Equation of state for dark energy in $f(T)$ gravity

TL;DR

The paper investigates the dark-energy equation of state $w_{ m DE}$ within $f(T)$ gravity, showing that single-term exponential or logarithmic models cannot realize phantom-divide crossing. By constructing a combined $f(T)$ model that blends both terms, it demonstrates that $w_{ m DE}$ can cross from $>-1$ to $<-1$, a behavior favored by recent data. Using a $y_H$-formalism, the authors derive the cosmological evolution and constrain the model with SNe Ia, BAO, and CMB observations, obtaining a best-fit around $u\approx 0.83$ with a competitive $\chi^2$ compared to $\Lambda$CDM. Overall, the work suggests that torsion-based modified gravity can accommodate dynamical dark energy while remaining consistent with current cosmological measurements.

Abstract

We study the cosmological evolutions of the equation of state for dark energy $w_{\mathrm{DE}}$ in the exponential and logarithmic as well as their combination $f(T)$ theories. We show that the crossing of the phantom divide line of $w_{\mathrm{DE}} = -1$ can be realized in the combined $f(T)$ theory even though it cannot be in the exponential or logarithmic $f(T)$ theory. In particular, the crossing is from $w_{\mathrm{DE}} > -1$ to $w_{\mathrm{DE}} < -1$, in the opposite manner from $f(R)$ gravity models. We also demonstrate that this feature is favored by the recent observational data.

Figures (12)

• Figure 1: $w_{\mathrm{DE}}$ as a function of the redshift $z$ for $\vert{p}\vert=0.1$ (solid line), $0.01$ (dashed line), $0.001$ (dash-dotted line) and $\Omega_{\mathrm{m}}^{(0)} = 0.26$ in the exponential $f(T)$ theory, where the left and right panels are for $p>0$ and $p<0$, respectively.
• Figure 2: $w_{\mathrm{DE}}$ as a function of $\vert{ T/T_0 }\vert$, where the thin solid line shows $w_{\mathrm{DE}}=-1$ (cosmological constant). Legend is the same as Fig. \ref{['fig-1']}.
• Figure 3: $\vert{ T/T_0 }\vert$ as a function of the redshift $z$ for $\vert{p}\vert=0.1$.
• Figure 4: $\rho^{\star}_{\mathrm{DE}} \equiv \rho_{\mathrm{DE}}/\rho_{\mathrm{DE}}^{(0)}$ as a function of the redshift $z$, where the thin solid line shows $w_{\mathrm{DE}}=-1$ (cosmological constant). Legend is the same as Fig. \ref{['fig-1']}.
• Figure 5: $\Omega_{\mathrm{DE}}$ (dashed line), $\Omega_{\mathrm{m}}$ (solid line) and $\Omega_{\mathrm{r}}$ (dash-dotted line) as functions of the redshift $z$ for $\vert{p}\vert=0.1$. Legend is the same as Fig. \ref{['fig-1']}.