How The Life Begin

De Sitter space Ekpyrotic universe  − a string-theory-related model depicting a  five-dimensional ,  membrane -shaped universe; an alternative to the  Hot Big Bang Model , whereby the universe is described to have originated when two membranes collided at the fifth dimension Extra dimensions in string theory  for 6 or 7 extra space-like dimensions all with a compact topology History of the center of the Universe Holographic principle List of cosmology paradoxes Theorema Egregium  − The "remarkable theorem" discovered by  Gauss , which showed there is an intrinsic notion of curvature for surfaces. This is used by  Riemann  to generalize the (intrinsic) notion of curvature to higher-dimensional spaces Three-torus model of the universe Zero-energy universe  – hypothesis that the total amount of energy in the universe is exactly zero

Milne model ("spherical" expanding) Main article:  Milne model If one applies  Minkowski space -based  special relativity  to expansion of the universe, without resorting to the concept of a  curved spacetime , then one obtains the Milne model. 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. Spatial geometry of this model is an unbounded  hyperbolic space . The entire universe is contained within a  light cone , namely the future cone of the Big Bang. For any given moment t> 0 of  coordinate time (assuming the Big Bang has t = 0), the entire universe is bounded by a  sphere  of radius exactly  c  t. The apparent paradox of an infinite universe contained within a sphere is explained with  length contraction : the galaxies farther away, which a

When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive. These meanings of open and closed are different from the mathematical meaning of open and closed used for sets in topological spaces and for the mathematical meaning of open and closed manifolds, which gives rise to ambiguity and confusion. In mathematics, there are definitions for a  closed manifold  (i.e., compact without boundary) and  open manifold  (i.e., one that is not compact and without boundary). A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the  Friedmann–Lemaître–Robertson–Walker  (FLRW) model the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.

Universe with negative curvature A hyperbolic universe, one of a negative spatial curvature, is described by  hyperbolic geometry , and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of  hyperbolic 3-manifolds , and their classification is not completely understood. Those of finite volume can be understood via the  Mostow rigidity theorem . For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called "horn topologies", so called because of the shape of the  pseudosphere , a canonical model of hyperbolic geometry. An example is the  Picard horn , a negatively curved space, colloquially described as "funnel-shaped".

Universe with positive curvature Universe in an expanding sphere. The galaxies farthest away are moving fastest and hence experience length contraction and so become smaller to an  observer in the centre . A positively curved universe is described by  elliptic geometry , and can be thought of as a three-dimensional  hypersphere , or some other  spherical 3-manifold (such as the  Poincaré dodecahedral space ), all of which are quotients of the 3-sphere. Poincaré dodecahedral space , a positively curved space, colloquially described as "soccerball-shaped", as it is the quotient of the 3-sphere by the  binary icosahedral group , which is very close to  icosahedral symmetry , the symmetry of a soccer ball. This was proposed by  Jean-Pierre Luminet  and colleagues in 2003 and an optimal orientation on the sky for the model was estimated in 2008.

In a universe with zero curvature, the local geometry is  flat . The most obvious global structure is that of  Euclidean space , which is infinite in extent. Flat universes that are finite in extent include the  torus  and  Klein bottle . Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. These are the  Bieberbach manifolds . The most familiar is the aforementioned  3-torus universe . In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The  ultimate fate of the universe  is the same as that of an open universe. A flat universe can have  zero total energy .

The curvature of the universe places constraints on the topology. If the spatial geometry is  spherical , i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite. Many textbooks erroneously state that a flat universe implies an infinite universe; however, the correct statement is that a flat universe that is also  simply connected  implies an infinite universe. For example, Euclidean space is flat, simply connected, and infinite, but the  torus  is flat, multiply connected, finite, and compact. In general,  local to global theorems  in  Riemannian geometry  relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in  Thurston geometries . The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish

Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a  disc , have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration. However, there exist many finite spaces, such as the  3-sphere  and  3-torus , which have no edges. Mathematically, these spaces are referred to as being  compact without boundary. The term compact basically means that it is finite in extent ("bounded") and  complete . The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the universe is typically assumed to be a  differentiable manifold . A mathematical object that possesses all these properties, compact without boundary and differentiable, is termed a  close

One of the presently unanswered questions about the universe is whether it is infinite or finite in extent. For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled up with a finite amount of material, while an infinite universe is unbounded and no numerical volume could possibly fill it. Mathematically, the question of whether the universe is infinite or finite is referred to as  boundedness . An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale."

Global structure covers the  geometry and the  topology  of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. The universe is often taken to be a  geodesic manifold , free of  topological defects ; relaxing either of these complicates the analysis considerably. A global geometry is a local geometry plus a topology. It follows that a topology alone does not give a global geometry: for instance, Euclidean 3-space and  hyperbolic 3-space  have the same topology but different global geometries. As stated in the introduction, investigations within the study of the global structure of the universe include: Whether the universe is  infinite  or finite in extentWhether the geometry of the global universe is flat, positively curved, or negatively curvedWhether the topology is  simply connected  like a sphere or multiply connect

These and other astronomical measurements constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on  spacetime intervals , we can approximate 3-space by the familiar  Euclidean geometry . The  Friedmann–Lemaître–Robertson–Walker (FLRW) model  using  Friedmann equations  is commonly used to model the universe. The FLRW model provides a curvature of the universe based on the mathematics of  fluid dynamics , that is, modeling the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Another way of saying this is that if all forms of  dark energy  are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it

General relativity  explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the  density parameter , represented with Omega (Ω). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way, If Ω = 1, the universe is flatIf Ω > 1, there is positive curvatureif Ω < 1 there is negative curvature One can experimentally calculate this Ωto determine the curvature two ways. One is to count up all the mass-energy in the universe and take its average density then divide that average by the critical energy density. Data from  Wilkinson Microwave Anisotropy Probe  (WMAP) as well as the  Planck spacecraft  give values for the three constituents of all the mass-energy in the universe – normal mass ( baryonic matter  and  dark matter ), relativistic particles ( photons and  neutrinos ), and 

The  curvature  is a quantity describing how the geometry of a space differs locally from the one of the  flat space . The curvature of any locally  isotropic space  (and hence of a locally isotropic universe) falls into one of the three following cases: Zero curvature (flat); a drawn triangle's angles add up to 180° and the  Pythagorean theorem  holds; such 3-dimensional space is locally modeled by  Euclidean space  E 3 .Positive curvature; a drawn triangle's angles add up to more than 180°; such 3-dimensional space is locally modeled by a region of a  3-sphere  S 3 .Negative curvature; a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally modeled by a region of a  hyperbolic space  H 3 . Curved geometries are in the domain of  Non-Euclidean geometry . An example of a positively curved space would be the surface of a sphere such as the Earth. A triangle drawn from the equator to a pole will have at least two angles equal 90°, which makes

As stated in the introduction, there are two aspects to consider: its local geometry, which predominantly concerns the curvature of the universe, particularly the  observable universe , andits  global geometry, which concerns the topology of the universe as a whole. The observable universe can be thought of as a sphere that extends outwards from any observation point for 46.5 billion light years, going farther back in time and more  redshifted  the more distant away one looks. Ideally, one can continue to look back all the way to the  Big Bang ; in practice, however, the farthest away one can look using light and other  electromagnetic radiation  is the  cosmic microwave background (CMB), as anything past that was opaque. Experimental investigations show that the observable universe is very close to  isotropic  and  homogeneous . If the observable universe encompasses the entire universe, we may be able to determine the structure of the entire universe by observation. However, if th

The shape of the universe is the  local and  global geometry  of the  universe . The local features of the geometry of the universe are primarily described by its  curvature , whereas the  topology  of the universe describes general global properties of its shape as of a continuous object. The shape of the universe is related to  general relativity , which describes how  spacetime  is curved and bent by mass and energy. Cosmologists distinguish between the  observable universe  and the global universe. The observable universe consists of the part of the universe that can, in principle, be observed by light reaching Earth within the age of the universe. It encompasses a region of space that  currently  forms a ball centered at Earth of estimated radius 46 billion light-years (4.4×10 26  m). This does not mean the universe is 46 billion years old; in fact, the universe  is believed to be 13.8 billion years old , but  space itself has also expanded , causing the  size of the observable u

Is presence in Goldilocks belt enough for having life on a planet? No, besides distance from the sun, if the atmospheric condition of the planet is accurate to form and sustain water to its surface, can only have the possibility of life. For instance, like Earth and Mars, Venus too considered in the habitable zone of the sun, but life chosen the earth only. Why? NASA's Mars rover mission evidences the ancient bacterial life on mars . Later, due to the thin atmospheric layer it was not able to sustain water to its surface. On the other hand, Venus is too hot to origin the life. Its atmosphere consist a very thick layer of carbon dioxide. It absorbs sun energy and restricts revert it back, thus create a non habitable furnace.   Bottlenecks for origin of life in the Goldilocks zoned planets: Billions planets in such zones in the universe orbit around different stars. For instance, NASA claims its recently discovered  TRAPPIST-1 planetary system have perfect chances of alien life