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Register a new userFalse vacuum as an unstable state: possible cosmological implications
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Added by
Krzysztof Urbanowski
Publication date
2013
fields
Physics
and research's language is
English
Authors
K. Urbanowski
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Recent LHC results concerning the mass of the Higgs boson indicate that the vacuum in our Universe may be unstable. We analyze properties of unstable vacuum states from the point of view of the quantum theory of unstable states. From the literature it is known that some of false vacuum states may survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time $t$ has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t to infty$. Properties of the instantaneous energy at transition times are also analyzed for a given model. It is shown that at this time region large and rapid fluctuations of the instantaneous energy take place. This suggests analogous behavior of the cosmological constant at these time regions.
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We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power--like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t to infty$. This means that the energy density in the unstable vacuum state should have analogous properties and hence the cosmological constant $Lambda = Lambda (t)$ too. The conclusion is that $Lambda$ in the Universe with the unstable vacuum should have a form of the sum of the bare cosmological constant and of the term of a type $1/t^{2}$: $Lambda(t) equiv Lambda_{bare} + d/ t^{2}$ (where $Lambda_{bare}$ is the cosmological constant for the Universe with the true vacuum).
We study the cosmology with the running dark energy. The parametrization of dark energy with the respect to the redshift is derived from the first principles of quantum mechanics. Energy density of dark energy is obtained from the quantum process of transition from the false vacuum state to the true vacuum state. This is the class of the extended interacting $Lambda$CDM models. We consider the energy density of dark energy parametrization $rho_text{de}(t)$, which follows from the Breit-Wigner energy distribution function which is used to model the quantum unstable systems. The idea that properties of the process of the quantum mechanical decay of unstable states can help to understand the properties of the observed universe was formulated by Krauss and Dent and this idea was used in our considerations. In the cosmological model with the mentioned parametrization there is an energy transfer between the dark matter and dark energy. In such a evolutional scenario the universe is starting from the false vacuum state and going to the true vacuum state of the present day universe. We find that the intermediate regime during the passage from false to true vacuum states takes place. The intensity of the analyzed process is measured by a parameter $alpha$. For the small value of $alpha$ ($0<alpha <0.4$) this intermediate (quantum) regime is characterized by an oscillatory behavior of the density of dark energy while the for $alpha > 0.4$ the density of the dark energy simply jumps down. In both cases (independent from the parameter $alpha$) the today value of density of dark energy is reached at the value of $0.7$. We estimate the cosmological parameters for this model with visible and dark matter. This model becomes in good agreement with the astronomical data and is practically indistinguishable from $Lambda$CDM model.
We describe here how the late time behavior of the decaying states, which is predicted to deviate from an exponential form, while normally of insignificant consequence, may have important cosmological implications in the case of false vacuum decay. It may increase the likelihood of eternal inflation, and may help explain the likelihood of observing a small vacuum energy at late times, as well as arguing against decay into a large negative energy (anti-de Sitter space), vacuum state as has been motivated by some string theory considerations. Several interesting open questions are raised, including whether observing the cosmological configuration of a metastable universe can constrain its inferred lifetime.
We study the dynamics of false vacuum bubbles. A nonminimally coupled scalar field gives rise to the effect of negative tension. The mass of a false vacuum bubble from outside observers point of view can be positive, zero, or negative. The interior false vacuum has de Sitter geometry, while the exterior true vacuum background can have geometry depending on the vacuum energy. We show that there exist expanding false vacuum bubbles without the initial singularity in the past.
In this review we present a theory of cosmological constant and Dark Energy (DE), based on the topological structure of the vacuum. The Multiple Point Principle (MPP) is reviewed. It demonstrates the existence of the two vacua into the SM. The Froggatt-Nielsens prediction of the top-quark and Higgs masses is given in the assumption that there exist two degenerate vacua in the SM. This prediction was improved by the next order calculations. We also considered B.G. Sidharths theory of cosmological constant based on the non-commutative geometry of the Planck scale space-time, what gives an extremely small DE density providing the accelerating expansion of the Universe. Theory of two degenerate vacua - the Planck scale phase and Electroweak (EW) phase - also is reviewed, topological defects in these vacua are investigated, also the Compton wavelength phase suggested by B.G. Sidharth was discussed. A general theory of the phase transition and the problem of the vacuum stability in the SM is reviewed. Assuming that the recently discovered at the LHC new resonance with mass $m_S simeq 750$ GeV is a new scalar $S$ bound state $6t + 6bar t$, earlier predicted by C.D. Froggatt, H.B. Nielsen and L.V. Laperashvili, we try to provide the vacuum stability in the SM and exact accuracy of the MPP.
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