![]() ![]() They don’t have the same brightness, but they have the same size. Let us assume that there is a class of objects which have the same true size no matter where it is in the universe, which means they are like standard candles. Depending on how the matter is distributed in the space, there are smaller variations in the curvature. The universe has a certain topology, but locally it can have wrinkles. $$ds^2 = c^2dt^2 - \left \$$ Global Topology of the Universe $$ds^2 = a^2(t)\left ( dr^2 r^2d\theta^2 r^2sin^2\theta d\varphi^2 \right )$$įor space–time, the line element that we obtained in the above equation is modified as − The Metric for flat (Euclidean: there is no parameter for curvature) expanding universe is given as − The model depends on the component of the universe. In the future, when the scale factor becomes 0, everything will come closer. Basically, it is equal to half of the base times height, i.e. The comoving distance which is the distance between the objects at a present universe, is a constant quantity. The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. If the value of the scale factor becomes 0 during the contraction of universe, it implies the distance between the objects becomes 0, i.e. Step 4 − The following image is the graph for the universe that starts contracting from now. Step 3 − The following image is the graph for the universe which is expanding at a faster rate. The t = 0 indicates that the universe started from that point. Step 2 − The following image is the graph of the universe that is still expanding but at a diminishing rate, which means the graph will start in the past. the value of comoving distance is the distance between the objects. Step 1 − For a static universe, the scale factor is 1, i.e. Let us see how the scale factor changes with time in the following steps. ![]() The expansion of the universe is in all the directions. The space is forward for photon in all directions. Suppose a photon is emitted from a distant galaxy. Model for Scale Factor Changing with Time In this chapter, we will understand in detail regarding the Robertson-Walker Metric. Horizon Length at the Surface of Last Scattering.Velocity Dispersion Measurements of Galaxies. ![]()
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