 Respective to matter density, can be re-written with account of in the form

and then, for the total energy change during "s" eras,

The term with the sum by "p" gives the main contribution to this expression because it contains an exponent with a large power.Leaving only this term and averaging , one gets in its right hand side the expression formula_124 which coincides with ; all other terms in the sum (also terms with η"s" in their powers) lead only to corrections of a relative order 1/"s".Therefore,

By virtue of the almost certain character of the relation between τ"s" and "s" can be written as

which determines the value of the double logarithm of density increase averaged by given double-logarithmic time intervals τ or by a given number of eras "s".