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 R2 or X2. 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.
Highlights
Symmetry 2021, 13, 2254. https://Constantly appearing new cosmological data, on the one hand, call attention to the generalized theory of gravity
There is a need to include in the description the initial inflationary period of the development of the Universe
A more complex version of the description is the inclusion of various fields in the cosmological model such as scalar field φ
Summary
Appearing new cosmological data, on the one hand, call attention to the generalized theory of gravity. We will try to consider the most generalized model, which would include in an arbitrary form F ( R, T, X, φ) both Myrzakulov’s gravity and a scalar field in the form of k-essence. To consider this model, the Noether symmetry is used here. + ṪFRT + ẊFRX + φFRφ ] − a3 FX X − 12 φ2 For this most general form of the cosmological model with a scalar field, the Euler–. It is important to obtain an analytical solution to the Lagrangian of the model
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