Gravity, Scale Invariance and the Hierarchy Problem

Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We argue that this hierarchy can be generated by a non-perturbative effect relating the low energy and the Planck-scale physics. The effect is manifested in the existence of an instanton configuration contributing to the vacuum expectation value of the Higgs field. We analyze such configurations in several toy models and in a phenomenologically viable theory encompassing the Standard Model and General Relativity in a scale-invariant way. Dynamical gravity and a non-minimal coupling of it to the Higgs field play a crucial role in the mechanism.Comment: 42 pages, 11 figures. v2: published versio

On stability of electroweak vacuum during inflation

We study Coleman-De Luccia tunneling of the Standard Model Higgs field during inflation in the case when the electroweak vacuum is metastable. We verify that the tunneling rate is exponentially suppressed. The main contribution to the suppression is the same as in flat space-time. We analytically estimate the corrections due to the expansion of the universe and an effective mass term in the Higgs potential that can be present at inflation.Comment: 9 pages, 2 figures, dependence of the grav. corrections to the bounce action on non-minimal coupling updated, corresponding references adde

Out of this world neutrino oscillations

We study how vacuum neutrino oscillations can be affected by a causal, nonlinear and state-dependent modification of quantum field theory that may be interpreted using the many-worlds formulation of quantum mechanics. The effect is induced by a Higgs-neutrino Yukawa interaction that causes a nonlinear interference between the neutrino mass eigenstates. This leads to a tiny change in the oscillation pattern of light, active neutrinos without altering the oscillation frequencies. At large baselines where the oscillations disappear, the nonlinear effect is also suppressed and does not source correlations between the mass eigenstates once they are entangled with the environment. Our example provides a way to compute effects of nonlinear quantum mechanics and field theory that may probe the possible physical reality of many worlds.Comment: 9 pages, 1 figure. v2: version published in PR

Conformal symmetry: towards the link between the Fermi and the Planck scales

If the mass of the Higgs boson is put to zero, the classical Lagrangian of the Standard Model (SM) becomes conformally invariant (CI). Taking into account quantum non-perturbative QCD effects violating CI leads to electroweak symmetry breaking with the scale $v \sim \Lambda_{\rm QCD}\sim 100$ MeV which is three orders of magnitude less than it is observed experimentally. Depending on the mass of the top quark, the radiative corrections may lead to another minimum of the effective potential for the Higgs field with $v \gtrsim M_P$, where $M_P$ is the Planck mass, at least $16$ orders of magnitude more than it is observed. We explore yet another source of CI breaking associated with gravity. We suggest a non-perturbative mechanism that can reproduce the observed hierarchy between the Fermi and the Planck scales, by constructing an instanton configuration contributing to the vacuum expectation value of the Higgs field. The crucial role in this effect is played by the non-minimal coupling of the Higgs field to the Ricci scalar and by the approximate Weyl invariance of the theory for large values of the Higgs field.Comment: 12 pages, 6 figures; v2: published versio

Solving puzzles of spontaneously broken spacetime symmetries

We establish a classical analog of the Nambu-Goldstone theorem for spontaneous breaking of spacetime symmetries. It provides a counting rule for independent Nambu-Goldstone fields and states which of them are gapped. We demonstrate that only those symmetry group generators give rise to independent Nambu-Goldstone fields that act non-trivially on a vacuum at the origin of coordinates. Other generators give rise to auxiliary fields that must be excluded from a theory by the means of inverse Higgs constraints. The physical meaning of the inverse Higgs phenomenon and an application of our results to theories of massive gravity are discussed.Comment: 13 pages, extended version of the published pape

Euclidean classical solutions in quantum field theory and gravity: Higgs vacuum metastability and the hierarchy problem

The thesis is dedicated to two groups of questions arising in modern particle physics and cosmology. The first group concerns with the problem of stability of the electroweak (EW) vacuum in different environments. Due to its phenomenological significance, the problem attracts high attention in recent research. We contribute to this research in two directions. First, we study decay rate of the EW vacuum at the inflationary stage of the universe. While in a low density, low temperature environment characteristic of the present-day universe the Standard Model EW vacuum is safely long-lived, the situation may be different during inflation. We estimate tunneling transition via Coleman-De Luccia instanton in this case and confirm that it is exponentially suppressed, contrary to the claims made in the literature. Second, we compute the lifetime of the EW vacuum in a scale-invariant extension of the Standard Model and gravity, known as the Higgs-Dilaton theory. The theory passes phenomenological tests and provides us with a plausible cosmological scenario. To confirm its viability, it is necessary to check if the EW vacuum in this theory is sufficiently safe. We perform this check and find that features of the Higgs-Dilaton theory yield additional stabilization of the low-energy vacuum, compared to the Standard Model case. Another group of questions addressed in the thesis is related to the hierarchy problem. Combining quantum scale invariance with the absence of new degrees of freedom above the EW scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We suggest that this hierarchy can be a manifestation of a non-perturbative effect relating low-energy and strong-gravity domains of the theory. To support this suggestion, we construct instanton configurations and investigate their contribution to the vacuum expectation value of the Higgs field. The effect we find relies on properties of the theory in the ultraviolet regime. Non-minimal coupling of the Higgs field to the Ricci scalar and an approximate Weyl invariance of the theory in this regime are important ingredients of the mechanism. Dynamical gravity plays a crucial role in the effect as it leads to existence of instanton solutions suitable for generating the EW scale

Non-perturbative production of fermionic dark matter from fast preheating

We investigate non-perturbative production of fermionic dark matter in the early universe. We study analytically the gravitational production mechanism accompanied by the coupling of fermions to the background inflaton field. The latter leads to the variation of effective fermion mass during preheating and makes the resulting spectrum and abundance sensitive to its parameters. Assuming fast preheating that completes in less than the inflationary Hubble time and no oscillations of the inflaton field after inflation, we find an abundant production of particles with energies ranging from the inflationary Hubble rate to the inverse duration of preheating. The produced fermions can account for all observed dark matter in a broad range of parameters. As an application of our analysis, we study non-perturbative production of heavy Majorana neutrino in the model of Palatini Higgs inflation.Comment: 38 pages, 9 figures, v2 matches the published versio