Planck Scale Research Articles

The zitterbewegung electron puzzle

This work is an updated revision of semiclassical descriptions for the electron, including the fully relativistic QED-P model from H. J. Wilson based on the original Dirac equation (DE). The models presented hereafter go beyond the depiction of the electron as a structureless nondimensional point like charge with momentum and position determined by a probabilistic interpretation of the wavefunction described in terms of an electronic density cloud. These models share features in common that provide useful insights concerning the nature of the electron; for instance, they all consider zitterbewegung, a light speed “trembling-along-the-way” electron motion, to be a real oscillatory motion of the electron. The last model presented in this review is the electron mass model from Val Baker et al. [Phys. Essays 32, 255 (2019)], where the electron mass is defined in terms of a holographic surface-to-volume ratio Φ and the relationship of the electric charge at the Planck scale to that at the electron scale, obtaining a value in agreement with the latest CODATA value. We discuss the relationship between these models. The large number of correspondences between the models should not be taken lightly and indicate, in our view, that something very fundamental about the nature of the electron is being put forward by this study.

A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed.

Gravity-improved metastability bounds for the Type-I seesaw mechanism

Right-handed neutrinos (RHN) destabilize the electroweak vacuum by increasing its decay rate. In the SM, the latter is dominated by physics at the RG scale at which λ reaches its minimum, μ∗SM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mu}_{\\ast}^{\ extrm{SM}} $$\\end{document} ∼ 1017 GeV. For large neutrino Yukawa coupling Yν, RHNs can push μ* beyond the Planck scale, implying that gravitational effects need to be taken into account. In this work, we perform the first comprehensive study of electroweak vacuum metastability in the type-I seesaw mechanism including these effects. Our analysis covers both low- and high-scale seesaw models, with two as well as three RHNs and for multiple values of the Higgs’ non-minimal coupling to gravity. We find that gravitational effects can significantly stabilize the vacuum, leading to weaker metastability bounds. We show that metastability sets the strongest bounds for low-scale seesaws with MN> 1 TeV. For high-scale seesaws, we find upper bounds on the allowed masses for the RHNs, which are relevant for high-scale leptogenesis. We also point out that Tr(Yν†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\ u}^{\\dagger } $$\\end{document}Yν), which is commonly used to express these metastability bounds, cannot be used for all of parameter space. Instead, we argue that bounds can always be expressed reliably through Tr(Yν†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\ u}^{\\dagger } $$\\end{document}YνYν†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\ u}^{\\dagger } $$\\end{document}Yν). Lastly, we use this insight to develop a new technique for an easier RG analysis applicable to scenarios with degenerate RHN masses.

Стандартная модель в ранней Вселенной

A new hypothesis is put forward that the gauge group of the
 Standard Model becomes simpler with increasing temperature
 of the Universe, i.e. when moving back in time to the moment
 of its occurrence. It is assumed that this simplification
 is achieved by contracting the gauge group with the contraction
 parameter, which decreases with increasing temperature.
 In this case, the Lagrangian of the Standard Model is
 divided into terms that differ in powers of the contraction parameter.
 This makes it possible to arrange in time the stages
 of development of the Standard Model as the Universe cools.
 The evolution of the properties of elementary particles and
 their interactions, starting from the Planck scale of 1019 GeV,
 is based on the explicit form of intermediate Lagrangians and
 explain the development of the Universe from simpler to more
 complicated structures - and not vice versa. The contraction
 hypothesis of the gauge group of the Standard Model contradicts
 the available experimental data on the Higgs boson production
 cross section.

Revisiting the refined Distance Conjecture

The Distance Conjecture of Ooguri and Vafa holds that any infinite-distance limit in the moduli space of a quantum gravity theory must be accompanied by a tower of exponentially light particles, which places tight constraints on the low-energy effective field theories in these limits. One attempt to extend these constraints to the interior of moduli space is the refined Distance Conjecture, which holds that the towers of light particles predicted by the Distance Conjecture must appear any time a modulus makes a super-Planckian excursion in moduli space. In this note, however, we point out that a tower which satisfies the Distance Conjecture in an infinite-distance limit of moduli space may be parametrically heavier than the Planck scale for an arbitrarily long geodesic distance. This means that the refined Distance Conjecture, in its most naive form, does not place meaningful constraints on low-energy effective field theory. This motivates alternative refinements of the Distance Conjecture, which place an absolute upper bound on the tower mass scale in the interior of moduli space. We explore two possibilities, providing evidence for them and briefly discussing their implications.

Zero-point Energy Conundrum for Spin 1 Particles

The zero-point energy concept results in an infinite energy that has not yet been fully resolved. This paper reviews the zero-point energy for spin 1 particles utilizing the Proca equation. The need for the zero-point energy is confirmed in Santilli's synthesis of the neutron from the proton and the electron in the core of a star. A possible resolution lies in establishing a cutoff energy (e.g., at the Planck scale) that negates the singularity. This singularity is avoided by establishing a restricted energy region that precludes exceeding the cutoff energy scale except under extreme circumstances (e.g., during a big bang/big crunch event). Potential energy functions, analogous to the Higgs potential or the short range hard core nuclear interaction, are introduced as possible mechanisms to establish the cutoff energy.

A fairy tale of winter - a theory about dark energy, dark matter, and inflation

This fairy tale begins with the journey of the famous Zhuang Zhou dreaming of a butterfly: I often do not know whether I am living in a dream, dreaming of a butterfly, or is a butterfly dreaming of me? Furthermore, there is the saying that those who believe it will see it, while for those who see it, it is then too late to believe it. The first thing I believe in is the holographic principle, and the holographic dark energy brought about by the holographic principle. Not until last year, I began to believe that there must be a new energy scale in between the Planck scale and the standard model scale. I also believe that this new scale is related to the minimal axion model. The results of the journey described in this paper are the following: 1. There is a new energy scale, which we will call the intermediate energy scale, and the best choice is GeV. 2. The minimal axion exists, and under the new scale, there is no new physics. The axion plays both the roles of inflation and dark matter. New physics between the new scale and the Planck scale may exist because in this energy range, quantum gravity becomes important. 3. The dark energy is holographic dark energy. Then all of the observable effects of all three predictions about dark energy, dark matter, and cosmic inflation are to be observed.

Schrödinger and Klein–Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

The Schrödinger equation of the Schwarzschild black hole (BH) has been recently derived by the author and collaborators. The BH is composed of a particle, the ‘electron’, interacting with a central field, the ‘nucleus’. Via de Broglie’s hypothesis, one interprets the ‘electron’ in terms of BH horizon’s modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schrödinger equation and the Schrödinger equation of the s states of the hydrogen atom permits us to solve the same equation. The quantum gravitational quantities analogous of the fine structure constant and of the Rydberg constant are not constants, but the dynamical quantities have well-defined discrete spectra. The spectrum of the ‘gravitational fine structure constant’ is the set of non-zero natural numbers. Therefore, BHs are well-defined quantum gravitational systems obeying Schrödinger’s theory: the ‘gravitational hydrogen atoms’. By identifying the potential energy in the BH Schrödinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH described as a ‘gravitational hydrogen atom’ is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having a radius equal to the oscillating gravitational radius. Nontrivial consequences emerge from this result: (i) BHs have neither horizons nor singularities; (ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schrödinger equation give the BH Klein–Gordon equation and the corresponding eigenvalues.

30 years in: Quo vadis generalized uncertainty principle?

According to a number of arguments in quantum gravity, both model-dependent and model-independent, Heisenberg’s uncertainty principle is modified when approaching the Planck scale. This deformation is attributed to the existence of a minimal length. The ensuing models have found entry into the literature under the term generalized uncertainty principle. In this work, we discuss several conceptual shortcomings of the underlying framework and critically review recent developments in the field. In particular, we touch upon the issues of relativistic and field theoretical generalizations, the classical limit and the application to composite systems. Furthermore, we comment on subtleties involving the use of heuristic arguments instead of explicit calculations. Finally, we present an extensive list of constraints on the model parameter β, classifying them on the basis of the degree of rigor in their derivation and reconsidering the ones subject to problems associated with composites.

Zero-point Energy Conundrum for Spin ½ Particles

The zero-point energy concept results in an infinite energy that has not yet been fully resolved. A previous paper provided a resolution for spin 0 particles within the scope of the Klein-Gordon equation. This paper reviews the zero-point energy issue for spin ½ particles utilizing the Dirac equation. The need for the zero-point energy is confirmed in Santilli's synthesis of the neutron from the proton and the electron in the core of a star. A possible resolution lies in establishing a cutoff energy (e.g., at the Planck scale) that negates the singularity. This singularity is avoided by establishing a restricted energy region that precludes exceeding the cutoff energy scale except under extreme circumstances (e.g., during a big bang/big crunch event). Potential energy functions, analogous to the Higgs potential or the short range hard core nuclear interaction, are introduced as possible mechanisms to establish the cutoff energy.

Quantum Black Holes in Conformal Dilaton–Higgs Gravity on Warped Spacetimes

A promising method for understanding the geometric properties of a spacetime in the vicinity of the horizon of a Kerr-like black hole can be developed by applying the antipodal boundary condition on the two opposite regions in the extended Penrose diagram. By considering a conformally invariant Lagrangian on a Randall–Sundrum warped five-dimensional spacetime, an exact vacuum solution is found, which can be interpreted as an instanton solution on the Riemannian counterpart spacetime, R+2×R1×S1, where R+2 is conformally flat. The antipodal identification, which comes with a CPT inversion, is par excellence, suitable when quantum mechanical effects, such as the evaporation of a black hole by Hawking radiation, are studied. Moreover, the black hole paradoxes could be solved. By applying the non-orientable Klein surface, embedded in R4, there is no need for instantaneous transport of information. Further, the gravitons become “hard” in the bulk, which means that the gravitational backreaction on the brane can be treated without the need for a firewall. By splitting the metric in a product ω2g˜μν, where ω represents a dilaton field and g˜μν the conformally flat “un-physical” spacetime, one can better construct an effective Lagrangian in a quantum mechanical setting when one approaches the small-scale area. When a scalar field is included in the Lagrangian, a numerical solution is presented, where the interaction between ω and Φ is manifest. An estimate of the extra dimension could be obtained by measuring the elapsed traversal time of the Hawking particles on the Klein surface in the extra dimension. Close to the Planck scale, both ω and Φ can be treated as ordinary quantum fields. From the dilaton field equation, we obtain a mass term for the potential term in the Lagrangian, dependent on the size of the extra dimension.

Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity

A fine tuned rainbow gravity describes both relativistic quantum particles and anti-particles alike. That is, the ratio y=E/EP in the rainbow functions g0(y) and g1(y) should be fine tuned into 0≤y=E/EP≤1⇒y=|E|/EP, otherwise rainbow gravity will only secure Planck's energy scale Ep as the maximal energy for relativistic particles and the anti-particles are left unfortunate (in the sense that their energies will be indefinitely unbounded). Using this fine tuning we discuss the rainbow gravity effect on Klein-Gordon (KG) oscillators in Som-Raychaudhuri cosmic string rainbow gravity spacetime background. We use the rainbow functions: (i) g0(y)=1, g1(y)=1−ϵyn,n=1,2, loop quantum gravity motivated pairs, (ii) g0(y)=g1(y)=(1−ϵy)−1, a horizon problem motivated pair, and (iii) g0(y)=(eϵy−1)/ϵy, g1(y)=1, a gamma-ray bursts motivated pair. We show that the energies obtained using the first two rainbow functions in (i) completely comply with the rainbow gravity model and secure Planck's energy Ep as the maximal energy for both particles and anti-particles. The rainbow function pair in (ii) has no effect on massless KG-oscillators. Whereas, the one in (iii) does not show any eminent tendency towards the Planck's energy as the maximal energy.

Ultraviolet sensitivity in Higgs-Starobinsky inflation

The general scalar-tensor theory that includes all the dimension-four terms has parameter regions that can produce successful inflation consistent with cosmological observations. This theory is in fact the same as the Higgs-Starobinsky inflation, when the scalar is identified with the Standard Model Higgs boson. We consider possible dimension-six operators constructed from non-derivative terms of the scalar field and the Ricci scalar as perturbations. We investigate how much suppression is required for these operators to avoid disrupting the successful inflationary predictions. To ensure viable cosmological predictions, the suppression scale for the sixth power of the scalar should be as high as the Planck scale. For the other terms, much smaller scales are sufficient.

Estimation of imprints of the bounce in loop quantum cosmology on the bispectra of cosmic microwave background

Primordial non-Gaussianity has set strong constraints on models of the early universe.Studies have shown that Loop Quantum Cosmology (LQC), which is an attempt to extend inflationary scenario to planck scales, leads to a strongly scale dependent and oscillatory non-Gaussianity. In particular, the non-Gaussianity function f NL (k 1, k 2, k 3) generated in LQC, though similar to that generated during slow roll inflation at small scales, is highly scale dependent and oscillatory at long wavelengths. In this work, we investigate the imprints of such a primordial bispectrum in the bispectrum of Cosmic Microwave Background (CMB).Inspired by earlier works, we propose an analytical template for the primordial bispectrum in LQC.We write the template as a sum of strongly scale dependent and oscillatory part, which captures the contribution due to the bounce, and a part which captures the scale invariant behaviour similar to that of slow roll. We then compute the reduced bispectra of temperature and electric polarisation and their three-point cross-correlations corresponding to these two parts.We show that the contribution from the bounce to the reduced bispectrum is negligible compared to that from the scale-independent part. Thus, we conclude that the CMB bispectra generated in LQC will be similar to that generated in slow roll inflation. We conclude with a discussion of our results and its implications to LQC.

Constraining Lorentz invariance violation with next-generation long-baseline experiments

Unified theories such as string theory and loop quantum gravity allow the Lorentz Invariance Violation (LIV) at the Planck Scale (MP ~ 1019 GeV). Using an effective field theory, this effect can be observed at low energies in terms of new interactions with a strength of ~ 1/MP. These new interactions contain operators with LIV coefficients which can be CPT-violating or CPT-conserving. In this work, we study in detail how these LIV parameters modify the transition probabilities in the next-generation long-baseline experiments, DUNE and Hyper-K. We evaluate the sensitivities of these experiments in isolation and combination to constrain the off-diagonal CPT-violating (aeμ, aeτ, aμτ) and CPT-conserving (ceμ, ceτ, cμτ) LIV parameters. We derive approximate compact analytical expressions of appearance (νμ → νe) and disappearance (νμ → νμ) probabilities in the presence of these LIV parameters to explain our numerical results. We explore the possible correlations and degeneracies between these LIV parameters and the most uncertain 3ν oscillation parameters, namely, θ23 and δCP. We find that for non-maximal values of θ23 (θ23 ≠ 45°), there exist degenerate solutions in its opposite octant for standalone DUNE and Hyper-K. These degeneracies disappear when we combine the data from DUNE and Hyper-K. In case of no-show, we place the expected upper bounds on these CPT-violating and CPT-conserving LIV parameters at 95% C.L. using the standalone DUNE, Hyper-K, and their combination. We observe that due to its access to a longer baseline and multi-GeV neutrinos, DUNE has a better reach in probing all these LIV parameters as compared to Hyper-K. Since the terms containing the CPT-conserving LIV parameters are proportional to neutrino energy in oscillation probabilities, Hyper-K is almost insensitive to the CPT-conserving LIV parameters because it mostly deals with sub-GeV neutrinos.

How robust are particle physics predictions in asymptotic safety?

The framework of trans-Planckian asymptotic safety has been shown to generate phenomenological predictions in the Standard Model and in some of its simple new physics extensions. A heuristic approach is often adopted, which bypasses the functional renormalization group by relying on a parametric description of quantum gravity with universal coefficients that are eventually obtained from low-energy observations. Within this approach a few simplifying approximations are typically introduced, including the computation of matter renormalization group equations at 1 loop, an arbitrary definition of the position of the Planck scale at 10^{19},textrm{GeV}, and an instantaneous decoupling of gravitational interactions below the Planck scale. In this work we systematically investigate, both analytically and numerically, the impact of dropping each of those approximations on the predictions for certain particle physics scenarios. In particular we study two extensions of the Standard Model, the gauged B-L model and the leptoquark S_3 model, for which we determine a set of irrelevant gauge and Yukawa couplings. In each model, we present numerical and analytical estimates of the uncertainties associated with the predictions from asymptotic safety.

Ruling out light axions: The writing is on the wall

We revisit the domain wall problem for QCD axion models with more than one quark charged under the Peccei-Quinn symmetry. Symmetry breaking during or after inflation results in the formation of a domain wall network which would cause cosmic catastrophe if it comes to dominate the Universe. The network may be made unstable by invoking a “tilt” in the axion potential due to Planck scale suppressed non-renormalisable operators. Alternatively the random walk of the axion field during inflation can generate a “bias” favouring one of the degenerate vacua, but we find that this mechanism is in practice irrelevant. Consideration of the axion abundance generated by the decay of the wall network then requires the Peccei-Quinn scale to be rather low - thus e.g. ruling out the DFSZ axion with mass below \sim∼ 11 meV, where most experimental searches are in fact focused.

Warm inflation in [formula omitted] gravity

In this work, we explored warm inflation in the background of f(R,T) gravity in the strong dissipation regime. Considering scalar field for FLRW universe, we derived modified field equations. We then deduced slow-roll parameters under slow-roll approximations followed by power spectrum for scalar and tensor perturbations and their corresponding spectral indices. We have considered Chaotic and Natural potentials and estimated scalar spectral index and tensor-to-scalar ratio for constant as well as variable dissipation factor Γ. We found that both the rejected potentials can be revived under the context of f(R,T) gravity with suitable choice of the model parameters. Further, it is seen that within the warm inflationary scenario both the potentials can yield result consistent with Planck 2018 and BICEP/Keck bounds at the Planckian and sub-Planckian energy scales.

Probing the dark dimension with Auger data

By combining swampland conjectures with observational data, it was recently pointed out that our universe could stretch off in an asymptotic region of the string landscape of vacua. Within this framework, the cosmological hierarchy problem (i.e. the smallness of the cosmological constant in Planck units: Λ∼10−122MPl4) can be naturally resolved by the addition of one mesoscopic (dark) dimension of size ∼λΛ−1/4∼1μm. The Planck scale of the higher dimensional theory, MUV∼λ−1/3Λ1/12MPl2/3∼1010GeV, is tantalizingly close to the energy above which the Telescope Array (TA) and the Pierre Auger collaborations found conclusive evidence for a sharp cutoff of the flux of ultra-high-energy cosmic rays (UHECRs). It was recently suggested that since physics becomes strongly coupled to gravity beyond MUV, universal features deep-rooted in the dark dimension could control the energy cutoff of the source spectra ∝E−γexp(−E/MUV), where E is the cosmic ray energy and γ a free parameter. Conversely, in the absence of phenomena inborn within the dark dimension, we would expect a high variance of the cosmic ray maximum energy Emax characterizing the source spectra ∝E−γexp(−E/Emax), reflecting the many different properties inherent to the most commonly assumed UHECR accelerators. The most recent analysis of Auger and TA data exposed strong evidence for a correlation between UHECRs and nearby starburst galaxies, with a global significance post-trial of 4.7σ. Since these galaxies are in our cosmic backyard, the flux attenuation factor due to cosmic ray interactions en route to Earth turns out to be negligible. This reasoning implies that for each source, the shape of the observed spectrum should roughly match the emission spectrum by the starburst, providing a unique testing ground for the dark dimension hypothesis. Using Auger data, we carry out a maximum likelihood analysis to characterize the shape of the UHECR emission from the galaxies dominating the anisotropy signal. We show that the observed spectra from these sources could be universal only if λ≲10−3.

First Experimental Survey of a Whole Class of Non-Commutative Quantum Gravity Models in the VIP-2 Lead Underground Experiment

This study is aimed to set severe constraints on a whole class of non-commutative space-times scenarios as a class of universality for several quantum gravity models. To this end, slight violations of the Pauli exclusion principle—predicted by these models—are investigated by searching for Pauli forbidden Kα and Kβ transitions in lead. The selection of a high atomic number target material allows to test the energy scale of the space-time non-commutativity emergence at high atomic transition energies. As a consequence, the measurement is very sensitive to high orders in the power series expansion of the Pauli violation probability, which allows to set the first constraint to the “triply special relativity” model proposed by Kowalski-Glikman and Smolin. The characteristic energy scale of the model is bound to Λ>5.6·10−9 Planck scales.