Dark torsion as the cosmic speed-up

Abstract: It is shown that the recently detected acceleration of the universe can be understood by considering a modification of the teleparallel equivalent of General Relativity (TEGR), with no need of dark energy. The solution also exhibits phases dominated by matter and radiation as expected in the standard cosmological evolution. We perform a joint analysis with measurements of the most recent type Ia supernovae (SNe Ia), Baryon Acoustic Oscillation (BAO) peak and estimates of the CMB shift parameter data to constraint the only new parameter this theory has.

• The paper reinterprets cosmic acceleration by attributing it to torsion in a modified teleparallel framework, eliminating the need for dark energy.
• The work derives modified Friedmann equations with second-order field dynamics and empirically constrains model parameters using supernovae, BAO, and CMB data.
• The study demonstrates that the torsion-based model successfully transitions through different cosmic phases, potentially mimicking phantom dark energy behavior.

Overview of "Dark torsion as the cosmic speed-up"

The paper by Gabriel R. Bengochea and Rafael Ferraro presents a reinterpretation of the cosmological acceleration, typically attributed to dark energy, using a modification of the teleparallel equivalent of General Relativity (TEGR). Instead of invoking dark energy, the authors explore a model where torsion, a geometric property, is responsible for the universe's accelerating expansion. This approach provides an alternative to typical modifications of General Relativity, such as the well-known $f(R)$ gravity models, by relying on teleparallelism.

Theoretical Framework

The authors build their framework on teleparallel gravity, distinguishing it from General Relativity by its use of the Weitzenböck connection, which has null curvature but non-zero torsion. In this context, they introduce $f(L_T)$ gravity, where the Lagrangian density is a function of the torsion scalar $L_T$. Unlike modifications in $f(R)$ gravity that can lead to complex fourth-order equations, $f(L_T)$ results in simpler second-order field equations.

Core Contributions

1. Modified Friedmann Equations: The paper derives modified Friedmann equations from the TEGR framework and proposes a specific functional form, $f(L_T) = L_T - \frac{\alpha}{(-L_T)^n}$, aimed at describing the universe's accelerated expansion. This model naturally transitions through the key phases of cosmological evolution, including radiation and matter domination.
2. Observational Analysis: Utilizing recent Type Ia supernovae data, along with Baryon Acoustic Oscillation (BAO) and Cosmic Microwave Background (CMB) shift parameter constraints, the paper provides an empirical evaluation of the model. The analysis focuses on constraining the model's new parameters, notably $n$ and the matter density parameter $\Omega_m$. The study finds a configuration ($n = -0.10$, $\Omega_m = 0.27$) that aligns well with these observations.
3. Implications of Torsion: Distinctly, the paper postulates that the torsion field could account for the late-time acceleration of the universe without introducing dark energy. The paper explores the effective equation of state for dark torsion, noting that the model allows for a transition to a late accelerating phase, potentially behaving like phantom dark energy when $n > 0$.

Implications and Future Directions

The findings suggest substantial implications for both theoretical physics and observational cosmology. This framework challenges the prevailing dark energy paradigm and reinvigorates discussions on the role of torsion in gravity. Practically, this could influence further theoretical investigations into alternative gravity models and stimulate new tests at cosmological scales.

Looking to the future, the paper's results could spur more comprehensive studies integrating a wider array of cosmological observations, particularly those involving large-scale structure formation and gravitational lensing, to further validate the model. Additionally, refining the model with improved astronomical data could help ascertain more precise constraints on the torsion parameters.

In conclusion, Bengochea and Ferraro's work presents a compelling alternative to dark energy-driven cosmic acceleration, leveraging the geometric properties of torsion. This approach opens new avenues in cosmological research, inviting further exploration into the fundamental nature of gravity and the universe's dynamics.