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Register a new userBlack holes and quantum theory on manifolds with singular potentials
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Added by
Jose M Munoz-Castaneda
Publication date
2016
fields
Physics
and research's language is
English
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Quantum theory on manifolds with boundaries have been studied extensively through von Neumann analysis of self adjoint operators. We approach the issues through introduction of singular $delta$ and $delta$ potentials. The advantages of this are pointed out as a model for black hole and in several other examples.
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Within the framework of Galileon inflation with quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a Galileon function as $G(phi)=g_I(phi)big(1+g_{II}(phi)big)$ and show that in the presence of first term $g_I(phi)$ both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68% CL of Planck observations. Besides, the second term $g_{II}(phi)$ can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales $ksim10^{12}~rm Mpc^{-1}$, $10^{8}~rm Mpc^{-1}$, and $10^{5}~rm Mpc^{-1}$, which causes PBHs production in mass scales around $10^{-13}M_{odot}$, $10^{-5}M_{odot}$, and $10 M_{odot}$, respectively. Observational constraints confirm that PBHs with a mass scale of $10^{-13}M_{odot}$ can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function $Omega_{rm GW}sim (f/f_c)^n$, where the power index equals $n=3-2/ln(f_c/f)$ in the infrared limit $fll f_{c}$.
Pairs of standard model fermions can annihilate to produce mini black holes with gauge quantum numbers of the Higgs boson at $M_{Planck}$. This leads to a Nambu-Jona-Lasinio model at the Planck scale with strong coupling which binds fermion pairs into Higgs fields. At critical coupling the renormalization group dresses these objects, which then descend in scale to emerge as OBSERVABLE boundstate Higgs bosons at low energies, and we obtain the multi-Higgs spectrum of a scalar democracy. The observed Higgs boson is a gravitationally bound $bar{t}t$ composite. Sequential states may be seen at the LHC, and/or its upgrades.
We examine the LHC phenomenology of quantum black holes in models of TeV gravity. By quantum black holes we mean black holes of the smallest masses and entropies, far from the semiclassical regime. These black holes are formed and decay over short distances, and typically carry SU(3) color charges inherited from their parton progenitors. Based on a few minimal assumptions, such as gauge invariance, we identify interesting signatures for quantum black hole decay such as 2 jets, jet + hard photon, jet + missing energy and jet + charged lepton, which should be readily visible above background. The detailed phenomenology depends heavily on whether one requires a Lorentz invariant, low-energy effective field theory description of black hole processes.
Evidences for the primordial black holes (PBH) presence in the early Universe renew permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known model is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage.
We consider the application of peaks theory to the calculation of the number density of peaks relevant for primordial black hole (PBH) formation. For PBHs, the final mass is related to the amplitude and scale of the perturbation from which it forms, where the scale is defined as the scale at which the compaction function peaks. We therefore extend peaks theory to calculate not only the abundance of peaks of a given amplitude, but peaks of a given amplitude and scale. A simple fitting formula is given in the high-peak limit relevant for PBH formation. We also adapt the calculation to use a Gaussian smoothing function, ensuring convergence regardless of the choice of power spectrum.
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