in a flat Universe?

    Hi everyone! I'm not very good at math as I'm in high school, and so probably did something wrong in this, but I did some calculations and am now wondering if a flat Universe requires Ω0 ≠ 1? I started with the Friedmann equation, If you divide by 3 and take the inverse of both sides, you...
  20. T

    What is a flat universe?

    What is a "flat" universe? Hi I read about the different shapes that are postulated for the shape of the universe. But what is meant by a "flat" universe? Is it the shape of a sheet, or blanket? If it is, why would the universe expand in suck a manner? It doesn't seem to make sense that it...
  21. C

    Discovering the Universe's Flatness: Insights from an Amateur Astronomer

    "Flat Universe"question. Hello, everyone! I'll start by saying that astronomy or physics are not my majors here; I'm a freshman Med School student, however I've recently started amateur astronomy as a hobby. Naturally I had to increase my knowledge on this subject so I started visiting...
  22. T

    Exploring Hartle-Hawking & Hawking-Turok Models for a Flat Universe

    Hi there! I'm new here and am currently looking into the Hartle-Hawking and Hawking-Turok Quantum creation models. What I've read about the Hartle-Hawking model is that it predicted a Closed Universe. But isn't that the opposite of what we have learned? The WMAP sattelite has confirmed the...
  23. A

    What does a flat universe mean?

    Sorry quick question from the ignorant (of maths or physics) but what does it mean to say that the universe is flat? I assume this does not mean it only has two dimensions! I do understand that it means that it has neither negative nor positive curvature, but what exactly does it mean in...
  24. S

    Understanding a "Flat Universe"

    Now I don't quite understand what a flat universe means. Clearly we are not talking about dimensions right? Obviously universe has more than 2 dimensions. So what does flat stand for ? Don't start with Euclidian Geometry please.
  25. L

    Big bang contradicts flat universe?

    big bang contradicts flat universe?? Hi, the data says our universe is flat, but we are also told it starts from big bang into a 3 dimensional world. How can our universe is flat from all direction while we live now in 3 D universe from a big bang? it has to be a curve if it is from big...
  26. S

    Flat universe and wormholes

    Its said that a wormhole could allow effective FTl travel by creating short cuts in the fabric of space tme. but if the universe is flat , how would this be a short cut? Doesnt the universe need to be curved for that?
  27. C

    What is the Fate of a Flat Universe?

    Homework Statement In a non-accelearting Universe, if the density of the Universe is equal to the critical density, then the Universe is A. open. B. closed. C. flat. D. empty.Homework Equations The Attempt at a Solution I believe the correct answer is flat, but I just wanted to see if...
  28. G

    Confused about implications of flat universe

    I recently saw a YouTube video of a 2009 lecture by Lawrence Krauss. He says that we now know unambiguously that the universe (and I just mean the universe that we can see, back to the big bang, not the multiverse or the foam or any of that) is flat. But it seems to me that a flat universe with...
  29. A

    Flat universe? Projection?

    Sorry 'bout posting so many topics but there are too many things that are unclear to me. CMBR measurements suggest the universe is pretty much FLAT, but I don't see it as flat, and forget our planet, all those vast spaces in every spatial dimension - all that is flat? It obviously has depth...
  30. S

    Does flat Universe have a center?

    If geometry of spacetime is flat in intergalactic medium (empty space), why then there is no point of asking where is the center of Universe?
  31. Ranku

    History and geometry of flat universe

    1. The present universe is observed to be flat. Was it always flat, before it started its accelerated expansion? 2. Is the Riemann tensor zero for this flat universe? Is its geometry that of special relativity? I'd appreciate if Marcus or Ich or any other science advisor weighed in on...
  32. T

    The first CMB peak - Flat Universe

    The size of bouncing lumps of charged particles, DM and photons in the primordial universe is supposed to be around 220,000 lyr (= sound horizon since the acoustic speed is approx 0.6c). If we then calculate the angle A subtended at Earth by a lump of this size W, some 13.8 Glyr away D (back at...
  33. B

    Small Flat Universe? How is it Possible?

    So, I now understand based on things that I have read, and things that people on this forum have told me, that the universe if flat, must be infinite. My question is, when we look into the farthest reaches of space, we see a small, finite baby universe. How is this possible? The universe can...
  34. B

    Light beam in a flat universe

    I know this is a commonly adressed topic, but it is one in which things are hazy to me. If the universe is finite (which we don't know), and flat (which we are becoming ever more increasingly certain about), then how could a light beam fired from a point in the universe not ever reach its...
  35. J

    Gravitational Expansion & Flat Universe

    I would appreciate help in objectively disproving the following "alternative physics" proposition: "The large-scale geometry of the universe is compelled to be eternally flat because gravity causes the universe to expand at exactly the escape velocity of its mass/energy contents." This...
  36. Holocene

    Exploring the Shape of a Flat Universe

    I just want to make sure my understanding is correct. In a "flat" universe, the total density of the universe matches the "critical density". As a result, the universe will expand forever, and never "fall back" into itself. The shape of a flat universe, as the name suggests, is flat like a...
  37. PhanthomJay

    Is the Universe Really Flat Despite the Existence of Gravity?

    It seems to me that current thinking leans toward an expanding and accelerating universe that is neither positively nor negatively curved, but rather, essentially, 'Flat'. How does this thinking not contradict with the fact that gravity, which surely exists, is the curvature of spacetime in...
  38. K

    Evidence for a flat universe vs. circular logic

    Interpretation: The Cosmic Background Radiation is evidence of a flat universe. Problem: How does a teacher show that all the knowledge necessary for this interpretation does not require the assumption of a flat universe?
  39. Loren Booda

    Ultimate configuration of a flat universe

    Do the matter and radiation of a flat universe, as time approaches infinity, conform to a spherical shell?
  40. P

    Flat Universe possess an edge?

    I have read from Universe by Freedman, Kaufmann that our universe is largly flat so it would mean there are edges in our universe. Our universe would be like a flat piece of paper that is continually expanding. A more realistic picture might be a diagram of Einstien's fabric of space time which...
  41. I

    Flat Universe Theory: Questions & Answers

    I realize this may be a really obvious question, but wikipedia and google haven't help settle my curiousity. If the universe is in fact a flat universe, as I believe has been proven with experimentation, this, if I am not mistaken, means the universe will continue to expand to a limit without...
  42. U

    What does it mean for the universe to be "flat"?

    what does it mean for the universe to be "flat"? What is the difference if the universe was flat or curved at all?
  43. J

    Flat Universe: Exploring Why Expansion is Accelerating

    As far as I am aware scientists agree that the universe is flat, open or closed. However, if galaxies get further away from each other the gravitational attraction between them would decrease as the universe expands. Why is the universe speeding up not a real possibility?
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