Cosmological Consequences of Domain Walls Biased by Quantum Gravity

TL;DR

The paper investigates how quantum gravity can explicitly break a discrete ${\mathbb Z}_2$ symmetry, biasing domain walls formed by a real singlet S and driving their annihilation. Using a minimal model with dimension-five QG operators at scale $\Lambda_{\rm QG}$, the authors connect domain-wall annihilation to a spectrum of cosmological outcomes: dark radiation, potential early matter domination, particle dark matter production, a stochastic gravitational-wave background, primordial black holes, and even classical wormholes to baby universes. They derive expressions for the wall tension $\sigma$, bias $V_{\rm bias}$, and the annihilation fraction $\alpha_{\rm ann}$, and show how these control the observable signals, subject to constraints from $\Delta N_{\rm eff}$, GW measurements, and PBH limits. The work highlights that high-scale quantum gravity effects can imprint measurable low-energy cosmology, offering a suite of tests for future GW detectors, DM searches, and probes of the early universe, including a provocative multiverse scenario via baby universes. Overall, the paper provides a coherent framework linking swampland-inspired symmetry breaking to a broad set of cosmological phenomena with clear experimental consequences.

Abstract

One of the simplest standard model extensions leading to a domain wall network is a real scalar $S$ with a $Z_2$ symmetry spontaneously broken during universe evolution. Motivated by the swampland program, we explore the possibility that quantum gravity effects are responsible for violation of the discrete symmetry, triggering the annihilation of the domain wall network. We explore the resulting cosmological implications in terms of dark radiation, dark matter, gravitational waves, primordial black holes, and wormholes connected to baby universes.

Figures (6)

• Figure 1: A schematic illustration of the main ideas explored in this paper. A global ${\cal Z}_2$ symmetry in the dark sector is broken by QG effects leading to a biased DW network, which annihilates and generates Particles, GWs, or PBHs. Relativistic particles can contribute as Dark Radiation to $\Delta N_{\rm eff}$ (Sec. \ref{['sec:particleprod']}). Non-relativistic particles can contribute to DM (Sec. \ref{['sec:darkmatter']}) if stable or to an Early Matter Era if unstable and sufficiently abundant (Sec. \ref{['sec:matter_era']}). GWs can be tested in current and future interferometers (Sec. \ref{['sec:GW formation']}). PBHs arise from super-horizon DWs that annihilate sufficiently later than the others, allowing them to grow large enough to be contained within their Schwarzschild radius (Sec. \ref{['sec:PBH formation']}). Wormholes enter this picture in two distinct ways. First, virtual wormholes --- arising in the path integral in QG --- can serve as non-perturbative sources of global symmetry breaking Giddings:1987cgMaldacena:2004rfArkani-Hamed:2007cpnHebecker:2018ofvVanRiet:2020pcnDaus:2020vtf. Second, classical wormholes can form within Einstein gravity when DWs inflate into "baby universes" (Sec. \ref{['sec:wormhole_formation']}). This occurs if the DWs grow larger than the Hubble horizon of the universe dominated by the vacuum bias $V_{\rm bias}$, experienced by observers located inside the DW. In this scenario, the DW induces a classical wormhole geometry connecting the PBH to the baby universe. Being eternally-inflating, those baby universe leads to the existence of a multiverse. In short, we are left with the intriguing sequence of events where virtual wormholes are potentially responsible for the discrete symmetry breaking that sets the stage for classical wormholes connecting our universe to a multiverse.
• Figure 2: The GW spectra in Eq. \ref{['eq:GW_DW_ann']} originating from the annihilation of domain walls together with the sensitivities reached by the different on-going (solid) and planned (dotted) GW experiments and the expected astrophysical GW foregrounds (see text for details). Model 1 can explain the recently detected NG15 signal NANOGrav:2023gorGouttenoire:2023ftk, while models 2 and 3 can explain 100$\%$ of DM in terms of PBHs produced from DW annihilation, see Tab. \ref{['tab:table_values']} for more details. The three benchmark models are also indicated with stars $\star$ in Fig. \ref{['fig:BrokenZ2_QG_PBHs']}.
• Figure 3: Model-independent cosmological consequences of a DW network annihilating with energy fraction $\alpha_{\rm ann}=\rho_{\rm DW}/\rho_{\rm rad}$ under the effect of a bias energy density $V_{\rm bias}$. The light gray region shows the BBN constraints in Eq. \ref{['eq:Delta_N_eff_app']}. The dashed blue regions show the GW constraints including the astrophysical foregrounds, which are displayed in Fig. \ref{['fig:fit-DW2']}. We show the regions for which PBHs are excluded by CMB observations Ali-Haimoud:2016mbvPoulin:2017bweSerpico:2020ehh (yellow), LIGO-Virgo-Kagra LIGOScientific:2019kanDeLuca:2020qqa (blue), microlensing constraints CalchiNovati:2013jpjCalchiNovati:2013jpjNiikura:2017zjdSmyth:2019whbSugiyama:2019dgt (purple) with the two super-imposed dotted regions being the best-fit of the PBH interpretation for HSC and OGLE events Niikura:2019kqiSugiyama:2021xqgKusenko:2020pcg. The brown boundary can explain 100$\%$ of DM. In the red region, Hawking evaporation leads to an overproduction of cosmic rays DeRocco:2019fjqLaha:2019ssqKeith:2021guqCarr:2009jmBoudaud:2018hqbLaha:2020ivkDasgupta:2019caeCoogan:2020tufKorwar:2023kpy, yet it may also contribute to the $511~\rm keV$ excess indicated in greenDeRocco:2019fjqLaha:2019ssqKeith:2021guq. Finally, the lack of observed energy injection from Hawking radiation in the CMB Poulin:2016anjStocker:2018avmPoulter:2019ooo and BBN Carr:2009jmAcharya:2020jbvKeith:2020jww excludes the yellow and green regions. Above the dashed purple line, at least one baby universe is produced in our past lightcone $f_{\rm baby}>1$ leading to the possibility of a multiverse Linde:2015edk. Above the dashed green line, PBHs dominate the energy density of the universe before evaporating $\beta>\beta_c$. We chose $\ell \equiv L/t = 0.8$ in Eq. \ref{['eq:F_function_PBH']}, a conservative value in terms of PBH production. In the dark gray region on the right, the DW formation temperature is larger than the maximal temperature allowed by BICEP/Keck BICEP:2021xfz$T_{\rm form}>T_{\rm max}$, see Eq. \ref{['eq:T_max']}. These constraints are applied to the $\mathbb{Z}_2$ singlet with Quantum Gravity bias in Fig. \ref{['fig:BrokenZ2_QG_PBHs']}.
• Figure 4: Application of the $N_{\rm eff}$, GW, PBH constraints and baby universe efficient production regions of Fig. \ref{['fig:DW_generic']} to the parameter space of the $\mathbb{Z}_2$-symmetric singlet broken by QG, cf. Eq. (\ref{['eq:combination']}). In the top-right gray triangle, DW networks annihilate after dominating the universe, which would lead to a universe very different from ours. On the boundary of it, DW networks annihilate with a significant energy density fraction, leading to efficient particles, GWs, PBHs and baby universe production. In contrast to Fig. \ref{['fig:DW_generic']} where the constraints on GW from DW annihilation assume that the astrophysical foreground -- shown in gray in Fig. \ref{['fig:fit-DW2']} -- can not be subtracted (pessimistic approach), the GW constraints of the present plot assume complete astrophysical foreground subtraction (optimistic approach). Along the dashed orange lines labeled "Particle DM" the scalar particles $s$ can be produced from DW annihilation with the observed relic abundance, see Sec. \ref{['sec:darkmatter']}.
• Figure 5: Production of baby universes by DW networks. This arises when a closed DW configuration -- modeled to be spherical and shown with the black circle -- becomes larger than the Hubble horizon $H_b^{-1}$ of a universe dominated by the bias energy $V_{\rm bias}$ -- shown with the dashed purple circle and given by Eq. \ref{['eq:H_b']}. The orange arrows represent the pressure $V_{\rm bias}+\sigma/R$ driving the DW to locally move inward in the comoving coordinates experienced by an observed located close to the DW. The purple arrows show the volume expansion induced by the bias energy $V_{\rm bias}$ acting as a cosmological constant in the bulk.