Narrow Results

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a local field redefinition containing an infinite number of higher derivatives. It is also shown that the current–current amplitude is invariant with the field redefinition, and thus the unitarity of Einstein gravity is preserved.

Within the background field formalism of quantum gravity, I show that if the quantum fluctuations are limited to diffeomorphic gauge transformations rather than the physical degrees of freedom, as in conventional quantum field theory, all the quantum corrections vanish on shell and the effective action is equivalent to the classical action. In principle, the resulting theory is finite and unitary, and requires no renormalization. I also show that this is the unique parameterization that renders the path integral independent of the on-shell condition for the background field, a form of background independence. Thus, a connection is established between background independence and renormalizability and unitarity.

In this paper, we show the existence of an invariant minimum speed in space–time by forming the basis of a deformed special relativity so-called symmetrical special relativity (SSR). Such observer-independent minimum speed emerges from Dirac’s large number hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure of the symmetrical space–time with two limits of speed, namely the speed of light c and a minimum speed V. Such minimum speed is associated with a background reference frame for representing the vacuum energy related to the cosmological constant. So the symmetry in space–time given by the invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio, i.e. $m_p∕m_e=1836.15267343(11)$ given in terms of the universal minimum speed V. Furthermore, we investigate how the minimum speed in space–time plays a fundamental role in the quantization of energy in hydrogen atom.

We aim to investigate the theory of Lorentz violation with an invariant minimum speed called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus, we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So, we are able to realize that there is a similarity between SSR and a new space with variable negative curvature ($-\infty <{ℛ}<0$) connected to a set of infinite cosmological constants ($0<\mathrm{\Lambda }<\infty$), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological “constant” varying in time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally, we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.

Although it’s widely believed that gravity should have a quantum nature like every other force, the conceptual obstacles to constructing a quantum theory of gravity compel us to explore other perspectives. Gravity is not like any other force. It alone defines a universal spacetime geometry upon which quantum fields evolve. We feel gravity because matter causes spacetime to bend. Time flows at unequal rates at different locations. The rate at which time flows, and the causal structure it provides, may be required to have a classical description in order for quantum theory to be well-formulated. I discuss arguments for this proposition, but ultimately conclude that we must turn to experiment to guide us.

In this paper, we study black hole entropy universality within the conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in conformal Weyl gravity via both the Nöther current method and Wald’s entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case, we couple the conformal Weyl gravity field equations to a near horizon (linear) $U(1)$ gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However, despite non-universality, the respective black hole entropies are in congruence with Wald’s entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call $\gamma$ and relating to the Weyl anomaly coefficient. The construction follows an ${AdS}_2/{CFT}_1$ correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work.

The Seiberg–Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper, relying upon the pure-gravity form of the action functional considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein equations, and whether the Seiberg–Witten map can lead to a solution of such equations when the underlying classical geometry is Schwarzschild. We find that, if one first obtains the non-commutative field equations by varying the action of Ref. 2 with respect to all non-commutative fields, and then tries to solve these equations by expressing the non-commutative fields in terms of the commutative ones via Seiberg–Witten map, no solution of these equations can be obtained when the commutative background is Schwarzschild.

Gravity is specifically the attractive force between two masses separated at a distance. Is this force a derived or a fundamental interaction? We believe that all fundamental interactions are quantum in nature but a derived interaction may be classical. Severe challenges have appeared in many quantum theories of gravity. None of these theories has thus far attained its goal in quantizing gravity and some have met remarkable defeat. We are led to ponder whether gravitation is intrinsically classical and that there would exist a deeper and structurally different underlying theory which would give rise to classical gravitation, in the sense that statistical mechanics, quantum or classical, provides the underlying theory of classical thermodynamics.

In this article, we review recent studies on multiple dual 2D CFT descriptions of the Kerr-Newman black hole, in terms of the Kerr/CFT and Reissner-Nordström/CFT correspondences. A microscopic hair conjecture is suggested.

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.

We review on the models of gravity with a constraint by the Lagrange multiplier field. The constraint breaks general covariance or Lorentz symmetry in the ultraviolet region. We report on the F(R) gravity model with the constraint and the proposal of the covariant (power-counting) renormalized gravity model by using the constraint and scalar projectors. We will show that the model admits flat space solution, its gauge-fixing formulation is fully developed, and the only propagating mode is (higher derivative) graviton, while scalar and vector modes do not propagate. The preliminary study of FRW cosmology indicates to the possibility of inflationary universe solution is also given.

Based on the smallest physical constant of the product of space interval, time interval, and energy, the fractal quantum gravity (FQG) theory has demonstrated that every particle or physical system consists of these smallest units in fractal structures. The general relativity is an approximation of the FQG equation when the quantum effect is negligible, while the quantum theory is an approximation of the FQG equation when the interaction between space, time, and energy is very weak or negligible. The stationary-action principle can be derived from the FQG equation. The mass range of possibly existing elementary particles and an accelerating expansion evolution model of the universe can be obtained through the FQG equation. This FQG equation satisfied almost all the requirements of a quantum gravity theory and there is no free constant needed in the FQG theory. It looks promising that the FQG theory may offer a novel way to calculate all the free constants in the Standard Model of particle physics and general relativity.

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, $m\ne m_e+\frac{E_1}{c^2}$, where the electron is initially in its ground state; m_e is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein’s famous equation, $m\ne \frac{E}{c^2}$. In this paper, we also improve several drawbacks of the original pioneering works.

In this short paper we study how black hole singularities can be tackled in the context of nonlocal ghost-free gravity, in which the action is characterized by the presence of non-polynomial differential operators containing infinite order covariant derivatives. The ghost-freeness condition can be preserved by requiring that such nonlocal operators are made up of exponential of entire functions, thus avoiding the emergence of extra unhealthy poles in the graviton propagator. We will mainly focus on how infinite order derivatives can regularize the singularity at the origin by making explicit computations in the linear regime. In particular, we will show that this kind of non-polynomial operators can smear out point-like distribution and that the Schwarzschild metric can not be a solution of the field equations in the ghost-free infinite derivative gravity.

The following sections are included:

• Definition of the theory and its canonical formulation
• Quantization: propagators and the superficial degree of divergence
• Gravitational waves and observational bounds
• Acknowledgments
• References

Pauli Exclusion Principle violating transitions in atoms and nuclei are predicted from many models of non-commutative space-time, such as θ-Poincaré theory. Exclusion sensitivity curves from DAMA/LIBRA and BOREXINO are so powerful to exclude many non-commutative space-time models until the Planck energy scale. A new frontier of quantum gravity phenomenology is opened, inspiring future underground projects with a higher sensitivity then current experiments.

We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies E ≫ M_P and finite scattering angles θ_s, so as to approach the collapse regime. Our basic tool is the extension of the recently proposed, unified form of radiation to the Amati-Ciafaloni-Veneziano reduced-action model. By resumming eikonal scattering diagrams, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius R, fully agrees with previous calculations for small angles θ_s ≪ 1 but, for sizeable angles θ_s ∼ 1 acquires an exponential cutoff of the large frequency region (ω > 1/R), due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity ⟨N⟩ ∼ Gs ≫ 1 and a well-defined frequency cutoff of order 1/R. The latter corresponds to the Hawking temperature for a black hole of mass somewhat smaller than E.

Some recent results on black holes in effective loop quantum gravity are presented. Quantum gravity effects might allow the transition of a black hole into a white hole, when the Planck density is reached. I briefly review previous studies and focus on the random nature of the bouncing lifetime which was not previously taken into account. I show that, when we consider a stochastic lifetime, the signal emitted by bouncing black holes might explain fast radio bursts. Then, I present new results on the absorption cross sections calculated for a quasi Schwarzschild black hole including loop quantum gravity corrections. The black hole geometry deformation due to quantum effects has consequences for the cross sections and the Hawking spectrum.

The emergence of R² (Starobinsky) inflation from the semi-classical modification of gravity due to matter quantum fields (trace anomaly) clearly points out the importance of fundamental physics and the first principles in the construction of successful cosmological models. Along with the observational success, R² gravity is also an important step beyond general relativity (GR) towards quantum gravity. Furthermore, several approaches of quantum gravity to date are strongly indicating the presence of non-locality at small time and length scales. In this regard, ultraviolet (UV) completion of R² inflation has been recently studied in a string theory-inspired ghost-free analytic non-local gravity. We discuss the promising theoretical predictions of non-local R²-like inflation with respect to the key observables such as tensor-to-scalar ratio, tensor tilt which tell us about the spectrum of primordial gravitational waves, and scalar Non-Gaussianities which tell us about the three-point correlations in the CMB fluctuations. Any signature of non-local physics in the early Universe will significantly improve our understanding of fundamental physics at UV energy scales and quantum gravity.