The generalized uncertainty principles (GUP) and modified dispersion relations (MDR) are much like two faces for one coin in research for the phenomenology of quantum gravity which apparently plays an important role in estimating the possible modifications of the black hole thermodynamics and the Friedmann equations. We first reproduce the horizon area for different types of black holes and investigate the quantum corrections to Bekenstein-Hawking entropy (entropy-area law). Based on this, we study further thermodynamical quantities and accordingly the modified Friedmann equation in four-dimensional de Sitter-Schwarzschild, Reissner-Nördstrom and Garfinkle-Horowitz-Strominger black holes. In doing this we applied various quantum gravity approaches. The MDR parameter relative to the GUP one is computed and the properties of the black holes are predicted. This should play an important role in estimating response of quantum gravity to the various metric-types of black holes. We found a considerable change in the thermodynamics quantities. We find that the modified entropy of de-Sitter-Schwarzshild and Reissner-Nördstrom black holes starts to exist at a finite standard entropy. The Garfinkle-Horowitz-Strominger black hole shows a different entropic property. The modified specific heat due to GUP and MDR approaches vanishes at large standard specific heat, while the corrections due to GUP result in different behaviors. The specific heat of modified de-Sitter-Schwarzshild and Reissner-Nördstrom black holes seems to increase, especially at large standard specific heat. In the early case, the black hole cannot exchange heat with the surrounding space. Accordingly, we would predict black hole remnants which may be considered as candidates for dark matter.
We investigate the hypothetical process of gravitational Cherenkov radiation, which may occur in modified gravity theories. We obtain a useful constraint on a modified dispersion relation for propagating modes of gravitational waves, which could be predicted as a consequence of violation of the Lorentz invariance in modified theories of gravity. The constraint from gravitational Cherenkov radiation and that from direct measurements of the gravitational waves emitted by a compact binary system are complementary to each other.
Considering corrections produced by modified dispersion relations on the equation of state parameter of radiation, we study the induced black hole metric inspired by Kiselev's ansatz, thus defining a deformed Reissner-Nordström metric. In particular, we consider thermodynamic properties of such a black hole from the combined viewpoints of the modified equation of state parameter and the phenomenological approach to the quantum gravity problem called rainbow gravity.
In this paper, employing the modified dispersion relation, we have derived the general modified Friedmann equations and the corresponding modified entropy relations for the Friedmann-Robertson-Walker (FRW) Universe. In this setup, we find that when the big bounce happens, its energy scale and its corresponding modified entropy behavior are sensitive to the value of $k$. In contrast to the previous work with $k=0$, our work mainly demonstrates that the bouncing behavior for the closed Universe with $k=1$ appears at the normal energy limit of the modified dispersion relation introduced, and when…
In this paper, we will deform the usual energy-momentum dispersion relation of a photon gas at an intermediate scale between the Planck and electroweak scales. We will demonstrate that such a deformation can have non-trivial effects on the physics of dumb holes. So, motivated by the physics of dumb holes, we will first analyse the effect of such a deformation on thermodynamics. Then we observe that the velocity of sound also gets modified due to such a modification of the thermodynamics. This changes the position of the horizon of a dumb hole, and the analogous Hawking radiation from a dumb ho…
Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the later is currently analyzed on the basis of the available observational data from gamma ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homo…
Deviation from standard dispersion relations for electrons and photons in the form of an extra term proportional to an arbitrarily high power of momentum is studied. It is shown that observational constraints lead to a region in the parametric space that is similar in shape to the region obtained earlier in a theory in which the extra term was proportional to third power of momentum.
Recent observations of anomalous line-of-sight velocity dispersions of two ultra-diffuse galaxies (UDGs) provide a stringent test for modified gravity theories. While NGC 1052-DF2 exhibits an extremely low dispersion value ($σ\sim 7.8_{-2.2}^{+5.6}$ km/s), the reported dispersion value for NGC 1052-DF44 is quite high ($σ\sim 41.0 \pm 8$ km/s). For DF2, the dynamical mass is almost equal to the luminous mass suggesting the galaxy have little to no `dark matter' in $Λ$CDM whereas DF4 requires a dynamical mass-to-light ratio of $\sim 30$ making it to be almost entirely consists of dark matter. It…
In this manuscript, we investigate the effects of a modified dispersion relation on the thermodynamics of Schwarzschild black hole surrounded by the quintessence matter. We find that the MDR-correction states the same lower bound on the horizon, while the quintessence matter specifies the upper bound to the horizon depending on the state parameter. Due to MDR-correction and quintessence matter presence, we observe modifications in equation of state and specific heat functions of black hole. We show that a remnant can occur according to quintessence matter, and the black hole's stability depend…
In this work we continue the systematic study of observable effects emerging from modified dispersion relations. We study the motion of test particles subject to a general first order modification of the general relativistic dispersion relation as well as subject to the $κ$-Poincaré dispersion relation in spherical symmetry. We derive the corrections to the photon sphere, the black hole shadow, the Shapiro delay and the light deflection and identify the additional dependence of these observables on the photons' four momentum, which leads to measurable effects that can be compared to experiment…
Planck scale inspired theories which are also often accompanied with maximum energy and/or momentum scale predict deformed dispersion relations compared to ordinary special relativity and quantum mechanics. In this paper we resort to the methods of statistical mechanics in order to determine the effects of a deformed dispersion relation along with upper bound in partition function as maximum energy and/or momentum scale can have on the thermodynamics of photon gas. We have analyzed two distinct quantum gravity models in this paper
The Hamiltonian formulation of modified dispersion relations (MDRs) allows for their implementation on generic curved spacetimes. In turn it is possible to derive phenomenological effects. I will present how to construct the kappa-Poincare dispersion relation on curved spacetimes, its spherically symmetric realizations, among them the kappa deformation of Schwarzschild spacetime, and its implementation on Friedmann-Lemaitre-Robertson-Walker spacetimes with arbitrary scale factor. In addition we will construct the general first order modifications of the general relativistic dispersion relation…
Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corr…
Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massle…
We study the thermodynamics of a moving Schwarzschild black hole, identifying the temperature and entropy in a relativistic scenario. Furthermore, we set arguments in a framework relating invariant geometrical quantities under global spacetime transformations and the dispersion relation of the system. We then extended these arguments in order to consider more general dispersion relations, and identify criteria to rule them out.
Forecasting Sensitivity to Modified Dispersion Effects in Pulsar Timing Arrays
École polytechnique, Institut polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo（宇宙物理与数学卡弗里研究所（WPI），UTIAS，东京大学）
In recent years Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We here propose a general strategy of analysis of the effects of modifications of dispersion r…
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lemaître-Robertson-Walker (FLRW) geometry that is locally identical to the $κ$-Poincaré dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of parti…
Newtonian gravity predicts the existence of white dwarfs with masses far exceeding the Chandrasekhar limit when the equation of state of the degenerate electron gas incorporates the effect of quantum spacetime fluctuations (via a modified dispersion relation) even when the strength of the fluctuations is taken to be very small. In this paper, we show that this Newtonian "super-stability" does not hold true when the gravity is treated in the general relativistic framework. Employing dynamical instability analysis, we find that the Chandrasekhar limit can be reassured even for a range of high st…
The tunneling behavior of fermions with half-integral spin from a higher dimensional charged anti-de Sitter (AdS) black hole in de Rham, Gabadadze and Tolley (dRGT) massive gravity is investigated via a modified Hamilton-Jacobi equation. The results demonstrate that the modified thermodynamic quantities not only are related to the properties of the higher dimensional charged AdS black hole in dRGT massive gravity but also depend on the parameter $β$, the coupling constant $σ$ and the mass of emitted particles $m$. In addition, the modified Hawking temperature is higher than the original temper…
Many quantum theories of gravity propose Lorentz violating dispersion relations of the form $ω= |k|\, f(|k|/M)$, with recovery of approximate Lorentz invariance at energy scales much below $M$. We show that a quantum field with this dispersion predicts drastic low energy Lorentz violation in atoms modelled as Unruh-DeWitt detectors, for any $f$ that dips below unity somewhere. As an example, we show that polymer quantization motivated by loop quantum gravity predicts such Lorentz violation below current ion collider rapidities.
Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such a minimal length scale is that photons should exhibit dispersion. In 2009 the observation of a short gamma ray burst seemed to bound the minimal length scale to distances smaller than the Planck length, implying that spacetime appeared continuous to distances below the Planck length. This poses a challenge for such minimal distance models. Here we propose a modification of the position and momentum operators, ${\hat x}$ and ${\hat p}$, which lead to a minimal length scale…
We develop a technique to construct analytical solutions of the linear perturbations of inflation with a nonlinear dispersion relation, due to quantum effects of the early universe. Error bounds are given and studied in detail. The analytical solutions describe the exact evolution of the perturbations extremely well even when only the first-order approximations is used.
We model the velocity dispersion of the ultra-diffuse galaxy NGC 1052-DF2 using Newtonian gravity and modified gravity (MOG). The velocity dispersion predicted by MOG is higher than the Newtonian gravity prediction, but it is fully consistent with the observed velocity dispersion that is obtained from the motion of 10 globular clusters.
For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires non-trivial background dynamics before the onset of standard radiation-dominated cosmology; we d…
Recent observations of ultra-dwarf galaxy NGC1052-DF2 started an interesting discussion between dark matter hypothesis and modified gravity theories. Reported low velocity dispersion (< 10.5 km/s at 90% confidence level) derived from the kinematic data of 10 globular clusters in the galaxy points towards an extraordinarily low dynamical mass ($\sim$ $3.4 \times 10^{8} M_{\odot}$) which is of the same order of the luminous mass ($\sim$ $2.0 \times 10^{8} M_{\odot}$) in the galaxy. This has been interpreted as the first evidence of a galaxy `without Dark Matter'. It has been argued that dark mat…
We investigate the effects of a modified dispersion relation proposed by Majhi and Vagenas on the Reissner-Nordstrom black hole thermodynamics in a universe with large extra dimensions. It is shown that entropy, temperature and heat capacity receive new corrections and charged black holes in this framework have less degrees of freedom and decay faster compared to black holes in the Hawking picture. We also study the emission rate of black hole and compare our results with other quantum gravity approaches. In this regard, the existence of the logarithmic prefactor and the relation between dimen…
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $κ$-Poincaré quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum sp…
