In mathematical physics, Minkowski space or Minkowski spacetime is a combination of Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded..
What is cosmology directly related to?
Cosmology draws on advances from many scientific disciplines, including astrophysics, plasma physics, nuclear physics, particle physics, relativity, and quantum mechanics. The origins of today's cosmology began with the observation in the early 1500s by Nicolaus Copernicus that the Earth revolves around the Sun..
What is the basis of Minkowski space?
An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors. If one wishes to work with non-orthonormal bases it is possible to have other combinations of vectors..
What is the concept of Minkowski space?
Minkowski space or spacetime is used in mathematical physics and special relativity. It combines 3-dimensional Euclidean Space and time into a 4-dimensional manifold, where the interval of spacetime that exists between any two events is not dependent on the inertial frame of reference..
General Relativity forms the basis for the disciplines of cosmology (the structure and origin of the Universe on the largest scales) and relativistic astrophysics (the study of galaxies, quasars, neutron stars, etc.), and has led to a number of dramatic predictions concerning the physical world: Black holes.
Minkowski space is not endowed with a Euclidean geometry, and not with any of the generalized Riemannian geometries with intrinsic curvature, those exposed by the model spaces in hyperbolic geometry (negative curvature) and the geometry modeled by the sphere (positive curvature).
The geometry of Minkowski spacetime is pseudo-Euclidean, thanks to the time component term being negative in the expression for the four dimensional interval. This fact renders spacetime geometry unintuitive and extremely difficult to visualize.
Of particular interest thereby is the formulation of cosmology in Minkowski space. Rather than an expansion of space, spatial curvature, and small-scale inhomogeneities and anisotropies, this frame exhibits a variation of mass, length and time scales across spacetime.
Is a problem in Minkowski space?
If the time it took on Earth to develop observers can be considered typical, the most likely epoch for observers to emerge in the Universe is around the equality between Λ and , setting , and
Thus, neither the observed value of Λ nor the comparable size of today seem problematic in Minkowski space
5 1 2
What is cosmology in Minkowski space?
Of particular interest thereby is the formulation of cosmology in Minkowski space
Rather than an expansion of space, spatial curvature, and small-scale inhomogeneities and anisotropies, this frame exhibits a variation of mass, length and time scales across spacetime
Alternatively, this may be interpreted as an evolution of fundamental constants
What is the gravitating vacuum energy density in Minkowski space?
For the gravitating vacuum energy density in Minkowski space, one therefore has 5
2
Observed cosmological tensions A conformal transformation was used in section 4
3 to cast a Universe where we occupy a conformal top-hat inhomogeneity into one where we reside in the smooth cosmological FRLW background geometry
Cosmology in minkowski space
Maximally symmetric Lorentzian manifold with a negative cosmological constant
In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe. Paul Dirac was the first person to rigorously explore anti-de Sitter space, doing so in 1963.
Maximally symmetric Lorentzian manifold with a positive cosmological constant
In mathematical physics, n-dimensional de Sitter space is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian analogue of an n-sphere.
A five-dimensional space is a space with five dimensions
Geometric space with five dimensions
A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. Whether or not the universe is five-dimensional is a topic of debate.
In mathematics
Topological space in group theory
In mathematics, a homogeneous space is, very informally, a space that looks the same everywhere, as you move through it, with movement given by the action of a group. Homogeneous spaces occur in the theories of Lie groups, algebraic groups and topological groups. More precisely, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively. The elements of G are called the symmetries of X. A special case of this is when the group G in question is the automorphism group of the space X – here automorphism group can mean isometry group, diffeomorphism group, or homeomorphism group. In this case, X is homogeneous if intuitively X looks locally the same at each point, either in the sense of isometry, diffeomorphism, or homeomorphism (topology). Some authors insist that the action of G be faithful, although the present article does not. Thus there is a group action of G on X which can be thought of as preserving some geometric structure on X, and making X into a single G-orbit.
In mathematical physics
Spacetime used in theory of relativity
In mathematical physics, Minkowski space combines inertial space and time manifolds with a non-inertial reference frame of space and time into a four-dimensional model relating a position to the field. A four-vector (x,y,z,t) consists of a coordinate axes such as a Euclidean space plus time. This may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally.
