Related papers: Modified gravity and Space-Time-Matter theory
We study the correspondence between two theoretical frameworks for describing dark energy, $f(R)$ gravity and higher-dimensional Space-Time-Matter (STM) or induced-matter theory. We show that the Hubble expansion parameter in $f(R)$ gravity…
We study the accelerating expansion and the induced dark energy of the $5D$ Ricci-flat universe which is characterized by having a big bounce as opposed to a big bang. We show that the arbitrary function $\mu(t)$ contained in the $5D$…
In Spacetime-Matter theory we assume that the 4D induced matter of the $5D $ Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as an induced scalar field. Then we show that the conventional 4D quintessence and…
We consider the space-time-matter theory (STM) in a five-dimensional vacuum space-time with a generalized FLRW metric to investigate the late-time acceleration of the universe. For this purpose, we derive the four-dimensional induced field…
The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D…
We extend the Induced Matter Theory of gravity (IMT) to 5D curved spacetimes by using the Weitzenb\"ock representation of connections on a 5D curved spacetime. In this representation the 5D curvature tensor becomes null, so that we can make…
The standard theory of General Relativity (GR) currently provides the most reliable description of all gravitational events in Astrophysics and Cosmology. However, current Astronomy allows measurements that contradict the predictions of GR…
The metric $f(R)$ theories of gravity are generalized to five-dimensional spacetimes. By assuming a hypersurface-orthogonal Killing vector field representing the compact fifth dimension, the five-dimensional theories are reduced to their…
Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary…
In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embeded into a 5D spacetime, where gravity is described by a Brans-Dicke theory in vacuum. Once we impose the embeding…
We use $(4+1)$ split to derive the 4D induced energy density $\rho $ and pressure $p$ of the $5D$ Ricci-flat cosmological solutions which are characterized by having a bounce instead of a bang. The solutions contain two arbitrary functions…
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they…
We investigate the possibility to recover a four-dimensional (4D) general theory of relativity, as embedded in a 5D spacetime where gravity is governed by a five-dimensional (5D) Brans-Dicke (BD) theory of gravity. Employing the…
We develop the reconstruction program for the number of modified gravities: scalar-tensor theory, $f(R)$, $F(G)$ and string-inspired, scalar-Gauss-Bonnet gravity. The known (classical) universe expansion history is used for the explicit and…
We discuss the possibility of explaining observations usually related to the existence of dark matter by passing from the general relativity (GR) theory to a modified theory of gravity, the embedding theory proposed by Regge and Teitelboim.…
We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of $f(R)$, $f(G)$ or $f(R,G)$ gravity, model with non-linear gravitational coupling or string-inspired…
The $f(R)$ Modified Gravity is a modification of Einstein's general theory of relativity, which aims to explain issues beyond The Standard Model of Cosmology such as dark energy and dark matter. As a theory of gravitation that govern major…
We propose a new unified model that describes~dark energy and dark matter in the context of $f(R,\phi )$ gravity using a massive scalar field in five dimensions. The scalar field is considered in the bulk that surrounds the 3-brane in…
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…
We review modified $F(R)$ gravity as realistic candidate to describe the observable universe expansion history. We show that recent cosmic acceleration, radiation/matter-dominated epoch and inflation could be realized in the framework of…