False Vacuum Research Articles

Gravity-improved metastability bounds for the Type-I seesaw mechanism

Right-handed neutrinos (RHN) destabilize the electroweak vacuum by increasing its decay rate. In the SM, the latter is dominated by physics at the RG scale at which λ reaches its minimum, μ∗SM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mu}_{\\ast}^{\ extrm{SM}} $$\\end{document} ∼ 1017 GeV. For large neutrino Yukawa coupling Yν, RHNs can push μ* beyond the Planck scale, implying that gravitational effects need to be taken into account. In this work, we perform the first comprehensive study of electroweak vacuum metastability in the type-I seesaw mechanism including these effects. Our analysis covers both low- and high-scale seesaw models, with two as well as three RHNs and for multiple values of the Higgs’ non-minimal coupling to gravity. We find that gravitational effects can significantly stabilize the vacuum, leading to weaker metastability bounds. We show that metastability sets the strongest bounds for low-scale seesaws with MN> 1 TeV. For high-scale seesaws, we find upper bounds on the allowed masses for the RHNs, which are relevant for high-scale leptogenesis. We also point out that Tr(Yν†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\ u}^{\\dagger } $$\\end{document}Yν), which is commonly used to express these metastability bounds, cannot be used for all of parameter space. Instead, we argue that bounds can always be expressed reliably through Tr(Yν†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\ u}^{\\dagger } $$\\end{document}YνYν†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\ u}^{\\dagger } $$\\end{document}Yν). Lastly, we use this insight to develop a new technique for an easier RG analysis applicable to scenarios with degenerate RHN masses.

A note on the stability of generic spherically symmetric thin-shell wormhole supported by a false vacuum

In the stability analysis of the Schwarzschild thin-shell wormhole (TSW) performed by Poisson and Visser in Poisson and Visser (1995) the equation of state (EoS) of the surface matter on the throat satisfies β2σ=∂p∂σ in which σ and p are the surface energy density and the surface transverse pressure. In this Letter, we show that β2σ=−1 has to be excluded as it results in the radius of the equilibrium a0=3M a radius which was problematic and later on was treated by Varela in Varela (2015). Furthermore, we present a formalism on the mechanical stability of generic spherically symmetric TSWs supported by a surface energy–momentum tensor of the form σ=−p corresponding to β2σ=−1. Such an EoS with σ>0 describes the so-called vacuum matter or dark energy, however, here it is called false vacuum because σ<0. We obtain the general conditions upon which such a TSW remains stable against a mechanical linear perturbation. In particular, we apply our formalism to first the TSW constructed in the Reissner–Nordström (RN) spacetime and then in the Bronnikov–Zaslavskii (BZ) closed black hole. We show that in both cases stable TSW exists, however, for the former TSW, it corresponds to the non-black hole RN solution.

Quantum master equation for the vacuum decay dynamics

The quantum master equation required to describe the dynamics of gravity-related vacuum decay is still challenging. We aim to study this issue. Our model consists of the spacetime and scalar field with self-interaction potential. The environment is chosen as spacetime while the system is formed by the vacua of the scalar field. We demonstrate that the quantum dynamics of the vacua can be described by the Redfield equation, which can depict the evolution of both coherence and the comoving volume fraction of the vacuum. Under the Markovian limit, coherence monotonically decreases with time, leading to the initial quantum state to decohere into a classical state. This helps the understanding of the decoherence of the universe. We also highlight that in certain circumstances, the evolution of the vacuum system may display non-Markovian dynamics. In specific scenarios, the classical limit of the quantum master equation is consistent with the classical master equation. In the steady state, the dominant vacuum corresponds to the smallest cosmological constant, and various dS vacua can reach equilibrium states.

Primordial black holes from strong first-order phase transitions

We study the formation of primordial black holes (PBHs) in strongly super-cooled first-order phase transitions. The mechanism is based on the presence of remnants dominated by the false vacuum that scale slower with the expansion of the Universe than their surroundings where this energy was already converted into radiation. We compute the PBH formation from these remnants including the contribution from the false vacuum and the bubble walls, by estimating the collapse using the hoop conjecture and by considering both regions collapsing immediately when entering the horizon and sub-horizon regions that collapse as their compactness grows. We show that for exponential bubble nucleation rate, Γ ∝ eβt, the primordial black hole formation implies β/H ≳ 3.8, where H denotes the Hubble rate, if the potential energy of the false vacuum is ∆V ≲ (1012 GeV)4, as otherwise a too large abundance of long-lived PBHs forms. The observed dark matter abundance can be formed in asteroid mass PBHs if β/H ≃ 3.8 and 105 GeV ≲ ∆V1/4 ≲ 108 GeV. Finally, we consider also the effect of the second order correction to the exponential nucleation rate showing that the PBH abundance is mainly determined by the average radius of the true vacuum bubbles.

Triggering Higgs vacuum decay

The Standard Model Higgs potential seems unstable at field values h > htop ~ 1010 GeV. Vacuum decay can be triggered by N ~ 4π/λ ~ 1000 overlapped Higgs bosons with energy λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\lambda } $$\\end{document}htop. However, this configuration is stimulated by ultra-high energy collisions with a exp(−O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(N)) suppression, comparable to spontaneous vacuum decay: no ‘Higgspolosion’ enhancement arises. This implies that ultra-high energy cosmic ray collisions are safe, despite that their number (in production sites) likely is tens of orders of magnitude higher than what usually estimated (in space). We speculate on how vacuum decay could be induced classically, forming a in-coming wave of N boosted Higgs bosons at futuristic ultra-high energy colliders, and on how the resulting vacuum bubble could be controlled to extract energy.

(In)stability of de Sitter vacuum in light of distance conjecture and emergence proposal

The distance conjecture claims that as the modulus traverses along the trans-Planckian geodesic distance, the effective field theory becomes invalid by a descent of a tower of states from UV. Moreover, according to the recent (strong version of) emergence proposal, the kinetic term of the modulus is entirely generated by the wavefunction renormalization in which a tower of states are integrated out. Assuming these two conjectures, we explore the role of a tower of states coupled to the modulus in (in)stability of the de Sitter (dS) vacuum by studying the one-loop effective potential generated by a tower of states. We find that a fermionic tower of states makes the effective potential more or less consistent with the dS swampland conjecture: either the slope or the curvature of the potential is sizeable. In contrast, the effective potential generated by a bosonic tower of states seems to allow the stable dS vacuum. Therefore, in order to argue the instability of the dS vacuum, the additional ingredient like supersymmetry breaking needs to be taken into account.

Anisotropic Segre [(11)(1,1)] dark energy following a particular equation of state

A generally anisotropic equation of state originally derived in the context of Newman-Janis rotating systems allows for vacuum energy at a specific density. In this paper we examine the possibility of using that equation of state for cosmological dark energy. We treat the case of large scale ordering of the directions of the energy-momentum tensor eigenvectors with a Bianchi cosmological model, and treat the case where the ordering is random on small scales with an effectively isotropic FLRW system. We find particular spacetimes which evolve towards a vacuum energy/ de Sitter like configuration in either case. In the anisotropic Bianchi case, the system can have behavior reminiscent of big bounce cosmologies, in which the matter content approaches vacuum energy at large scale factor and can behave in a variety of ways at small scale factor. For particular conditions in the effectively isotropic case, we can evolve between true and false vacuum configurations, or between radiation like and vacuum energy configurations. We also show how some simpler equations of state behave under the same assumptions to elucidate the methods for analysis.

Emerging Newtonian potential in pure R2 gravity on a de Sitter background

In [27] Alvarez-Gaume et al. established that pure mathcal{R} 2 theory propagates massless spin-2 graviton on a de Sitter (dS) background but not on a locally flat background. We build on this insight to derive a Newtonian limit for the theory. Unlike most previous works that linearized the metric around a locally flat background, we explicitly employ the dS background to start with. We directly solve the field equation of the action {left(2kappa right)}^{-1}int {d}^4xsqrt{-g}{mathcal{R}}^2 coupled with the stress-energy tensor of normal matter in the form Tμν = Mc2δ( overrightarrow{r} ) {delta}_{mu}^0{delta}_{nu}^0 . We obtain the following Schwarzschild-de Sitter metric d{s}^2=-left(1-frac{Lambda}{3}{r}^2-frac{kappa {c}^2}{48pi Lambda}frac{M}{r}right){c}^2d{t}^2+{left(1-frac{Lambda}{3}{r}^2-frac{kappa {c}^2}{48pi Lambda}frac{M}{r}right)}^{-1}d{r}^2+{r}^2d{varOmega}^2 which features a potential V(r)=-frac{kappa {c}^4}{96pi Lambda}frac{M}{r} with the correct Newtonian tail. The parameter Λ plays a dual role: (i) it sets the scalar curvature for the background dS metric, and (ii) it partakes in the Newtonian potential V(r). We reach two key findings. Firstly, the Newtonian limit only emerges owing to the de Sitter background. Most existing studies of the Newtonian limit in modified gravity chose to linearize the metric around a locally flat background. However, this is a false vacuum to start with for pure mathcal{R} 2 gravity. These studies unknowingly omitted the information about Λ of the de Sitter background, hence incapable of attaining a Newtonian behavior in pure mathcal{R} 2 gravity. Secondly, as Λ appears in V(r) in a singular manner, viz. V(r) ∝ Λ−1, the Newtonian limit for pure mathcal{R} 2 gravity cannot be obtained by any perturbative approach treating Λ as a small parameter.

Probing primordial black holes from a first order phase transition through pulsar timing and gravitational wave signals

In this work, we assess the sensitivity reach of pulsar timing array (PTA) measurements to probe pointlike primordial black holes (PBHs), with an extended mass distribution, which originate from collapsed Fermi balls that are formed through the aggregation of asymmetric U(1) dark fermions trapped within false vacuum bubbles during a dark first order phase transition (FOPT). The PBH formation scenario is mainly characterized by the dark asymmetry, strength of the FOPT, rate of FOPT, and the percolation temperature. Meanwhile, for PBH masses of interest lying within 10−10M⊙ − 102M⊙, the relevant signal for PTA measurements is the Doppler phase shift in the timing signal, due to the velocity change induced by transiting PBHs on pulsars. Taking the dark asymmetry parameter to be 10−4 and 10−5, we find that percolation temperatures within the 0.1 − 10 keV range, FOPT rates above 103 times the Hubble parameter at percolation, and FOPT strengths within 10−6 − 0.1 can give rise to PBHs that can be probed by an SKA-like PTA observation. On the other hand, the accompanying gravitational wave (GW) signal from the FOPT can be used as a complementary probe, assuming that the peak frequency lies within the \U0001d4aa(10−10) − \U0001d4aa(10−7) Hz range, and the peak GW abundance is above the peak-integrated sensitivity curves associated with pulsar timing observations that search for stochastic GWs. At the fundamental level, a quartic effective potential for a dark scalar field can trigger the FOPT. By performing a parameter scan, we obtained the class of effective potentials that lead to FOPT scenarios that can be probed by SKA through pulsar timing and GW observations.

Exact solutions for vacuum decay in unbounded potentials

Exact solutions for vacuum decay in unbounded potentials

Electroweak vacuum decay in metric-affine gravity

We investigate the stability of the electroweak vacuum in metric-affine gravity in which the Standard Model Higgs boson can be non-minimally coupled to both the Ricci scalar and the Holst invariant. We find that vacuum stability is improved in this framework across a wide range of model parameters.

Multi-skyrmion states in the Skyrme model with a false vacuum potential* *Y. L. M. was supported in part by the National Science Foundation of China (11875147, 12147103).

We study multi-skyrmion states using the Skyrme model with a false vacuum potential up to baryon number using the product ansatz. It is found that both the false and true vacuum potentials can result in a cluster structure for the multi-skyrmion states. We also analyze the effect of explicit chiral breaking on the masses and contour surfaces of the baryon number density of the multi-skyrmion states.

Effective field theory of the two Higgs doublet model

We revisit the effective field theory of the two Higgs doublet model at tree level. The introduction of a novel basis in the UV theory allows us to derive matching coefficients in the effective description that resum important contributions from the Higgs vacuum expectation value. The new basis typically provides a significantly better approximation of the full theory prediction than the traditional approach that utilizes the Higgs basis, particularly for alignment away from the decoupling limit.

Gauge theory on fiber bundle of hypercomplex algebras

I introduce a way of constructing a fiber bundle whose fibers are given by hypercomplex algebras and woven by appropriate structure group, and present that a novel gauge theory can be built on the hypercomplex fiber bundle. In this work, I aim to answer a question about how nature selects one preferred vacuum among degenerate physical vacua, called vacuum selection problem. In the end, I found presence of the impenetrable domain wall that prohibits phase transition between the two vacua. To be specific, I found that in this theory, one particular vacuum between two degenerate physical vacua for Higgs-like scalar potential can be dynamically chosen with priority due to intrinsic even parity of both a scalar field and its vacuum under a Z2 symmetry, even though its scalar potential is given to be Z2-symmetric under both odd- and even-parity transformations of the scalar field. This means that the vacuum selection problem can be resolved in this gauge theory. I suggest that this work may be a gateway to addressing the theoretical origin of the true physical vacuum that nature takes.

Higgs Field-Induced Triboluminescence in Binary Black Hole Mergers

We conjecture that the Higgs potential can be significantly modified when it is in close proximity to the horizon of an astrophysical black hole, leading to the destabilization of the electroweak vacuum. In this situation, the black hole should be encompassed by a shell consisting of a “bowling substance” of the nucleating new-phase bubbles. In a binary black-hole merger, just before the coalescence, the nucleated bubbles can be prevented from falling under their seeding horizons, as they are simultaneously attracted by the gravitational potential of the companion. For a short time, the unstable vacuum will be “sandwiched” between two horizons of the binary black hole, and therefore the bubbles may collide and form micro-black holes, which are rapidly evaporated by thermal emission of Hawking radiation of all Standard Model species. This evaporation, being triggered by a gravitational wave signal from the binary black-hole merger, can manifest itself in observations of gamma rays and very-high-energy neutrinos, which makes it a perfect physics case for multi-messenger astronomical observations.

Spontaneous vacuum decay in low-energy collisions of heavy nuclei beyond the monopole approximation

The problem of spontaneous vacuum decay in low-energy collisions of heavy nuclei is considered beyond the scope of the monopole approximation. The time-dependent Dirac equation is solved in a rotating coordinate system with $z$-axis directed along the internuclear line and the origin placed at the center of mass. The probabilities of electron-positron pair creation and the positron energy spectra are calculated in the approximation neglecting the rotational coupling. The two-center potential is expanded over spherical harmonics and the convergence with respect to the number of terms in this expansion is studied. The results show that taking into account the two-center potential instead of its spherically symmetric part preserves all the signatures of the transition to the supercritical regime that have been found in the framework of the monopole approximation and even enhances some of them.

A functional approach to the Van der Waals interaction

We evaluate the quantum interaction energy between two neutral atoms, using a functional integral approach. In our setup, each atom has an electron bound to the nucleus via a harmonic potential. The resulting expression for the vacuum energy becomes the Van der Waals interaction at the first non-trivial order in an expansion in powers of the fine structure constant, encompassing both the long and short distance behaviours. We also explore the opposite, strong-coupling limit, which yields a result for the interaction energy as well as a threshold for the existence of a vacuum decay probability, manifested here as an imaginary part for the effective action. In the weak-coupling limit, we also study the effect of using a general central potential for the internal structure of the atoms.

ANISOTROPIC TILTED SPHERICAL FALSE VACUUM MODEL

In this paper, a tilted spherically symmetric cosmological model with perfect fluid distribution along with heat conduction has been considered. To get a generalized solution, I have assumed the model to be False Vacuum (i.e. ), where p being the isotropic pressure and is the matter density of the fluid. The various physical properties of the model are also discussion as the concluding remark

Gravitational waves from the high temperature electroweak symmetry nonrestoration

The high temperature electroweak symmetry nonrestoration (SNR) opens a window to realize baryogenesis at high energy scales, which can alleviate the tight phenomenological constraints. An effective way to realize the electroweak SNR is to extend the Standard Model (SM) by adding a second Higgs doublet and a few new singlet fermions which interact with the second Higgs through a five-dimension operator. In this scenario, the second Higgs has a nonvanishing vacuum expectation value above the electroweak scale and thus breaks the electroweak symmetry. As the temperature decreases, the SM electroweak phase transition occurs and the Universe is located at SM electroweak vacuum. We show that the electroweak phase transition is the first order and the gravitational waves (GWs) generated during this process can be detected by the future GW experiments such as LISA, TianQin, DECIGO, and BBO.

Cosmic bounce and phantom-like equation of state from tunnelling

We allow a scalar field on a flat FLRW background metric to tunnel between two degenerate vacua. The resulting true vacuum state then violates the Null Energy Condition, and the corresponding homogeneous fluid induces a bounce, after which it has a phantom-like equation of state and asymptotically leads to a de Sitter phase. The mechanism presented here requires no exotic matter or modified gravity, it is purely generated by quantum fluctuations and is valid for a generic double well potential.