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).

Do we live in de Sitter space?

But that doesn’t necessarily mean the toy universe shows how space-time and gravity emerge in our universe. However, in reality, we inhabit a positively curved “de Sitter (dS) space,” which resembles the surface of a sphere that’s expanding without bounds.

Is de Sitter space curved?

De Sitter spacetime is a very simple curved background that enjoys the same degree of symmetry as the Minkowski spacetime, both having ten Killing vectors. More importantly, it is also a good model of our universe in the far past and the far future, as suggested by our current observations and the theory of inflation.

Is Minkowski maximally symmetric?

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).

Is de Sitter asymptotically flat?

Only spacetimes which model an isolated object are asymptotically flat. An even simpler generalization, the de Sitter-Schwarzschild metric solution, which models a spherically symmetric massive object immersed in a de Sitter universe, is an example of an asymptotically simple spacetime which is not asymptotically flat.

Is de Sitter space finite?

We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states.

What is maximally symmetric spaces?

Maximally symmetric space is a space that is both homogeneous and isotropic. Such a space possesses the largest possible number of Killing vectors which in an n-dimensional manifold equals n(n+1)/2.

How do you know if spacetime is flat?

A spacetime is locally flat if and only if no geodesical deviation exists for congruences of all kinds of geodesics.

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.

Is the universe homogeneous?

Although the universe is inhomogeneous at smaller scales, it is statistically homogeneous on scales larger than 250 million light years. The cosmic microwave background is isotropic, that is to say that its intensity is about the same whichever direction we look at.

Is sphere a symmetric space?

Basic examples of Riemannian symmetric spaces are Euclidean space, spheres, projective spaces, and hyperbolic spaces, each with their standard Riemannian metrics.