Abstract:
It is shown that the inflationary model is the result of the symmetry of the generalized
F(R, T, X, ϕ)-cosmological model using the Noether symmetry. It leads to a solution, a particular
case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case
of cosmological models F(R, X, ϕ) and F(T, X, ϕ) the Monge–Ampère equation is still obtained, one
of the solutions including the Starobinsky model. For these models, it is shown that one can obtain
both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In
this case, the scalar field ϕ has similar time dependences, exponential and exponential. The resulting
form of the Lagrangian of the model allows us to consider it as a model with R
2 or X
2
. However, it is
also shown that previously less studied models with a non-minimal relationship between R and X
are important, as one of the possible models. It is shown that in this case the power-law model can
have a limited evolutionary period with a negative value of the kinetic term.
