Entanglement between pair-created twin universes with opposite time arrows should leave a birthmark on CMB spectrum

Abstract

Why (and how) the Universe was born is one of the ultimate questions in physics. Another big puzzle is about the arrow of time: why is there only one direction of time? Are these two issues related? One way to solve both puzzles at one stroke is to posit that our universe was pair-created with a twin, whose time arrow is opposite to ours. If so, then the twins must naturally be quantum entangled. In Euclidean quantum gravity, this implies the existence of a Euclidean wormhole bridging the twin universes. Each universe is then in a mixed-state and the mutual entanglement shall leave signatures in the cosmic microwave background (CMB) power spectrum. Invoking the Klebanov-Susskind-Banks wormhole as a toy model for the sake of tractability, we show that the entanglement selects a novel and unique global vacuum for the total inflaton perturbations in both universes. This is equivalent to imposing a simple harmonic oscillator boundary condition on the Euclidean wavefunction of the total perturbations, and it turns out that the entanglement enhances the CMB power spectrum for long-wavelength modes. Such a birthmark renders our notion refutable.

Figures (3)

• Figure 1: Universes I and II are connected by a wormhole at $\dot{a}(\tau_{\mathrm{I,II}})=0$. Depending on the model, the throat may be smoothed out, however, at the cost of losing analytic analysis.
• Figure 2: Modification of normalized temperature anisotropy spectrum due to the entanglement between the twin universes based on Eq. \ref{['Pn-ew']}. Here, we assume that the universe was initially nucleated as dS, and after the horizon crossing ($y\ll 1$), it transitioned to power-law expansion. Since the entanglement originated before inflation, $\lambda$ in Eq. \ref{['rn']} should be determined by the cosmological constant before the transition, while $P_{\mathrm{BD}}$ acquires time-dependence due to the power-law expansion after the transition. (For $n\gg 1$, $l\sim kd_{\mathrm{LSS}}\sim (d_{\mathrm{LSS}}/R_{c})n\sim 0.1 n$.) We used CAMB lewis2011camb for the calculation.
• Figure 3: Entanglement entropy between perturbations across a Euclidean wormhole. The larger $\lambda\delta$ is, the shorter the wormhole's length $(\tau_{\mathrm{I}}-\tau_{\mathrm{II}})$, the more the entanglement.