# Higgs Vacuum Metastability - Overview Of Its Cosmological Aspects

Higgs vacuum metastability suggests that it is feasible and inevitable that a vacuum decay will occur with disastrous repercussions for the universe. This decay will take happen at some point in the future.

Several reasons might have caused the electroweak vacuum to degrade in the early Universe.

Higgs vacuum metastability may only be examined in the context of cosmology, considering the Universe's limited age.

The vacuum decay may occur in three ways, just as in any other quantum system. The transition will occur through quantum tunneling if the system is initially in a fake vacuum.

If enough energy is available, the system may be able to move classically past the barrier.

COPYRIGHT_OAPL: Published on https://www.oapublishinglondon.com/haha/higgs-vacuum-metastability/ by Alexander McCaslin on 2022-08-06T19:39:30.244Z

## Potential Effectiveness In Flat Spacetime

The prospect of quantum corrections undermining a classically stable vacuum has long been understood.

The potential instability in the Standard Model is only one example of a more generic issue that may also emerge in many other fundamental particle theories. Unbounded potential from below is a troublesome idea.

According to Yukawa's theory, a barrier will divide the low-field vacuum from an endlessly deep well on the opposite side.

This suggests that the lowest energy is indeed constrained from below, and quantum corrections produce a second local minimum beyond the barrier.

In general, the lower the logarithms, the more precise the outcome. In the Yukawa theory, any given scale option would only operate well across a restricted range of field values for the one-loop potential.

Theoretically, the size might be chosen to maximize the perturbative expansion such that the loop corrections are negligible.

In more realistic theories, choosing a function that perfectly cancels the loop correction is often impractical.

Instead, one picks a simpler function that makes the loop correction small enough. The renormalization group improvement effective potential is unbounded from below at high field values for arbitrarily tiny positive perturbations.

This is because g(μ) is a monotonically rising function, and greater loop corrections become highly crucial around the critical value.

The Standard Model contains considerably more particles than the basic Yukawa theory, but the primary rationale for potential vacuum instability remains the same.

The impact in the Standard Model is primarily due to the top quark, which is by far the heaviest and has the greatest Yukawa coupling.

The center values of the Standard Model couplings enable extrapolation to energy scales around the Planck scale. They are incompatible with the circumstance in which the electroweak vacuum is the lowest energy state.

The whole corpus of studies investigating features of vacuum instability is extensive. The most recent computation for ruDecaynning Standard Model parameters uses two-loop matching conditions, three-loop renormalization group development, and four-loop pure QCD corrections.

The bands indicate uncertainty of up to three from the Higgs mass, the top quark, and the vital coupling constants. A lower value is obtained using the unimproved one-loop effective potential with parameters renormalized at the electroweak scale.

## Expanding Universe Field Theory

We must use a method that includes gravitational effects to examine the repercussions of Higgs metastability. This is possible in a curved spacetime utilizing the framework of quantum field theory.

The line element reduces the Einstein equation to the Friedmann equations. The scalar curvature of gravity, represented as a function of the state parameter and the Hubble rateR, will be the essential quantity defining gravitational phenomena.

When the theory is not accessible, interactions will prohibit the creation of arbitrarily significant fluctuations through backreaction.

Because of the infrared divergence, there is no perturbative expansion based on a non-interacting propagator. In many methods, quantum field theory may be applied to de Sitter space.

One main method is to use approaches based on two-particle-irreducible diagrams. These are non-perturbative resummations of several types of Feynman diagrams.

The Higgs field produces a non-zero value, which is sometimes referred to as condensate.

In the Fokker-Planck equation, ultraviolet modes also contribute to the effective potential. It is substantially more challenging to calculate the effective potential of a quantized scalar field on a curved backdrop.

This is because the idea of a particle in curved space is no longer well-defined globally. A curved spacetime produces extra operators that relate to the scalar field.

The appropriate scale choice with a curved backdrop is heavily influenced by curvature. In the flat space situation, we may write the renormalization group improvement effective potential by selecting an optimum scale with a modest loop correction.

Curved space may have dramatically different predictions than flat space. The most noticeable distinction is the appearance of a direct non-minimal link between the Higgs and scalar curvature.

This may have a significant stabilizing or destabilizing influence in the early Universe.

## Decay In Vacuum

- Bubble Nucleation and Quantum Tunneling: The Standard Model's primary mechanism for vacuum decay is simply an extension of quantum tunneling to quantum field theories. The wave-function for particles trapped by a potential barrier may traverse the classically prohibited barrier area in conventional quantum mechanics, resulting in a non-zero chance of being detected on the opposite side. The decay rate is proportional to the action. The Euclidean action dictates the disintegration rate of this nucleated "true-vacuum" bubble. The pre-factor is the difference between the activity of a so-called bounce solution and that which rests in the fake vacuum. In the Standard Model, precise calculations of Euclidean action include estimating the fluctuations around the bounce solution of all fields that pair to the Higgs.
- Zero-Temperature Flat Spacetime: The bounce solution in flat space corresponds to a saddle point of the Euclidean action with one negative eigenvalue. Because the equation is exponentially dependent on the bounce action, only the bounce solutions with the lowest action will contribute. A non-minimal Higgs curvature coupling value alters the action and geometry of the bounce solution. The existence of a tiny black hole may promote vacuum decay, making it quicker. The catalysis of vacuum decay does not exclude cosmological theories, including primordial black holes. The vacuum decay rate becomes unaffected for black holes.
- Temperature Non-Zero: The presence of a heat bath with a temperature greater than zero has a considerable effect on the vacuum decay rate. Thermal fluctuations contribute positively to the quadratic term at the one-loop level. This increases the height of the potential barrier, which seems to slow the decay rate. The solution becomes independent of Euclidean time at the high-temperature limit and has the meaning of a sphaleron configuration.
- De Sitter Space Vacuum Decay: The theorem assures symmetry of the bounce no longer applies when expanding from flat to curved space. However, some evidence suggests symmetric solutions should still prevail in background metrics that obey this symmetry. This would cover the exciting specific situation of an inflationary, or de Sitter, backdrop. A Wick rotated metric may be inserted in a coordinate system to reveal the bounce's symmetry quickly. The bounces are compact and never approach the fake vacuum. The Coleman-de Luccia instanton, which explains quantum tunneling via potential barriers, dominates vacuum decay at Hubble rates. The Hawking-Moss instanton is the dominating mechanism above this. As vacuum decay channels, oscillating solutions have a greater action and are dominating.
- Negative Eigenvalues: Fluctuations around a bounce solution are examined in the gravitational situation. All of these are satisfied in a flat area. In flat space, symmetric bounce solutions may be demonstrated to have at least one negative eigenvalue. This is because they have zero modes, which correspond to translations of the bounce across space-time. An endless tower of high frequency, fast oscillating fluctuations with all negative eigenvalues exists. Because Q = 1 in flat space, it is evident that these "rapidly oscillating" modes are related to the gravitational sector.
- Bubbles After Nucleation Evolution: The bounce solution provides the configuration through which the vacuum state tunnels and establishes the beginning circumstances for its further development. In standard quantum physics, following tunneling, a particle with energy E emerges on the genuine vacuum side of the barrier at x2(E). The field appears in de Sitter space in a configuration corresponding to a slice halfway through the bounce solution (in Euclidean time). Bounces at limited temperature correspond to periodic bounces in Euclidean space. In this example, the temperature is the Gibbons-Hawking temperature of de Sitter space. The Euclidean 4-sphere is an analytic extension of De Sitter space back to de Sitter. This is because the metric is conformally flat in these coordinates, as it is in flat space.

## Constraints Of Cosmology

### History Of Universe

The Universe has to end up in the metastable electroweak-scale state for it to be in a metastable state right now.

The Higgs boson decay rate has to be slow enough that no bubbles of genuine vacuum nucleated in our former light cone.

The scale factor satisfies the Friedmann Equation, and the total energy density may be represented as a function of the scale factor.

The predicted number of bubbles is described in the prior lightcone as an equation using the Friedmann–Lemaître–Robertson–Walker metric. The pace of bubble nucleation may have varied considerably in the Universe's early history.

It is determined by the curvature of spacetime and the temperature, as well as any disturbances or non-equilibrium events that may catalyze or activate the decay process.

### Late Universe

Based on the nucleation rate, theories may be classified as stable, metastable, or unstable. If the rate surpasses the constraint, the Universe would not have lasted till now, and the vacuum is thought to be unstable.

The blue dashed line is the instability limit derived by accounting for the Universe's thermal history and assuming a high reheat temperature. Even if the predicted number of bubbles is huge, there is always a non-zero chance that no bubbles will form.

Because anthropic reasoning does not rule out bubbles striking us in the future, assuming the Universe lives for another length of time, it sets a limit that is not susceptible to the anthropic principle.

The quantity that counts in this case is the time derivative of the predicted number of bubbles.

### Universe Inflation

The rate of vacuum decay was substantially faster in the early Universe. It may be high enough to violate the constraint depending on the circumstance, and this can be used to restrict theories.

Higgs inflation is the minimum inflationary model, with a strong non-minimal curvature coupling of the Higgs field. This enables it to act as inflation without requiring a separate inflaton field.

In most models, inflation has a limited duration. The survival probability Psurvival is often used to explain vacuum stability during inflation.

It is defined as the percentage of volume remaining in the metastable vacuum after inflation. The constraints may be used to restrict the Hubble rate during inflation and other theoretical parameters.

This is accomplished by either utilizing the instanton tunneling rate calculation or the stochastic Starobinsky-Yokoyama technique.

Inflationary fluctuations in the Higgs field would cause the Hubble field to cross the potential barrier, resulting in vacuum instability. The Hubble rate would thus have an approximate upper limit.

The vacuum's survival probability per unit of time is not preserved but diminishes with time. The applicable instanton solution for Hubble rates around the bar is the Hawking-Moss instanton.

During inflation, high spacetime curvature changes the effective potential at the tree level. The non-minimal coupling produces a curvature-dependent effective mass.

The non-minimal curvature coupling is an extension of the Higgs-inflaton coupling. Because the inflaton field has a large value during inflation, the coupling creates an effective mass term for the Higgs field.

### Universe Reheating

The end of inflation is when the Universe no longer expands at an accelerating pace. This is the start of the so-called reheating phase.

When the energy density of the hot Big Bang exceeds that of the inflaton sector, reheating is considered complete.

A single-field inflation model is assumed with a canonical kinetic term and the potential.

When the gravitational backreaction barrier is achieved, particle creation will halt. Lattice field theory simulations were used to do more comprehensive computations on the process.

## People Also Ask

### Is The Higgs Field Metastable?

The Higgs field is not metastable in the notion of a false vacuum. It is energy-dependent and symmetric for high energies of the interactions involved (order of 100 GeV) and broken at lower energies.

### Is The Higgs Field A False Vacuum?

The Higgs field is assumed to be in a metastable condition, which means that although it is not presently changing, it is also not expected to be at its lowest energy level.

It's a phony vacuum with a lot of energy.

### Will The Higgs Boson Cause Vacuum Decay?

The Higgs field would burst out of its fake vacuum when the delicate equilibrium between quantum particles broke down, causing a domino reaction across the cosmos known as vacuum decay.

A bubble of vacuum decay would spread at the speed of light across the cosmos.

### What Is Vacuum Metastability?

A universe in a false vacuum condition is referred to as "metastable" since it is not actively disintegrating (rolling) but is also not entirely stable.

## Final Words

Higgs vacuum metastability in the late Universe yields limits on the Higgs and top masses, which are tightened by considering the hot radiation-dominated phase.

If the electroweak vacuum is metastable, bubbles of the genuine, negative-energy vacuum may be nucleated by quantum tunneling or classical excitation.

Once generated, a bubble spreads at the speed of light, killing everything in its path. Cosmological vacuum decay provides a unique relationship to gravity through the early Universe, opening scientists an observational window well beyond the capabilities of colliders.

The non-minimal coupling for chaotic quadratic inflation is restricted to be in the range 0.06 - 5, which is 15 orders of magnitude larger than the experimental limits from the Large Hadron Collider.