Inflation from the Symmetry of the Generalized Cosmological Model

Abstract

It is shown that the inflationary model is the result of the symmetry of the generalized $F(R,T,X,\phi )$-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 $F(R,X,\phi )$ and $F(T,X,\phi )$ 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 $\phi$ 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.