3D-brane universe model

 Ruslan Sharipov.   1 ... 10 11 12 ... ru The Lagrangian L is included in the action integral, which we considered in the previous post " The Lagrangian approach to deriving the equations of gravity in the new theory ". The Lagrangian L itself is expressed in the form of a three-dimensional integral of the Lagrangian density. As we see from these formulas, the Lagrangian density is the sum of two terms — the Lagrangian density of the gravitational field and the Lagrangian density of matter. The Lagrangian density of matter describes the dynamics of matter. It depends on a specific type of matter that can be cosmic dust, gas, liquid, solid, or even dark matter. We will leave the choice of Lagrangian density of matter for later. Now let's consider the choice of the Lagrangian density for the gravitational field. The dynamic variables of the gravitational field in the new theory are a three-dimensional metric and a scalar function denoted by the letter g w...

 Ruslan Sharipov   1 ... 9 10 11 ... ru The Lagrangian approach to deriving various equations is associated with the name of Joseph Louis Lagrange. Detailed information about him can be found in Wikipedia . In mechanics and in physics his name is associated with the so-called "least action principle". According to this principle, the evolution of a physical system occurs in such a way that some integral over time turns out to take the smallest possible value. This integral is called the action integral. It is usually denoted by the letter S. The function L in the integral S is called the Lagrange function or the Lagrangian. In field theories it is itself an integral over spatial variables. In the spatial integral L we see a function denoted by the same letter, but in a calligraphic style. This is the Lagrangian density. It is represented as the sum of two terms: the Lagrangian density of the gravitational field and the Lagrangian density of matter. We will discu...