Friedmann equation pdf file

In this report we make a detailed derivation of friedman equations, which are the dy namical equations of a homogeneous and isotropic universe. G describes the space time curvature including its dependence with time of universe heres where we plug in the frw geometries. The new general equation the first friedmann equation, including the curvature, k, and the cosmological constant. Examine the friedmann equation and its impact on our understanding of the evolution of the universe.

The equation of motion for rst can be obtained from the gravitational acceleration at the outer. This is a calculator for a friedmann equation based on the curvature. Heres where we tell the equations that the universe is homogeneous and isotropic. Although in newtonian theory, the universe must be static, milne 1 and mccrea. A set of equations that describes the expansion of the universe is called as the friedmann equations.

Later we will add corrections due to effects of gr. We need to find how the radius of the sphere changes with time. Einstein equations einstein equations are r 1 2 g 8. Einsteins equations which relate the scale factor at, energy density. Newtonian derivation consider a sphere, which expands in a homogeneous universe. Friedmann 18881925 the man who made the universe expand soviet mathematician and meteorologist most famous for contributions to cosmology first person to mathematically predict an expanding universe 1922 derived from einsteins general relativity einstein initially dismissed friedmann s equations. The equation for law of energy saving is proved to be transformed to the proper abel ordinary differential equation. Deriving the friedmann equations from general relativity. Gt 1 the lefthand member of 1 is the einstein tensor g. Pdf friedmanns equations in all dimensions and chebyshevs. Use the fact that mass inside comoving radius is preserved. Dividing by 2 leads to equation 17 in the lecture notes and the second friedmann equation at at 1 3 4.

The friedmann equations as a dynamical system the friedmann equations 1415 and the conservation equation 16 form a set of two independent equations for three variables a, p and. This is a very broad and rapidly developing science. For nonrelativistic particles the mass inside the sphere is constant. Pdf new exact solution of einsteinfriedman equations. Friedmann equation derivation after the lecture, you should be able to. Indeed, the derivation of this equations is intrinsically relativistic. Mathematical expression of that statement is given by the. Einstein equations are, to a universe that follows the coselectronic address. A new quasiperiodic solution of einsteinfriedman equations is presented here. We are going to work in the frame where c 1 and use einstein notation. Cosmology is the science about the structure and evolution of the universe on the large scale, its past, present and future.