Almost a century ago, Hubble discovered that the universe is expanding and that the rate at which galaxies move away from each other is proportional to the distance between them.
В 1998 в процессе наблюдения за вспышками сверхновых в дальних галактиках было сделано еще более шокирующее открытие,
In 1998 an even more shocking discovery was made while observing supernova outbreaks in distant galaxies,
This accelerated expansion of the Universe was attributed to the action of some "dark energy",
which grows and can even tear all the atoms in the Universe apart.
In this Chapter, I will try to explain what "dark energy"is,
that there is nothing supernatural in it and that everything happens in accordance with the Law of Conservation of Energy.
Try deal with question "why expands universe" and where source of energy its enlargement.
Consider a system of two galaxies A and B, located at a distance of R.
Recall the well-known formula from nuclear physics for the mass of the nucleus, which is the sum of the masses of protons and neutrons minus the binding energy divided by
squared the speed of light, and write a similar formula for the mass of a system of two galaxies.
In this formula, Ma and Mb are the masses of galaxies A and B respectively, Ea and Eb are the internal gravitational bond energies in galaxies respectively,
G is the gravitational constant, c is the speed of light. The last term in this formula expresses the gravitational energy of the bond between galaxies,
it is written on the basis of the classical Newtonian model of gravity.
The law of conservation of energy requires that if the galaxies contract, that is, the gravitational binding energies of Ea and Eb increase, then it must be
it is compensated by decrease of gravitational energy of communication between galaxies that can be made only by increasing distance between galaxies R.
Let's simplify the problem by assuming that both galaxies are exactly the same, that is, they have the same mass and internal gravitational energy connection they have
are identical and equally change in time. Then the above formula will be simplified to the following form
Next, we write the formula for the balance of gravitational binding energy for two values of E1 > E2 of their bond
are identical and equally change in time. Then the above formula will be simplified to the following form
where get
denote
and, in the end we get
From the obtained equation it is seen that if the increase in gravitational binding energy in galaxies would be constant, then
their rate of flight would be proportional to the square of the distance between them. While in Hubble's law it is proportional to
only the first degree of distance. We find an equation for changing the rate of increase of the gravitational binding energy at which
would be satisfied
Hubble law. Based on Hubble's law we write the differential equation
Solving this differential equation we find a function describing the change of distance in time
Then the speed and acceleration will be described by the following functionsи
From the obtained equations we find that in order to fulfill Hubble's law, the rate of increase of gravitational energy
the bonds of matter in galaxies should decrease exponentially