Jim said:I am simply trying to understand why dS space has a signature (4+1) ?
Good old familiar Minkowski space is of course, (3+1), crystal clear.
What is the role of the extra spatial dimension in dS ? Why should the manifold be 5-D ?
DeSitter dimensions refer to the number of spatial dimensions in a universe or space-time that follows the DeSitter model, which describes an expanding universe with a positive cosmological constant.
The DeSitter model is typically described using four dimensions, three spatial dimensions and one time dimension. However, it can also be generalized to higher dimensions, such as 5, 6, or even 10 dimensions, depending on the specific theory or model being used.
DeSitter dimensions play a crucial role in modern cosmology and theoretical physics. They are used to describe the geometry and expansion of our universe, as well as in models of string theory and other theories attempting to unify gravity with other fundamental forces.
Unlike the three dimensions of space and one dimension of time that we experience in our everyday lives, DeSitter dimensions are theoretical and describe the structure and behavior of the universe at a larger scale. They also have different properties and characteristics, such as being curved or expanding at an accelerated rate.
Currently, there is no direct evidence for the existence of higher dimensions, including DeSitter dimensions. However, some theories and models suggest that they may leave an imprint on observable phenomena, such as the cosmic microwave background radiation or the behavior of particles at high energies.