The purpose of this paper is to introduce a new way to inquire the quantum cosmology for a certain gravitational theory. Normally, the quantum cosmological model is introduced as the minisuperspace theory which is obtained by reducing the superspace where the Wheel-DeWitt equation is defined on using the symmetry provided by cosmological principle. Unlike that, the key of our approach is to reinterpret the cosmology in a classical dynamical way using a point-like Lagrangian and then quantize the point-like model. We apply the method into Einstein gravity, gravity with a cosmological constant and the $f(R)$-gravity, and get their wave equations respectively. By analsysing the exact solution for the quantum cosmology with and without a cosmological constant we demonstrate that the cosmological constant is essential and being a tiny positive number. We also show the possibility of explaining inflation under the quantum version of cosmology.
We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $ϕ^2(iϕ)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\varepsilon$-expansion. Particular attention is therefore paid to the two interesting cases $\varepsilon=1,2$, and the one-loop beta functions for the coupling associated with the interaction $iϕ^3$ and $-ϕ^4$ are computed. It is found that the $-ϕ^4$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived.
Freeze-in via the axion-photon coupling, $g_{\phi\gamma}$, can produce axions in the early Universe. At low reheating temperatures close to the minimum allowed value $T_{\rm reh}\approx T_{\rm BBN}\approx 10\,{\rm MeV}$, the abundance peaks for axion masses $m_\phi\approx T_{\rm reh}$. Such heavy axions are unstable and subsequently decay, leading to strong constraints on $g_{\phi\gamma}$ from astrophysics and cosmology. In this work, we revisit the computation of the freeze-in abundance and clarify important issues. We begin with a complete computation of the collision terms for the Primakoff process, electron-positron annihilation, and photon-to-axion (inverse-)decay, while approximately taking into account plasma screening and threshold effects. We then solve the Boltzmann equation for the full axion distribution function. We confirm previous results about the importance of both processes to the effective "relic abundance" (defined as density prior to decay), and provide useful fitting formulae to estimate the freeze-in abundance from the equilibrium interaction rate. For the distribution function, we find an out-of-equilibrium population of axions and introduce an effective temperature for them. We follow the evolution right up until decay, and find that the average axion kinetic energy is larger than a thermal relic by between 20\% and 80\%, which may have implications for limits on decaying axions from X-ray spectra. We extend our study to a two-axion system with quartic cross-coupling, and find that for typical/expected couplings, freeze-in of a second axion flavour by annihilations leads to a negligibly small contribution to the relic density.
False vacuum decay is the first-order phase transition of fundamental fields. Vacuum instability plays a very important role in particle physics and cosmology. Theoretically, any consistent theory beyond the Standard Model must have a lifetime of the electroweak vacuum longer than the age of the Universe. Phenomenologically, first-order cosmological phase transitions can be relevant for baryogenesis and gravitational wave production. In this thesis, we give a detailed study on several aspects of false vacuum decay, including correspondence between thermal and quantum transitions of vacuum in flat or curved spacetime, radiative corrections to false vacuum decay and, the real-time formalism of vacuum transitions.
A bstract Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green’s functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.
We study the renormalization of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction ${\ensuremath{\phi}}^{2}(i\ensuremath{\phi}{)}^{ϵ}$ using the Wilsonian approach and without any expansion in $ϵ$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalizable at the one-loop level only for integer values of $ϵ$, a result which is not yet established within the $ϵ$-expansion. Particular attention is therefore paid to the two interesting cases $ϵ=1,2$, and the one-loop beta functions for the coupling associated with the interaction $i{\ensuremath{\phi}}^{3}$ and $\ensuremath{-}{\ensuremath{\phi}}^{4}$ are computed. It is found that the $\ensuremath{-}{\ensuremath{\phi}}^{4}$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived.
While $CP$ violation has never been observed in the strong interactions, the QCD Lagrangian admits a $CP$-odd topological interaction proportional to the so called $\theta$ angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of $\theta$ against the phases of the quark masses, which constitutes the strong $CP$ problem. Here we report on recent challenges to this view based on a careful treatment of boundary conditions in the path integral and of the limit of infinite spacetime volume, which leads to $\theta$ dropping out of fermion correlation functions and becoming unobservable, implying that $CP$ is preserved in QCD.
We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.
Abstract Accurately determining bubble wall velocities in first-order phase transitions is of great importance for the prediction of gravitational wave signals and the matter-antimatter asymmetry. However, it is a challenging task which typically depends on the underlying particle physics model. Recently, it has been shown that assuming local thermal equilibrium can provide a good approximation when calculating the bubble wall velocity. In this paper, we provide a model-independent determination of bubble wall velocities in local thermal equilibrium. Our results show that, under the reasonable assumption that the sound speeds in the plasma are approximately uniform, the hydrodynamics can be fully characterized by four quantities: the phase strength α n , the ratio of the enthalpies in the broken and symmetric phases, Ψ n , and the sound speeds in both phases, c s and c b . We provide a code snippet that allows for a determination of the wall velocity and energy fraction in local thermal equilibrium in any model. In addition, we present a fit function for the wall velocity in the case c s = c b = 1/√(3).
We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as nonderivative one-loop corrections.
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