Interacting Induced Dark Energy Model

Abstract

Following the idea of the induced matter theory, for a non-vacuum five-dimensional version of general relativity, we propose a model in which the induced terms emerging from the extra dimension in our four-dimensional space-time, supposed to be as dark energy. Then we investigate the FLRW type cosmological equations and illustrate that when the scale factor of the fifth dimension has no dynamics, in early time the universe expands with deceleration and then in late time, expands with acceleration. In this case, the state parameter of the effective dark energy has a range of −1 <w X < 0 and it has the value −1/2 for present time. The results for current acceleration impose that Ω X• > 2Ω M • which is in agreement with the measurements. We show that the effective energy density of dark energy have been having the same order of magnitude of the effective energy density of matter from the early time in the decelerating epoch of the universe expansion until now. The model avoids the cosmological coincidence problem.

FLRW cosmology of induced dark energy model and open universe

“…where T (X) αβ is considered as dark energy component of the energy-momentum tensor [34]. For a 5D universe with an extra space-like dimension in addition to the three usual spatially homogenous and isotropic ones, metric (3), as a generalized FLRW solution, can be written as [34]…”

“…By assuming H ≡ ȧ/a, B ≡ ḃ/b and L ≡ l ′ /l and considering metric (5), the Einstein Eqs. (2) reduce as follows [34];…”

“…In this work, following the Induced Dark Energy (IDE) model introduced in Ref. [34], for a 5D version of GR, with generalized 5D Friedmann-Lemaître-Robertson-Walker (FLRW) metric, we investigate the cosmological implications of the model for an open universe. For this purpose, in the next section, with a brief review of the IDE model, we rewrite the cosmological equations and focus on the case of an open universe.…”

A higher dimensional cosmological model for the search of dark energy source

“…Since we are living in a 4D space-time, the hidden extra dimension in 5D is highly likely to be associated with the invisible DM and DE [83]. Few of the worth mentioning works on higher dimensional space-time during the last few years can be seen in [20,[84][85][86][87][88][89][90][91]93].…”