Equation of state for dark energy in $f(T)$ gravity (1011.0508v2)

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.

• The paper introduces a novel combined f(T) model that achieves phantom divide crossing in the dark energy equation of state.
• It contrasts exponential and logarithmic f(T) models, highlighting their limitations in reproducing dynamic cosmic phase transitions.
• The study demonstrates f(T) gravity’s viability for explaining cosmic acceleration without a cosmological constant and encourages further observational tests.

Overview of the Equation of State for Dark Energy in $f(T)$ Gravity

The paper "Equation of State for Dark Energy in $f(T)$ Gravity" explores an exploration of dark energy's equation of state ($w_{\mathrm{DE}$) within the framework of $f(T)$ gravity, emphasizing exponential and logarithmic $f(T)$ models, as well as their combination. The authors rigorously investigate the potential of these models to account for the cosmic acceleration observed in various astrophysical observations, emphasizing the conditions under which the equation of state can cross the "phantom divide line" ($w_{\mathrm{DE} = -1$).

Context and Motivation

Astronomical observations from sources such as Supernovae Ia, cosmic microwave background radiation, and baryon acoustic oscillations suggest that the universe is undergoing an accelerated expansion phase. This has traditionally been explained by dark energy in the context of general relativity or through modifications to gravitational theory. $f(T)$ gravity is one such modification wherein the teleparallelism approach, utilizing the torsion scalar $T$, is leveraged as an alternative to the standard curvature-based descriptions. The paper posits that by appropriately altering the functional form of $T$, it is possible to simulate dark energy effects without invoking a cosmological constant.

Main Contributions

The research highlights the cosmological implications of exponential and logarithmic $f(T)$ models:

• Exponential $f(T)$ Model: The paper demonstrates that in the exponential $f(T)$ setup, it is not feasible to achieve a crossing of the phantom divide line. This model confines the universe to either a non-phantom or phantom phase based on the sign of the parameter involved, thus not fully accommodating the entirety of observational data.
• Logarithmic $f(T)$ Model: Similar to the exponential case, the logarithmic model places constraints on the dynamical evolution of $w_{\mathrm{DE}$, lacking the capability for phantom line crossing. The behavior of dark energy in this model is analogous, with the universe maintaining a non-phantom phase.
• Combined Exponential and Logarithmic $f(T)$ Model: In a noteworthy pivot, the paper introduces a combined model that integrates both exponential and logarithmic components. This hybrid approach successfully facilitates the crossing of the phantom divide, displaying a transition from non-phantom to phantom phases, aligning with recent data trends. The result presents a promising avenue for reconciling $f(T)$ gravity with cosmological observations.

Theoretical and Practical Implications

This research offers significant implications for both theoretical physics and observational cosmology. The methodological framework and results support the viability of $f(T)$ gravity as a contender for explaining dark energy dynamics. Importantly, the demonstrated potential for phantom divide crossing in the combined model provides a plausible explanation for the dynamical properties observed in the dark energy equation of state, which traditional models often fail to accommodate without contrived mechanisms.

The study further invites future work to refine and test these models against emerging datasets, offering a fertile ground for further explorations in modified gravity theories. The authors highlight the necessity of extending these models to more complex scenarios and stress-testing them with broader cosmological observations, including structure formation and gravitational wave background studies, to fully ascertain their cosmological viability.

In summary, the paper provides a detailed analysis of $f(T)$ gravity's role in cosmological expansion, with an emphasis on innovations that allow for a crossing of the phantom divide. As such, it contributes to a broader understanding of alternative gravitational models in explaining dark energy, presenting a framework that holds potential both in theoretical developments and empirical fits to observational data.