Recently, various models of modified gravity have been proposed in order to solve the problem of dark energy (DE) and dark matter (DM), using a function f(R) which depends essentially on the Ricci scalar “R”. Various models of f(R) modified gravity were proposed, as R² inflation, which can describe the cosmic acceleration of the universe and also inflation, the Brans-Dicke theory, depending on the coupling constant ω, which is a model with a scalar field describing the gravitation, or the 1/R gravity which can explain the acceleration of the Universe’s expansion.
There are several ways to choose the form of the function f(R). Note that, only a few models that can describe dark energy, dark matter or inflation, and conditions for the cosmological viability of dark energy models were introduced. Recall that the modified gravity theories are considered as a perturbation theories around the Ricci scalar in the context of the Jordane frame or depending on a Ricci scalar and a new scalar field φ coupling in the Einstein frame.
On the other hand, there are other more generalized modified gravity depending on a scalar field whose the coupling with the Ricci scalar is described by a certain function f(R, φ). While the other models of f(R)-brane or f(R, φ)-brane, describe modified gravity in the brane world scenario in five-dimensional space-time.
Now, Bennai and colleagues proposed a new unified model that describes dark energy and dark matter in the context of f(R, φ) gravity using a massive scalar field in five dimensions.
“We study the evolution of a scalar fields φ in modified gravity in 5-dimensional braneworld model. We have supposed that dark matter (DM) and dark energy (DE) are only the interactions of the field φ and the 3-brane. For this reason, we described the modified gravity in 4-dimensional by the braneworld models. Recall that, the scalar field density on 3-brane depends on the curvature of space-time.”, said Bousder.
They have studied the evolution of the scalar field φ on the 3-brane and in the bulk, through a passage that transforms all parameters of 4-dimensional model to 5-dimensional one. The 5-dimensional theory depends on the field φ. They have shown that the description of dark energy, dark matter and ordinary matter is obtained by the evolution equation of the scalar field φ. They found a relation between the density of dark matter (DM) and the speed of the universe’s expansion and showed that expansion speed on the 3-brane depends on the expansion speed of bulk.
They also note that the mass of field φ creates dark matter, which changes over time. This is called chameleonic dark matter. On the other hand, they have shown that, the kinetic energy of scalar field, is responsible for the bulk’s expansion, which means that, the bulk generates an the accelerating expansion of the Universe. The decrease of the scalar field mass with the acceleration of Universe expansion, showed that the mass of the field φ is transformed to an energy (dark energy).
“We showed that the field φ describes both the accelerating expansion of the Universe and the dark matter. However, for the some reasons, we have shown that the bulk is also expanding. Thus, the expansion of the Universe depends on bulk expansion. The dark energy is then defined as the variation of a large values of the scalar field φ and the dark matter is described as a minimal values of the field φ.”, said Bennai.
References: M. Bousder, Z. Sakhi, M. Benna, “A new unified model of dark matter and dark energy in 5-dimensional f(R, φ) gravity”, International Journal of Geometric Methods in Modern Physics, Vol. 17, No. 13, 2050183 (2020). https://www.worldscientific.com/doi/10.1142/S0219887820501832 https://doi.org/10.1142/S0219887820501832
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