Shape of the universe

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Shape of the universe

 The shape of the universe:

The observable universe can be imagined as a sphere that stretches outwards from any observation point for 46.5 billion light-years, moving farther back in time and becoming more redshifted as one looks further away. We'll start with the three most fundamental sorts. The Universe can have one of three shapes:

-A flat Universe (Euclidean or zero curvature),

-A spherical or closed Universe (positive curvature), or

-A hyperbolic or open Universe (negative curvature).

The Wilkinson Microwave Anisotropy Probe (WMAP) of NASA measured background fluctuations to see if the universe is open or closed. Scientists stated in 2013 that the universe was flat with a 0.4 per cent margin of error.

The observable universe is finite in the sense that it has not existed indefinitely. It stretches 46 billion light years in all directions from us. While our universe is 13.8 billion years old, the observable universe extends further due to the expansion of the universe.

The density parameter, denoted by the symbol Omega (), is a quantity that general relativity uses to calculate the curvature of the universe. General relativity explains that mass and energy bend spacetime. The crucial energy density, or the mass-energy required for a universe to be flat, is equal to the average density of the cosmos divided by the density parameter. In other words,

  • If Ω = 1, the universe is flat.
  • If Ω > 1, there is positive curvature.
  • If Ω < 1 there is negative curvature.

One of the universe's unresolved issues is whether it is infinite or finite in size. For example, a finite universe has a finite volume that can theoretically be filled with a finite amount of material, whereas an infinite universe is unbounded and no numerical volume can potentially fill it. The mathematical concept of boundedness refers to the question of whether the cosmos is infinite or finite. In an infinite universe (unbounded metric space), points can be arbitrarily far apart: for any distance d, some points are at least d away. A finite universe is a bounded metric space with some distance d such that all points are within d of each other. The lowest such d is known as the universe's diameter.

In the case of a finite universe, the universe can have an edge or no edge. Many finite mathematical spaces, such as a disc, have a boundary or edge. Edged spaces are challenging to treat, both conceptually and technically. It is difficult to predict what might happen at the edge of such a cosmos. As a result, places with an edge are often omitted from consideration.

There are, however, numerous finite spaces with no edges, such as the 3-sphere and 3-torus. These spaces are referred to as compact without boundaries in mathematics. The phrase compact relates to something that is both finite ("bounded") and complete. The phrase "without boundary" refers to the absence of any borders in the space. Furthermore, to apply calculus, the world is often believed to be a differentiable manifold. A closed manifold is a mathematical object that has all of these properties: compact without boundaries and differentiable. Both the 3-sphere and the 3-torus are closed manifolds.

Examining light from the very early world, Buchert and his colleagues calculated that our universe may be doubly connected, which means that space is closed in on itself in all three dimensions, much like a three-dimensional doughnut. According to current scientific theories, nearly 85% of the cosmos, known as dark matter, is folded like an origami sheet.

During a cosmological period, the universe may be on the verge of collapsing (Phys.org)— Physicists have hypothesised a process for "cosmological collapse," which predicts that the universe will soon cease to expand and collapse in on itself, eradicating all matter as we know it.

Despite some significant uncertainty, all approaches indicate that the cosmos is open (i.e. the density parameter is less than one). However, we must keep in mind that we have not yet detected all of the stuff in the cosmos.

Cosmologists refer to this concept as the "closed universe." It's been around for a while, yet it contradicts current views about how the universe operates. As a result, it has been largely discarded in favour of a "flat universe," which extends without limit in all directions and does not loop around on itself. After 13.8 billion years of expansion, the comoving distance (radius) is presently around 46.6 billion light-years.

cosmological structure:

 The geometry and topology of the entire universe

—both the observable cosmos and beyond

—are covered by global structure.

While the local geometry does not totally dictate the global geometry, it does constrain the options, especially for geometry with constant curvature. It is common to assume that the universe is a geodesic manifold without any topological imperfections; loosening either of these assumptions dramatically complicates the analysis. A local geometry plus a topology constitutes a global geometry. As a result, a topology by itself cannot determine a global geometry. For instance, Euclidean 3-space and hyperbolic 3-space share the same topology but have different global geometries.

Investigations into the study of the universe's overall structure, as mentioned in the introduction, include

·       whether the size of the cosmos is unlimited or limited.

·       if the global universe's geometry is flat, favourably or negatively curved.

·       if the topology has a single, sphere-like connection or several connections, such as a torus.

The comoving coordinates, a particular set of which is conceivable and commonly acknowledged in modern physical cosmology, are the space-like slice of spacetime that cosmologists often deal with. The region of spacetime that can be observed is the backward light cone (all places within the cosmic light horizon, given time to reach an observer). Still, the associated phrase Hubble volume can be used to describe either the past light cone or comoving space up to the surface of the last scattering.

From the perspective of special relativity alone, it is ontologically naive to speak of "the shape of the universe (at a point in time)" because different points in space cannot be said to exist "at the same point in time" or of "the shape of the universe at a point in time" due to the relativity of simultaneity. However, by treating the time since the Big Bang (measured in the reference of the CMB) as a distinct universal time, the comoving coordinates (if well-defined) give a precise sense to those.

Curvature can be used to study the shape of the universe as seen below:

·       Universe with zero curvature

·       Universe with positive curvature

·       Universe with negative curvature

·       Curvature: open or closed

·       Milne model (Hyperbolic expanding)

 


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