Cosmic Hysteresis in Reconstructed $f(T)$ Bounce Models A Torsion-Based Thermodynamic Perspective

TL;DR

This work demonstrates that cosmic hysteresis—thermodynamic irreversibility manifested as nonzero work over cosmological cycles—arises generically in reconstructed $f(T)$ bounce cosmologies. By prescribing analytic bouncing scale factors, reconstructing the corresponding $f(T)$, and coupling to a canonical scalar field, the authors show that the sign change of the Hubble parameter, amplified by torsion corrections, yields asymmetric scalar-field dynamics and a closed $w_φ$–$a$ loop. Numerical simulations reveal substantial cycle-to-cycle dissipation, with a mean per-cycle work of roughly $-2.8\times10^{12}$ and secular drift in cycle amplitudes and periods, indicating a persistent, far-from-equilibrium evolution. The results attribute the arrow of time in these cyclic universes to geometric dissipation from torsion, suggesting a universal feature of modified gravity that persists beyond curvature-based theories. These findings open avenues for observational probes of bouncing scenarios and motivate further exploration of hysteresis across other geometric frameworks such as $f(Q)$ gravity and multi-field setups.

Abstract

We investigate the emergence of cosmic hysteresis in cyclic and bouncing cosmologies within the framework of reconstructed $f(T)$ gravity. In contrast to curvature-based modifications of General Relativity, teleparallel gravity attributes gravitation to spacetime torsion encoded in the torsion scalar $T$. By reconstructing viable $f(T)$ functions corresponding to analytically prescribed nonsingular bouncing scale factors and coupling the geometry to a minimally interacting canonical scalar field, we demonstrate that asymmetric scalar field dynamics between expansion and contraction phases give rise to a non-vanishing thermodynamic work integral $\oint p_φ\, dV$ over complete cycles. This hysteresis manifests as closed loops in the $(w_φ,a)$ plane, signifying thermodynamic memory and irreversibility. We derive the modified Friedmann equations, establish exact bounce and turnaround conditions, and discuss the implications of torsion-induced hysteresis for the cosmological arrow of time. Our results confirm that cosmic hysteresis is a generic feature of cyclic universes in modified gravity, extending beyond curvature-based theories.

Figures (7)

• Figure 1: Scale factor evolution in $f(T)$ bounce cosmology. The universe undergoes multiple contraction--expansion cycles, with bounces (red points) marking transitions from contraction to expansion, and turnarounds (green points) marking transitions from expansion to contraction. The smooth evolution demonstrates successful singularity avoidance in the reconstructed $f(T)$ model.
• Figure 2: Evolution of the Hubble parameter $H(t)$ (top panel) and torsion scalar $T = -6H^2$ (bottom panel). The Hubble parameter changes sign at each bounce and turnaround, while the torsion scalar $T$ remains strictly negative throughout the evolution, consistent with the teleparallel formulation. The noisy structure in the torsion scalar reflects numerical integration artifacts magnified by the quadratic dependence on $H$.
• Figure 3: Thermodynamic work performed per cosmological cycle in $f(T)$ gravity. The work integral $W = \oint p_\phi dV$ is computed for four complete cycles, revealing substantial variability. The mean work per cycle (dashed red line) is approximately $-1.7 \times 10^{13}$, with standard deviation $\pm 2.1 \times 10^{13}$. The non-zero work demonstrates irreversible thermodynamic behavior and confirms the presence of torsion-induced cosmic hysteresis.
• Figure 4: Secular evolution of scale factor extrema across cycles. The minima (bounces, red) and maxima (turnarounds, green) drift systematically over time, demonstrating that successive cycles are not identical. The minima decrease by an average of $\Delta a_{\min} \simeq -5.96$ per bounce, while maxima increase by $\Delta a_{\max} \simeq 4.97$ per turnaround. This asymmetric amplitude evolution is a signature of torsion-driven dissipation and non-equilibrium dynamics.
• Figure 5: Cosmic hysteresis loop in the equation-of-state parameter versus scale factor plane $(w_\phi, a)$. The closed loop structure demonstrates that the scalar field equation of state $w_\phi = p_\phi/\rho_\phi$ follows different trajectories during expansion and contraction, even when the scale factor $a$ takes identical values. Bounces (red) and turnarounds (green) are marked. The area enclosed by the loop is proportional to the irreversible thermodynamic work performed per cycle, providing a geometric visualization of torsion-induced thermodynamic memory.