Eternal inflation bubble collision signature on CMB remote dipole and quadrupole fields

TL;DR

This work derives the first analytic expression for the remote quadrupole field (RQF) signal produced by an eternal-inflation bubble collision and validates it against a new public code, RemoteField, which numerically computes RDF/RQF signals from a given primordial potential. By combining this with prior RDF results, the authors forecast constraints on bubble-collision parameters $A$ and $B$ using RDF/RQF reconstructions from next-generation data (CMB-S4 and LSST), finding the RQF E-mode quadrupole can tighten constraints by about an order of magnitude relative to the RDF dipole. They show that tomographic techniques, reducing the $\\\Lambda$CDM variance, could further improve sensitivity by a factor of a few to an order of magnitude, highlighting the potential of RDF/RQF to probe other superhorizon physics such as cosmic topology and domain walls. The framework offers a path to leverage small-scale CMB–galaxy correlations to access large-scale primordial signals beyond cosmic variance, with broad applicability to beyond-Standard-Model cosmology.

Abstract

The remote dipole and quadrupole fields (RDF/RQF) encode information about the observable universe as seen from remote places within our past light cone. Sensitive to the superhorizon inhomogeneites, they provide a unique way to probe physics at the largest scales, bypassing the limitations of cosmic variance inherent in the primary cosmic microwave background (CMB). In this work, we focus on the bubble collision predicted by the eternal inflation theory, which can leave distinct azimuthally symmetric patterns on the superhorizon scales, potentially detectable through the RDF and RQF. We present the first analytic expression of the RQF signal induced by bubble collision and validate it against numerical calculations performed with $\texttt{RemoteField}$, a new public software tool we developed, finding excellent agreement between the two. Combining our new RQF calculation with the corresponding RDF signal calculated by prior work, we forecast the constraining power on bubble collision parameters using RDF/RQF reconstruction. We find that, for an CMB-S4-like and an LSST-like experiment, the RDF reconstruction can provide comparable constraining power as that from the primary CMB alone; and the RQF reconstruction can improve the constraining power by about an order of magnitude. We argue that these constraints can be improved further by including more RDF/RQF multipoles included and by using tomographic techniques to mitigate the standard $Λ$CDM signal. We anticipate the framework we developed in this work to be broadly applicable to probe other superhorizon-scale physics, such as cosmic topology and domain walls.

Figures (7)

• Figure 1: Schematic diagrams showing different regions in the comoving space relevant to the bubble collision with $Z_c = 0.8$ from two different angles of view. The large yellow sphere and the large blue sphere depict our LSS and the electrons at $Z_e=7$ respectively. The flat surface represents the boundary with the upper region affected by the bubble collision and the lower region unaffected. The small spheres denote the electron LSS of three typical cases: entirely outside the region affected by the bubble collision (green), intersecting with the boundary (red), and lying entirely with in the region affected by the bubble collision (orange).
• Figure 2: The remote quadrupole field induced by the bubble collision with $Z_{c}=1$. In a coordinate that has the z-axis aligned with the direction of the collision, we plot the 1-D RQFs observed by the electrons at $Z_e = 0, 1, 2, 4$ as functions $\theta_{e}$. The total RQF is the sum of the SW, Doppler, and ISW contributions as given in Eq. \ref{['eq:q_SW']}, Eq. \ref{['eq:q_Doppler']}, and Eq. \ref{['eq:q_ISW']}, respectively. The orange curves are for $A=1, B=0$, and the blue curves are for $B=1, A=0$. The RQF approaches zero when $\theta_{e}\rightarrow 0$ and $\theta_{e}\rightarrow \pi$ because of the spin-weighted spherical harmonics ${}_{2}Y_{2 0}$. $q$ is dimensionless, as a fraction of the speed of light $c$.
• Figure 3: Same as Fig. \ref{['fig:RQF zc=1']}, the remote quadrupole field caused by the bubble collision for $Z_{c}=2$. The orange curves are for $A=1, B=0$ , and the blue curves are for $B=1, A=0$.
• Figure 4: The RQF field distribution induced by the bubble collision contributed by SW, Doppler and ISW effects from the analytic calculation (solid lines) and from numerical calculation generated by RemoteField (dashed lines) with $Z_c=1$, $Z_e=2$ and $A=10^{-5}, B=A=10^{-5}$. It shows an excellent agreement between the two sets of result.
• Figure 5: A numerically-calculated RQF induced by the bubble collision at $Z_e=2$ for $Z_c=1$ with $A=10^{-5}$ and $B=10^{-5}$. The left panel shows the spherical distribution viewed from 3D perspective, and the right panel shows the corresponding Mollview map. They clearly show the azimuthal symmetric pattern.