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Welcome to the Evolving Cosmos
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Before 19th century, the idea of static universe filled with ordinary, visible matter, and radiation was widely accepted among the astronomers; even when the first relativistic model of universe was developed by Einstein in 1917, he added an extra term to the field equations in order to stabilize universe and keep it static; this term was called cosmological constant. Cosmological constant is the energy density of the vacuum that acts against gravitational attracting force. But when astronomical observations revealed the expansion of the universe, and astronomers hypothesized that our universe had begun by a Big Bang, Einstein came to this idea that there was not any need to the cosmological constant in his equations, because the expansion of the universe could be aftermath of the Big Bang, preventing gravitational attracting force to collapse our universe. The expansion of our universe was expected to be decelerating, but today's observations show that the expansion of our universe is accelerating; and in order to explain this accelerated expansion of the universe, cosmologists hypothesized the term 'dark energy' that is a fluid with negative pressure filled our universe, and it works against gravity and accelerates the expansion of today's universe. There are different models of dark energy; the first one is again cosmological constant, because it exerts repulsive force; and also there are dynamic and evolving models of dark energy, e.g. scalar field.

 On the other hand astronomers have found evidence that more than 85 percent of mass in our universe is invisible; they call it 'dark matter'.

 In addition to these two strange components, dark matter and dark energy, cosmologists have added a bizarre phenomenon to our universe in order to solve issues with Big Bang model of universe; this phenomenon is called inflation or exponential expansion of universe just after the Big Bang.


So according to the modern cosmology, in addition to the visible (ordinary) matter and radiation, our universe contains two other mysterious components, dark matter and dark energy; and our universe is not a static universe, it is dynamic, evolutionary universe; and it has gone into different phases through its expansion over time. Just after the Big Bang, when it was in planck scale (the smallest scale in the universe), universe expanded exponentially to an astronomical scale, that is called inflationary era. Inflation happened in a very brief period of time and when it was ended the age of our universe was about 10-33 to 10-32 seconds. After inflation, radiation appeared in the universe; then dark matter and ordinary  matter dominated our universe; so the rapid expansion of the universe due to the inflation, was slowed down by the positive pressure of these fluids ( radiation, dark matter, and ordinary matter). But again through the appearance of dark energy, the expansion of the universe began to speed up and today's expansion of the universe is accelerating.

Big Bang model of the universe (with dark matter, dark energy, and inflation) is based on general theory of relativity and astronomical observations. The big issues with this model is the Big Bang itself, a singular point that gives birth to a planck scale universe, and inflation where general theory of relativity meets quantum mechanics.


      

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Numerical Solution of  Ordinary Differential Equations by Bulirsch-Stoer Method

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Numerical Solution of Ordinary Differential Equations by Bulirsch-Stoer MethodNumerical Solution of  Ordinary Differential Equations by Bulirsch-Stoer Method
 







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