arXiv subjects

Joseph Ntahompagaze

Publications and source records attributed to Joseph Ntahompagaze.

21 records · Page 2Linked to original sources

arXiv2017

Inflationary f(R) cosmologies

This paper discusses a simple procedure to reconstruct f (R)-gravity models from exact cosmological solutions of the Einstein field equations with a noninteracting classical scalar field-and-radiation background. From the kind of inflationary scenario we want, we show how the potential functions can be obtained. We then show how an f (R) gravitational Lagrangian density that mimics the same cosmological expansion as the scalar field-driven inflation of General Relativity can be reconstructed. As a demonstration, we calculate the slow-roll parameters (the spectral index n s and the tensor-to-scalar ratio r) and compare them to the Planck data.

gr-qc↗

arXiv2017

On $f(R)$ gravity in scalar-tensor theories

We study $f(R)$ gravity models in the language of scalar-tensor theories. The correspondence between $f(R)$ gravity and scalar-tensor theories is revisited since $f(R)$ gravity is a subclass of Brans-Dicke models, with a vanishing coupling constant ($ω=0$). In this treatment, four $f(R)$ toy models are used to analyze the early-universe cosmology, when the scalar field $ϕ$ dominates over standard matter. We have obtained solutions to the Klein-Gordon equation for those models. It is found that for the first model $\left(f(R)=βR^{n}\right)$, as time increases the scalar field decreases and decays asymptotically. For the second model $\left(f(R)=αR+βR^{n}\right)$ it was found that the function $ϕ(t)$ crosses the $t$-axis at different values for different values of $β$. For the third model $\left(f(R)=R-\frac{ν^{4}}{R}\right)$, when the value of $ν$ is small the potential $V(ϕ)$ behaves like the standard inflationary potential. For the fourth model $\left(f(R)=R-(1-m)ν^{2}\Big(\frac{R}{ν^{2}}\Big)^{m}-2Λ\right)$, we show that there is a transition between $1.5 1.55$. The slow-roll approximation is applied to each of the four $f(R)$ models and we obtain the respective expressions for the spectral index $n_{s}$ and the tensor-to-scalar ratio $r$.

gr-qc↗

arXiv2017

Reconstructing f(R) Gravity from a Chaplygin Scalar Field in de Sitter Spacetimes

We present a reconstruction technique for models of $f(R)$ gravity from the Chaplygin scalar field in flat de Sitter spacetimes. Exploiting the equivalence between $f(R)$ gravity and scalar-tensor theories, and treating the Chaplygin gas as a scalar field model in a universe without conventional matter forms, the Lagrangian densities for the $f(R)$ action are derived. Exact $f(R)$ models and corresponding scalar field potentials are obtained for asymptotically de Sitter spacetimes in early and late cosmological expansion histories. It is shown that the reconstructed $f(R)$ models all have General Relativity as a limiting solution.

gr-qc↗