Planck Energy Scale Research Articles

Investigating the Lorentz invariance violation effect using different cosmological backgrounds

Familiar concepts in physics, such as Lorentz symmetry, are expected to be broken at energies approaching the Planck energy scale as predicted by several quantum-gravity theories. However, such very large energies are unreachable by current experiments on Earth. Current and future Cherenkov telescope facilities may have the capability to measure the accumulated deformation from Lorentz symmetry for photons traveling over large distances via energy-dependent time delays. One of the best natural laboratories to test Lorentz invariance violation (LIV) signatures are gamma-ray bursts. The calculation of time delays due to the LIV effect depends on the cosmic expansion history. In most of the previous works calculating time lags due to the LIV effect, the standard ΛCDM (or concordance) cosmological model is assumed. In this paper, we investigate whether the LIV signature is significantly different when assuming alternatives to the ΛCDM cosmological model. Specifically, we consider cosmological models with a non-trivial dark-energy equation of state (EoS) (), such as the standard Chevallier–Polarski–Linder parameterization, the quadratic parameterization of the dark-energy EoS, and the Pade parameterizations. We find that the relative difference in the predicted time lags is small, of the order of at most a few percent, and thus likely smaller than the systematic errors of possible measurements currently or in the near future.

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.

Avenues of Quantum Field Theory in Curved Spacetime, Genova, 14-16 Sep 2022

The extreme conditions experienced in the early universe, close to a black hole or in the interior of a neutron star, provide the environment where the most violent natural phenomena take place. Our understanding of the physical processes occurring in these regimes is affected by the notorious difficulty in the development of a theory of quantum gravity, modelling the intertwining of the gravitational field and the quantum properties of the fields responsible for the other forces in nature. A different point of view is then achieved by defining a “mesoscopic” scale lying below the Planck energy scale but well away from the classical general relativity domain. At such a scale, the theoretical framework describing how quantized fields propagate in a curved background has accomplished outstanding results, like particle production in gravitational fields and black hole evaporation, establishing a highly non-trivial connection between thermodynamics, gravity, and quantum field theory.Aside from suggesting novel intersections between quantum fields and gravity, an unexplored landscape of original ideas is taking shape and inspiring new exciting problems. Quantum field theory in curved spacetime has recently been proposed as a new tool to probe nuclear and condensed matter physics phenomenology, with the recent advances in research at the nanoscale offering an intriguing test to the semiclassical approach even from tabletop experiments.Following this trend, the goal of Avenues of Quantum Field Theory in Curved Spacetime has been to bring together researchers working in different areas of quantum field theory with interest in its curved space applications in the area of gravity and beyond. The 3-days workshop - the third of a series initiated in 2018 in Japan, continued in Modena, and that had an unexpected stop due to the sadly well-known Covid19 facts - aimed to exchange ideas on what is (or is expected soon to become) topical and discuss potential interdisciplinary interactions in a stimulating and collaborative environment.List of The Editorial Board and Organising Committee is available in this pdf.

Thermodynamics of Schwarzschild black hole surrounded by quintessence in gravity's rainbow

According to some quantum gravity models, Lorentz invariance can be violated in the Planck energy scale. With this motivation, we analyze the thermal quantities and the stability of Schwarzschild black hole surrounded by quintessence in gravity's rainbow formalism. To do that, we consider the rainbow functions which are motivated by loop quantum gravity and gamma-ray bursts, and we derive Hawking temperature, specific heat, entropy and the equation of state function. We observe that the presence the quintessence matter field and rainbow gravity affect the stability of the black hole.

Quantum-Relativistic Properties of the Space-Time Bubbles and Their Evolution in a Multi-Bubble Universe

The quantum-relativistic properties of space-time bubbles introduced in the recently proposed multi-Bubbles Universe model have been studied and deepened in the framework of the electromagnetic Bridge theory. In this context, it is shown how the space-time fabric of the emerging universe and the primordial matter contained in it, can be considered the final result of the decay of a pre-universe formed by a BEC of neutral Planck bosons hidden under the space-time horizon, having the characteristics of balancing gravitons associated with the potential energy of the vacuum defined as the field of nothingness. The estimated mass of the Planck boson is compatible with the smallest of the Kaluza-Klein graviton with an energy mass of 2.68 TeV, this value allows to estimate the limit of the Planck energy scale characterized by a lepton particle with a rest mass of 1.27 TeV. It is also shown as an ancient multi-bubble universe obtained by the decay of a pre-universe redshifted nowadays at 2.725 K, provides a Planck blackbody spectrum perfectly in agreement with the cosmic microwave background radiation of our universe measured by the COBE satellite.

Search for quantum gravity using astrophysical neutrino flavour with IceCube

Along their long propagation from production to detection, neutrino states undergo quantum interference which converts their types, or flavours. High-energy astrophysical neutrinos, first observed by the IceCube Neutrino Observatory, are known to propagate unperturbed over a billion light years in vacuum. These neutrinos act as the largest quantum interferometer and are sensitive to the smallest effects in vacuum due to new physics. Quantum gravity (QG) aims to describe gravity in a quantum mechanical framework, unifying matter, forces and space-time. QG effects are expected to appear at the ultra-high-energy scale known as the Planck energy, $E_{P}\equiv 1.22\times 10^{19}$~giga-electronvolts (GeV). Such a high-energy universe would have existed only right after the Big Bang and it is inaccessible by human technologies. On the other hand, it is speculated that the effects of QG may exist in our low-energy vacuum, but are suppressed by the Planck energy as $E_{P}^{-1}$ ($\sim 10^{-19}$~GeV$^{-1}$), $E_{P}^{-2}$ ($\sim 10^{-38}$~GeV$^{-2}$), or its higher powers. The coupling of particles to these effects is too small to measure in kinematic observables, but the phase shift of neutrino waves could cause observable flavour conversions. Here, we report the first result of neutrino interferometry~\cite{Aartsen:2017ibm} using astrophysical neutrino flavours to search for new space-time structure. We did not find any evidence of anomalous flavour conversion in IceCube astrophysical neutrino flavour data. We place the most stringent limits of any known technologies, down to $10^{-42}$~GeV$^{-2}$, on the dimension-six operators that parameterize the space-time defects for preferred astrophysical production scenarios. For the first time, we unambiguously reach the signal region of quantum-gravity-motivated physics.

$${\mathcal {H}}$$olographic $${\mathcal {N}}$$aturalness and $${\mathcal {C}}$$osmological $${\mathcal {R}}$$elaxation

We rediscuss the main Cosmological Problems as illusions originated from our ignorance of the hidden information holographically stored in vacuo. The Cosmological vacuum state is full of a large number of dynamical quantum hairs, dubbed hairons, which dominate the Cosmological Entropy. We elaborate on the Cosmological Constant (CC) problem, in both the dynamical and time-constant possibilities. We show that all dangerous quantum mixings between the CC and the Planck energy scales are exponentially suppressed as an entropic collective effect of the hairon environment. As a consequence, the dark energy scale is UV insensitive to any Planckian corrections. On the other hand, the inflation scale is similarly stabilized from any radiative effects. In the case of the Dark energy, we show the presence of a holographic entropic attractor, favoring a time variation of $$\Lambda \rightarrow 0$$ in future rather than a static CC case, i.e., the $$w>-1$$ Dynamical DE is favored over a CC or a $$w<-1$$ phantom cosmology. In both the inflation and dark energy sectors, we elaborate on the Trans-Planckian problem, in relation with the recently proposed Trans-Planckian Censorship Conjecture (TCC). We show that the probability for any sub-Planckian wavelength modes to survive after inflation is completely negligible as a holographic wash-out mechanism. In other words, the hairons provide for a holographic decoherence of the transplanckian modes in a holographic scrambling time. This avoids the TCC strong bounds on the Inflaton and DE potentials.

On the Role of Einstein–Cartan Gravity in Fundamental Particle Physics

Two of the major open questions in particle physics are: (1) Why do the elementary fermionic particles that are so far observed have such low mass-energy compared to the Planck energy scale? (2) What mechanical energy may be counterbalancing the divergent electrostatic and strong force energies of point-like charged fermions in the vicinity of the Planck scale? In this paper, using a hitherto unrecognised mechanism derived from the non-linear amelioration of the Dirac equation known as the Hehl–Datta equation within the Einstein–Cartan–Sciama–Kibble (ECSK) extension of general relativity, we present detailed numerical estimates suggesting that the mechanical energy arising from the gravitationally coupled self-interaction in the ECSK theory can address both of these questions in tandem.

Model-independent Constraints on Lorentz Invariance Violation: Implication from Updated Gamma-Ray Burst Observations

Abstract Astrophysical observations provide a unique opportunity to test possible signatures of Lorentz invariance violation (LIV), due to the high energies and long distances involved. In quantum theory of gravity, one may expect the modification of the dispersion relation between energy and momentum for photons, which can be probed with the time lag (the arrival time delay between light curves in different energy bands) of gamma-ray bursts (GRBs). In this paper, by using the detailed time delay measurements of GRB 160625B at different energy bands, as well as 23 time delay GRBs covering the redshift range of z = 0.168–2.5 (which were measured at different energy channels from the light curves), we propose an improved model-independent method (based on the newly compiled sample of H(z) measurements) to probe the energy-dependent velocity due to the modified dispersion relation for photons. In the framework of a more complex and reasonable theoretical expression to describe the time delays, our results imply that the intrinsic time lags can be better described with more GRB time delay data. More importantly, through direct fitting of the time delay measurements of a sample of GRBs, our limit on the LIV energy scale is comparable to that with unknown constant for the intrinsic time lag, much lower than the Planck energy scale in both linear LIV and quadratic LIV cases.

Consistency analysis of a CPT-even and CPT-odd Lorentz-violating effective field theory in the electrodynamics at Planck scale by an influence of a background isotropic field

Based on the motivation that some quantum gravity theories predicts the Lorentz Invariance Violation (LIV) around Planck-scale energy levels, this paper proposes a new formalism that addresses the possible effects of LIV in electrodynamics. This formalism is capable of changing the usual electrodynamics through high derivative arbitrary mass dimension terms that includes a constant background field controlling the intensity of LIV in the models, producing modifications in the dispersion relations in a manner that is similar to the Myers–Pospelov approach. With this framework, it was possible to generate a CPT-even and CPT-odd generalized modifications of the electrodynamics in order to study the stability and causality of these theories considering the isotropic case for the background field. An additional analysis of unitarity at tree level was considered by studying the saturated propagators. After this analysis, we conclude that, while CPT-even modifications always preserve the stability, causality and unitarity in the boundaries of the effective field theory and therefore may be good candidates for field theories with interactions, the CPT-odd one violates causality and unitarity. This feature is a consequence of the vacuum birefringence characteristics that are present in CPT-odd theories for the photon sector.

Extragalactic background light inhomogeneities and Lorentz-Invariance Violation in gamma-gamma absorption and Compton scattering

AbstractAt energies approaching the Planck energy scale 1019GeV, several quantum-gravity theories predict that familiar concepts such as Lorentz (LIV) symmetry can be broken. Such extreme energies are currently unreachable by experiments on Earth, but for photons traveling over cosmological distances the accumulated deviations from the Lorentz symmetry may be measurable using the Cherenkov Telescope Array (CTA). To study the spectral hardening feature observed in some VHE gamma-ray blazars, we calculate the reduction of the EBL gamma-gamma opacity due to the existence of underdense regions along the line of sight to VHE -gamma ray sources and we compared with the possibility of a LIV signature. Considering the LIV effect, we found that the cosmic opacity for VHE-gamma rays with energy more than 10 TeV can be strongly reduced. I will further discuss the impact of LIV on the Compton scattering process, and how future CTA observations may open an exciting window on studies of the fundamental physics.

Composite Nambu–Jona-Lasinio inflation near infrared fixed point of the Hořava-Lifshitz theory

In this work, we first propose a cosmological scenario inherently based on the effective Nambu–Jona-Lasio (NJL) model near the infrared (IR) limit of the Hořava-Lifshitz (HL) theory. Having used the one-loop correction, we employ the NJL framework in the ultraviolet (UV) limit of the HL theory, with critical exponent z=3, to demonstrate in the IR limit that the symmetry of the potential at the critical coupling value is broken at z=1. We also derive the effective Higgs-like potential in the low energy regimes. Here the symmetry of the effective potential will be broken near z=1 at a certain value of the critical coupling. In our scenario, the scalar channel of the NJL model plays the role of a composite inflaton. We find that the Lorentz invariance (LI) appears at the IR regime of the HL theory and employ the standard inflationary (slow-roll) paradigm as a probe of physics at very high energy. We compute inflationary parameters and compare them with recent Planck 2015 data. Interestingly, we discover that the predictions of the model are in perfect agreement with the Planck analysis. Our salient feature is that we used inflation to quantify the IR and UV fixed points of underlying theory. We discover that the IR fixed point of HL gravity is compatible with the grand unified energy scale; whilst the UV fixed point is the Planck energy scale.

On a soliton-type spacetime defect

We review the construction of a particular soliton-type solution of the classical Einstein and matter-field equations. This localized finite-energy static classical solution can be interpreted as a single spacetime defect embedded in Minkowski spacetime and may give rise to several new effects. For a Skyrme-type theory with small enough matter-field energy scale compared to the Planck energy scale and for a sufficiently small defect length scale, the existence of a globally regular solution requires a negative active gravitational mass, so that the defect repels a distant test particle (“antigravity”). There also exist “stealth defects” which have a vanishing asymptotic gravitational mass. These stealth defects are, however, not entirely invisible as they bring about a new type of gravitational lensing.

Constraints on Lorentz Invariance Violation from Optical Polarimetry of Astrophysical Objects

Theories of quantum gravity suggest that Lorentz invariance, the fundamental symmetry of the Theory of Relativity, may be broken at the Planck energy scale. While any deviation from conventional Physics must be minuscule in particular at attainable energies, this hypothesis motivates ever more sensitive tests of Lorentz symmetry. In the photon sector, astrophysical observations, in particular polarization measurements, are a very powerful tool because tiny deviations from Lorentz invariance will accumulate as photons propagate over cosmological distances. The Standard-Model Extension (SME) provides a theoretical framework in the form of an effective field theory that describes low-energy effects due to a more fundamental quantum gravity theory by adding additional terms to the Standard Model Lagrangian. These terms can be ordered by the mass dimension d of the corresponding operator and lead to a wavelength, polarization, and direction dependent phase velocity of light. Lorentz invariance violation leads to an energy-dependent change of the Stokes vector as photons propagate, which manifests itself as a rotation of the polarization angle in measurements of linear polarization. In this paper, we analyze optical polarization measurements from 63 Active Galactic Nuclei (AGN) and Gamma-ray Bursts (GRBs) to search for Lorentz violating signals. We use both spectropolarimetric measurements, which directly constrain the change of linear polarization angle, as well as broadband spectrally integrated measurements. In the latter, Lorentz invariance violation manifests itself by reducing the observed net polarization fraction. Any observation of non-vanishing linear polarization thus leads to constraints on the magnitude of Lorentz violating effects. We derive the first set limits on each of the 10 individual birefringent coefficients of the minimal SME with d = 4 , with 95% confidence limits on the order of 10−34 on the dimensionless coefficients.

Phase space of a test particle in the presence of natural cutoffs

Physics at very high energies (close to the Planck energy scale) is in the center of modern physics challenges. At the high energy scales, or equivalently very short distances, the very notion of spacetime acquires a complicated structure. In this scale, there are limitations on the complete resolution of adjacent points in spacetime manifold. While the effect of a minimal measurable length on algebraic structure of a free particle’s phase space has been studied in the literature, the simultaneous effects of minimal length and maximal momentum have not been explored in this subject so far. Here, we are going to fill this gap. We study some properties of the algebraic structure of quantum field theories in the presence of natural cutoffs as a minimal length and a maximal momentum in a free particle’s phase space. Especially, we pay attention on the phase space trajectories of systems in the presence of natural cutoffs.

Limits on Lorentz invariance violation at the Planck energy scale from H.E.S.S. spectral analysis of the blazar Mrk 501

Some extensions to the Standard Model lead to the introduction of Lorentz symmetry breaking terms, expected to induce deviations from Lorentz symmetry around the Planck scale. A parameterization of effects due to Lorentz invariance violation (LIV) can be introduced by adding an effective term to the photon dispersion relation. This affects the kinematics of electron-positron pair creation by TeV $\gamma$ rays on the extragalactic background light (EBL) and translates into modifications of the standard EBL opacity for the TeV photon spectra of extragalactic sources. Exclusion limits are presented, obtained with the spectral analysis of H.E.S.S. observations taken on the blazar Mrk 501 during the exceptional 2014 flare. The energy spectrum, extending very significantly above 10 TeV, allows to place strong limits on LIV in the photon sector at the level of the Planck energy scale for linear perturbations in the photon dispersion relation, and provides the strongest constraints presently for the case of quadratic perturbations.

Rainbow\u2019s stars

In recent years, a growing interest in the equilibrium of compact astrophysical objects like white dwarf and neutron stars has been manifested. In particular, various modifications due to Planck-scale energy effects have been considered. In this paper we analyze the modification induced by gravity’s rainbow on the equilibrium configurations described by the Tolman–Oppenheimer–Volkoff (TOV) equation. Our purpose is to explore the possibility that the rainbow Planck-scale deformation of space-time could support the existence of different compact stars.

Constraining the existence of magnetic monopoles by Dirac-dual electric charge renormalization effect under the Planck scale limit

It was suggested by dimensional analysis that there exists a limit called the Planck energy scale coming close to which the gravitational effects of physical processes would inflate and struggle for equal rights so as to spoil the validity of pure nongravitational physical theories that governed well below the Planck energy. Near the Planck scale, the Planck charges, Planck currents, or Planck parameters can be defined and assigned to physical quantities such as the single particle electric charge and magnetic charge as the ceiling value obeyed by the low energy ordinary physics. The Dirac electric-magnetic charge quantization relation as one form of electric-magnetic duality dictates that, the present low value electric charge corresponds to a huge magnetic charge value already passed the Planck limit so as to render theories of magnetic monopoles into the strong coupling regime, and vice versa, that small and tractable magnetic charge values correspond to huge electric charge values. It suggests that for theoretic models in which the renormalization group equation provides rapid growth for the running electric coupling constant, it is easier for the dual magnetic monopoles to emerge at lower energy scales. Allowing charges to vary with the Dirac electric-magnetic charge quantization relation while keeping values under the Planck limit informs that the magnetic charge value drops below the Planck ceiling value into the manageable region when the electric coupling constant grows to one fourth at a model dependent energy scale, and continues dropping toward half the value of the Planck magnetic charge as the electric coupling constant continues growing at the model dependent rate toward one near Planck energy scale.

Testing the Equivalence Principle and Lorentz Invariance with PeV Neutrinos from Blazar Flares.

It was recently proposed that a giant flare of the blazar PKS B1424-418 at redshift z=1.522 is in association with a PeV-energy neutrino event detected by IceCube. Based on this association we here suggest that the flight time difference between the PeV neutrino and gamma-ray photons from blazar flares can be used to constrain the violations of equivalence principle and the Lorentz invariance for neutrinos. From the calculated Shapiro delay due to clusters or superclusters in the nearby universe, we find that violation of the equivalence principle for neutrinos and photons is constrained to an accuracy of at least 10^{-5}, which is 2 orders of magnitude tighter than the constraint placed by MeV neutrinos from supernova 1987A. Lorentz invariance violation (LIV) arises in various quantum-gravity theories, which predicts an energy-dependent velocity of propagation in vacuum for particles. We find that the association of the PeV neutrino with the gamma-ray outburst set limits on the energy scale of possible LIV to >0.01E_{pl} for linear LIV models and >6×10^{-8}E_{pl} for quadratic order LIV models, where E_{pl} is the Planck energy scale. These are the most stringent constraints on neutrino LIV for subluminal neutrinos.

Variation of the fundamental constants over the cosmological time: veracity of Dirac’s intriguing hypothesis

We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale (EP ∼ 1019 GeV) and, thus, how they have evolved over the cosmological time related to the temperature of the expanding universe. According to a previous paper (Nassif and Amaro de Faria, Jr. Phys. Rev. D, 86, 027703 (2012). doi:10.1103/PhysRevD.86.027703), we have shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant (α ≅ 1/137) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant (G) at the Planck scale. Thus, we will be able to verify the veracity of Dirac’s belief about the existence of “coincidences” between dimensionless ratios of subatomic and cosmological quantities, leading to a variation of G with time, that is, the ratio of the electrostatic to gravitational forces between an electron and a proton (∼1041) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by G, must vary inversely with time in the approximation of lower temperature or for times very far from the early period, to compensate for the time-variation of the Hubble parameter (H ∼ t−1). In short, we will show the validity of Dirac’s hypothesis only for times very far from the early period or T ≪ TP (∼1032 K).