Is de Sitter space flat?

A standard topic in an introductory General Relativity (GR) course is the study of maximally symmetric solutions. These are flat (Minkowski) spacetime, de Sitter spacetime (obtained when the cosmological constant is positive) and Anti-de Sitter spacetime (when the cosmological constant is negative).

What is negative curvature?

A surface has negative curvature at a point if the surface curves away from the tangent plane in two different directions. Any point on the inside of a torus has negative curvature because there are planar cuts that yield curves that bend in opposite directions with respect to the tangent plane at the point.

Is our universe a de Sitter space?

The early universe was radiation-dominated, because radiation has an exponent of −4, which is the biggest. Our universe is currently quite well approximated by de Sitter space.

Does the universe have negative curvature?

Any spatial section of the universe of a constant age (the proper time elapsed from the Big Bang) will have a negative curvature; this is merely a pseudo-Euclidean geometric fact analogous to one that concentric spheres in the flat Euclidean space are nevertheless curved.

What determines the curvature of space?

Gravity is the curvature of spacetime Gravity is the curvature of the universe, caused by massive bodies, which determines the path that objects travel. That curvature is dynamical, moving as those objects move. In Einstein’s view of the world, gravity is the curvature of spacetime caused by massive objects.

What is de Sitter spacetime?

In mathematical physics, n-dimensional de Sitter space (often abbreviated to dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian analogue of an n-sphere (with its canonical Riemannian metric).

Are AdS globally hyperbolic?

As a consequence of the timelike spatial (and null) infinity, the AdS space is not globally hyperbolic, that is there is no Cauchy hypersurface.

What does positive curvature mean?

This is what positive curvature means. If you have a triangle in positive curvature, the sum of the angles of a triangle is bigger than 180 degrees. Negative curvature, similarly, means the sum of the angles is less than 180 degrees. You might think about what this means on a Pringles potato chip!

Do spheres have positive curvature?

The flat surface at the left is said to have zero curvature, the spherical surface is said to have positive curvature, and the saddle-shaped surface is said to have negative curvature.

Which branch of astronomy that deals with the origin of the universe?

Cosmology
Cosmology is a branch of astronomy that involves the origin and evolution of the universe, from the Big Bang to today and on into the future. According to NASA, the definition of cosmology is “the scientific study of the large scale properties of the universe as a whole.”

Is de Sitter space closed?

The most symmetric vacuum solution to Einstein’s equation, of course, is the flat spacetime. This is precisely the de Sitter manifold with closed spatial sections. …

What is the curvature of spacetime?

According to Einstein’s theory of general relativity, massive objects warp the spacetime around them, and the effect a warp has on objects is what we call gravity. So, locally, spacetime is curved around every object with mass. Closed universe (top), open universe (middle), and flat universe (bottom).

Is space flat or curved?

Is space flat or curved? According to Einstein’s theory of general relativity, massive objects warp the spacetime around them, and the effect a warp has on objects is what we call gravity. So, locally, spacetime is curved around every object with mass.

Does the universe have a negative curvature?

If space has negative curvature, there is insufficient mass to cause the expansion of the universe to stop. In such a case, the universe has no bounds, and will expand forever.

What is the difference between spatial topology and spatial curvature?

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.