Expansion-contraction duality breaking in a Planck-scale sensitive cosmological quantum simulator

TL;DR

The paper proposes a quantum-gas analogue of cosmological perturbations driven by a Planck-scale Lorentz-violating dispersion, implemented in a quasi-2D dipolar Bose-Einstein condensate. By introducing an anisotropic scaling that dynamically modulates the dipole interactions, it realizes trans-Planckian damping and derives a modified dispersion $oxed{\omega_k^2 = k^2W_k + \frac{v(2-v)}{4\eta^2}(1+\Delta_k)}$, enabling a controlled study of duality between inflation and contraction. In the adiabatic limit the power spectrum remains dual and scale-invariant for $v=-1$ (inflation) and $v=3$ (contraction), but nonadiabatic damping $\Delta_k$ breaks this duality, producing observable low- or high-momentum tilts: contraction shows a blue tilt that can further freeze near the Unruh-like critical point $R=R_c$, while inflation preserves near scale invariance at observable scales. The approach provides a practical route to isolate Planck-scale signatures in analogue quantum cosmology and to distinguish competing early-universe models using currently realizable dipolar BEC platforms.

Abstract

We propose the experimental simulation of cosmological perturbations governed by a Planck-scale induced Lorentz violating dispersion, aimed at distinguishing between early-universe models with similar power spectra. Employing a novel variant of the scaling approach for the evolution of a Bose-Einstein condensate with both contact and dipolar interactions, we capture the hitherto unobserved phenomenon of trans-Planckian damping. We show that scale invariance, and in turn, the duality of the power spectrum is subsequently broken at large momenta for an inflating gas, and at small momenta for a contracting gas. We thereby furnish a Planck-scale sensitive approach to analogue quantum cosmology that can readily be implemented in the quantum gas laboratory.

Figures (6)

• Figure 1: Timeline of comoving horizon $|aH|^{-1}=|\frac{\eta}{v}|$ (corresponding to cosmological scale factor $a\propto |\eta|^v$), and comoving mode propagation prior to reaching current observable CMB scales. A scale-invariant power spectrum can be generated in the early epoch ($\eta<0$), either via inflation ($v=-1$), or via a contraction phase ($v=3$) leading up to bounce (set at $\eta=0$).
• Figure 2: Side-by-side comparison of dispersions corresponding to (a) well-known trans-Planckian models, and (b) quasi-2D dipolar BECs. One can simulate subluminal (e.g., Unruh 1995UnruhPRD) or superluminal (e.g., C-J for Corley-Jacobson 1996Corley.JacobsonPRD) cases by tuning $R$ and $A$. Dispersions with a minimum (such as those appearing in generalizations of the C-J type 2002Brandenberger.MartinIJMPA) can also be modeled via roton minimum tuning (dashed red line) 2006FischerPRA2017Chae.FischerPRL.
• Figure 3: Time evolution of inflation ($v=-1$) and contraction ($v=3$) power spectra $\mathcal{P}_{\delta\phi}$ for various values of relative dipolar strength $R$. The black vertical lines indicate the horizon crossing times ($|k\eta|=1$) corresponding to the low-momentum ($k=10^{-3},10^{-2}$) modes considered here. The scale-invariance duality is preserved for $R=0$, and broken for $R>0$.
• Figure 4: Scale dependence of the superhorizon power spectrum $P_{\delta\phi}$ corresponding to low-momentum ($k\ll1$) modes for inflation (black line) and contraction (dashed lines). Lorentz violation tilts the spectrum at small $k$ exclusively for contraction; to a blue tilt for $0<R<R_c$ and a red tilt at $R_c\sim0.835$.
• Figure 5: Modified dispersion $kW_k^{1/2}$ (y-axis) with respect to wavenumber $k$ (x-axis) for fixed dipolar strength $R=R_c$ (Unruh value) and various values of the scale factor $a$ and dimensionless sound speed $A$. The dashed black line corresponds to the standard Lorentz-invariant dispersion. On suppressing the free-particle term completely ($A\to\infty$), the dispersion exactly captures cosmological transplanckian dynamics wherein Lorentz-violation dominates the early stages of expansion ($a\sim1$) and the late stages of contraction ($a\ll1$). For small values of $A$, the free-particle term dominates large-$k$ modes as expansion proceeds ($a>1$) or in the early-stages of collapse ($a\sim 1$).