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What does Flat Universe mean?

I hear the term "Flat Universe" a lot, and I never quite figured out what it meant. Does this mean that the universe is similar to a flat plane?

Answer 1

Owen Atkinson

It means that Euclidean geometry is followed:

If three points in the universe are marked, the three angles add up to #180^circ#
Parallel lines remain at the same distance apart forever.
Pythagorus theorem applies to the universe.
Also, it means that each 'slice' of the universe is flat (imagine a cube split into smaller cubes, each slit being #x, y and z# planes in space).

The other terms are open and closed, closed being represented the most as a sphere and open universes as a continuous hyperbola. Images show common shapes and geometry of a plane of space for each of the three universe types:

#Omega_0="density parameter"="average density of the universe"/"critical energy density"#
A flat universe means that the universe will either expand forever at a continuously decreasing rate but never reaching 0, or expand slowly then speed up (but not accelerate). The value of #Omega_0# can actually be measured.

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Answer 2

Hailey Alvarez

In cosmology, a "flat universe" refers to a spatially flat or Euclidean universe geometry. This means that the geometry of the universe is consistent with Euclidean geometry on large scales, where parallel lines never meet and the internal angles of a triangle add up to 180 degrees. In a flat universe, the curvature of space is zero.

The concept of a flat universe is a key aspect of the prevailing cosmological model known as the Lambda-Cold Dark Matter (ΛCDM) model. According to this model, the total energy density of the universe, including both matter and energy, is precisely balanced to yield a flat geometry. Observational evidence from cosmic microwave background radiation, large-scale structure observations, and supernova measurements strongly supports the idea of a flat universe.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.