Abstract
In this study, making use of the f(R) theory of gravity in a D-dimensional Kaluza-Klein type framework, we discuss whether we need to assume additional dimensions in order to explain two stages (inflation and deceleration phases) of the universe. To reach this goal, we start with a higher dimensional form of the Friedmann equation written in the f(R) gravity. For the inflation era occurring after a beginning vacuum phase of the universe, we conclude that a 10-dimensional spacetime model is needed as predicted in the string theory. However, after using a fixed field condition, it is observed that additional dimensions are compactified on the standard four spacetime dimensions in the deceleration phase. Moreover, the additional dimensions may be responsible for the dynamics of the dark energy dominated era, that's why we can state that the source of dark energy may be the extra dimensions.
Highlights
According to the string theory [1], we need additional dimensions in order to describe the general structure of the universe or construct a unified form for the fundamental forces we observe in nature
The inability of the direct observation of fundamental particles of dark energy in the four dimensional framework has strengthened [4] the belief of the existence of the extra dimensions which are assumed to be compactified in every point at spatial scale of the four-dimensional spacetime
For the two regimes of the universe, we have investigated the existence of the extra dimensions in context of the Kaluza-Klein framework with the higher dimensional f (R) gravity
Summary
According to the string theory [1], we need additional dimensions in order to describe the general structure of the universe or construct a unified form for the fundamental forces we observe in nature. After creation of the matter during inflation, the universe enters a deceleration regime and it returns to an accelerated phase (the quintessence epoch) again In this sense, the known formation of the existence of the extra dimensions may yield more information at the point of understanding dark energy puzzle or the large-scale structure of the universe as a whole. Salti / Physics Letters B 791 (2019) 80–85 dicates a super accelerated inflation period after a vacuum state of the universe [15,16,17] From this point of view, in this study, the higher dimensional perspective with the Starobinsky model is directly examined to identify the super accelerated period. The existence of extra dimensions are discussed by considering the early inflationary regime, super accelerated phase and the deceleration epoch together with the Starobinsky model.
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