Curvature quintessence matched with observational data

TL;DR

This paper explores curvature quintessence by augmenting General Relativity with higher-order curvature invariants in a fourth-order gravity framework ${f(R)}$ and derives exact cosmological solutions in an FRW background. By choosing a power-law form $f(R)=f_0 R^n$ and a scale factor $a(t)=a_0 (t/t_0)^{\alpha}$, the authors obtain a family of solutions with an effective curvature equation of state $w_{(curv)}= -\frac{6n^2-7n-1}{6n^2-9n+3}$, where accelerated expansion occurs for certain $n$ and $w_{curv}$ approaches $-1$ as $n\to\infty$. They confront the model with observations via SNIa data and the age of the universe, finding degeneracies in $n$ but identifying viable ranges; WMAP age constraints further narrow the allowed $n$ to approximately $-0.450\le n<-0.370$ or $1.366<n<1.376$, both yielding acceleration. The conclusions argue that modest deviations from the Einstein-Hilbert action in the form $f(R)=f_0 R^{1+\varepsilon}$ can reproduce late-time acceleration and be consistent with current cosmological data, offering a scalar-field-free route to quintessence grounded in quantum gravity considerations.

Abstract

Quintessence issues can be achieved by taking into account higher order curvature invariants into the effective action of gravitational field. Such an approach is naturally related to fundamental theories of quantum gravity which predict higher order terms in loop expansion of quantum fields in curved space-times. In this framework, we obtain a class of cosmological solutions which are fitted against cosmological data. We reproduce encouraging results able to fit high redshift supernovae and WMAP observations. The age of the universe and other cosmological parameters are discussed in this context.

Figures (3)

• Figure 1: The behaviour of $\alpha$ in term of $n$. It is evident a region in which the power of the scale factor is more than one and a region in which it is always negative. The plot on the right represent the values of $n$ between 0 and 1.5.
• Figure 2: Behaviour of $w_{curv}$ against $n$. We have drawn a line for the value $w_{curv}=$$-1$ emphasizing the cosmological constant state equation value.
• Figure 3: Contour plots for the considered $n$-ranges using the SNIa data. It is evident that in the interval $1/2<n<1$ the models are non physical. The ranges $1/2(1-\sqrt{3})<n<1/2$ and $1/2<n<1$ give some indications on the best fit value of $n$, in the other cases the matching with SNIa is completely degenerate.