Dark Energy: the equation of state description versus scalar-tensor or modified gravity

Abstract

Dark energy dynamics of the universe can be achieved by equivalent mathematical descriptions taking into account generalized fluid equations of state in General Relativity, scalar-tensor theories or modified F(R) gravity in Einstein or Jordan frames. The corresponding technique transforming equation of state description to scalar-tensor or modified gravity is explicitly presented. We show that such equivalent pictures can be discriminated by matching solutions with data capable of selecting the true physical frame.

Figures (3)

• Figure 1: The distance moduli $\mu$ for the $\Lambda$CDM and the exponential potential models, obtained from the best fit parameters of Table II, are compared with SNeIa data in Riess04. The two curves practically coincide for $z\leq 2$.
• Figure 2: The CMBR angular power spectrum $Q \equiv l(l+1)C_l/2\pi$ for the two models, obtained with CAMB codes CAMB from the best fit parameters of Table II. The two curves do not coincide for small $l$'s, where the exponential potential gives higher values. We have to note that we are exploring a different range of $z$ with respect to that in Fig.1.
• Figure 3: Plot of the scalar-field equation of state versus ${\log}_{10}a$ with the best fit value of $\Omega_M = 0.298$. The vertical bar marks the today value of scale factor ${\log}_{10} a_0$. Only with this choice of variables, there is evidence of a transition from $w \approx -1$ in the past to $w\approx-0.5$ in the future. This means that other constant values of $w$ can be generically recovered from scalar-tensor theory, also for exponential potentials, so that $\Lambda$CDM does not coincides with exponential models for any $w$ and any $z$.