arXiv subjects

Gianluca Calcagni

Publications and source records attributed to Gianluca Calcagni.

At least 73 records · Page 4Linked to original sources

arXiv2017

Imprint of quantum gravity in the dimension and fabric of spacetime

We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within the framework of multifractional theories, whose key assumption is an anomalous scaling of the spacetime dimension in the ultraviolet and a slow change of the dimension in the infrared. This sole ingredient is enough to produce a scale-dependent deformation of the integration measure with also a fuzzy spacetime structure. We also compare the multifractional correction to lengths with the types of Planckian uncertainty for distance and time measurements that was reported in studies combining quantum mechanics and general relativity heuristically. This allows us to fix two free parameters of the theory and leads, in one of the scenarios we contemplate, to a value of the ultraviolet dimension which had already found support in other quantum-gravity analyses. We also formalize a picture such that fuzziness originates from a fundamental discrete scale invariance at short scales and corresponds to a stochastic spacetime geometry.

hep-th↗

arXiv2017

Detecting quantum gravity in the sky

Getting signatures of quantum gravity is one of the topical lines of research in modern theoretical physics and cosmology. This short review faces this challenge under a novel perspective. Instead of separating quantum-gravity effects of a specific model between UV and IR regimes, we consider a general feature, possibly common to many frameworks, where all scales are affected and spacetime geometry is characterized by a complex critical exponent. This leaves a log-oscillating modulation pattern in the cosmic microwave background spectrum and gives a unique opportunity, illustrated with the example of a multi-fractional theory, to test quantum gravities at cosmological scales.

gr-qc↗

arXiv2017

Entanglement entropy, scale-dependent dimensions and the origin of gravity

We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If quantum geometry hinders diffusion, for instance when its structure at some given scale is discrete or too rough, then the spectral dimension of spacetime vanishes at that scale and the entropy density blows up. A finite entanglement entropy is a key ingredient in deriving Einstein gravity in a semi-classical regime of a quantum-gravitational theory and, thus, our arguments strengthen the role of running dimensionality as an imprint of quantum geometry with potentially observable consequences.

hep-th↗

arXiv2017

Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

hep-th↗

arXiv2017

Stability of Schwarzschild singularity in non-local gravity

In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable under linear perturbations. Thus, non-locality may be not enough to cure all the singularities of general relativity. Finally, we show that the Schwarzschild solution can be generated by the gravitational collapse of a thin shell of radiation.

gr-qc↗

arXiv2017

Complex dimensions and their observability

We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on combinatorial or multifractal structures or as the partial breaking of continuous dilation symmetry in any conformal-invariant theory. With its infinite scale hierarchy, discrete scale invariance overlaps with the traditional separation between ultraviolet and infrared physics and it can leave an all-range observable imprint, such as a pattern of log oscillations and sharp features in the cosmic microwave background primordial power spectrum.

gr-qc↗

arXiv2017

Black holes in multi-fractional and Lorentz-violating models

We study static and radially symmetric black holes in the multi-fractional theories of gravity with $q$-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length $\ell_*$. In the $q$-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to $\ell_*$. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter--Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black hole thermodynamics. In the case with $q$-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

gr-qc↗

arXiv2017

Lorentz violations in multifractal spacetimes

Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with $q$-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is $E_*>10^{14}\,{\rm GeV}$ (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value $1/2$. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which $E_*> 10^{17}\,{\rm GeV}$ or greater.

gr-qc↗

arXiv2017

Multiscale spacetimes from first principles

Assuming only a smooth and slow change of spacetime dimensionality at large scales, we find, in a background- and model-independent way, the general profile of the Hausdorff and the spectral dimension of multiscale geometries such as those found in all known quantum gravities. Examples of various scenarios are given. In particular, we derive uniquely the multiscale measure with log oscillations of theories of multifractional geometry. Predictivity of this class of models and falsifiability of their abundant phenomenology are thus established.

gr-qc↗

arXiv2017

Multifractional theories: an unconventional review

We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent flow-equation theorem on dimensional flow in quantum gravity, in particular its enormous impact on the multifractional paradigm. We will also get some new theoretical results about the construction of multifractional derivatives and the symmetries in the yet-unexplored theory $T_γ$, the resolution of ambiguities in the calculation of the spectral dimension, the relation between the theory $T_q$ with $q$-derivatives and the theory $T_γ$ with fractional derivatives, the interpretation of complex dimensions in quantum gravity, the frame choice at the quantum level, the physical interpretation of the propagator in $T_γ$ as an infinite superposition of quasiparticle modes, the relation between multifractional theories and quantum gravity, and the issue of renormalization, arguing that power-counting arguments do not capture the exotic properties of extreme UV regimes of multifractional geometry, where $T_γ$ may indeed be renormalizable. A careful discussion of experimental bounds and new constraints are also presented.

hep-th↗

arXiv2017

Deformed symmetries in noncommutative and multifractional spacetimes

We clarify the relation between noncommutative spacetimes and multifractional geometries, two quantum-gravity-related approaches where the fundamental description of spacetime is not given by a classical smooth geometry. Despite their different conceptual premises and mathematical formalisms, both research programs allow for the spacetime dimension to vary with the probed scale. This feature and other similarities led to ask whether there is a duality between these two independent proposals. In the absence of curvature and comparing the symmetries of both position and momentum space, we show that $κ$-Minkowski spacetime and the commutative multifractional theory with $q$-derivatives are physically inequivalent but they admit several contact points that allow one to describe certain aspects of $κ$-Minkowski noncommutative geometry as a multifractional theory and vice versa. Contrary to previous literature, this result holds without assuming any specific measure for $κ$-Minkowski. More generally, no well-defined $\star$-product can be constructed from the $q$-theory, although the latter does admit a natural noncommutative extension with a given deformed Poincaré algebra. A similar no-go theorem may be valid for all multiscale theories with factorizable measures. Turning gravity on, we write the algebras of gravitational first-class constraints in the multifractional theories with $q$- and weighted derivatives and discuss their differences with respect to the deformed algebras of $κ$-Minkowski spacetime and of loop quantum gravity.

hep-th↗

arXiv2016

Standard Model in multiscale theories and observational constraints

We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) $q$-derivatives. Both theories can be formulated in two different frames, called fractional and integer picture. By definition, the fractional picture is where physical predictions should be made. (i) In the theory with weighted derivatives, it is shown that gauge invariance and the requirement of having constant masses in all reference frames make the Standard Model in the integer picture indistinguishable from the ordinary one. Experiments involving only weak and strong forces are insensitive to a change of spacetime dimensionality also in the fractional picture, and only the electromagnetic and gravitational sectors can break the degeneracy. For the simplest multiscale measures with only one characteristic time, length and energy scale $t_*$, $\ell_*$ and $E_*$, we compute the Lamb shift in the hydrogen atom and constrain the multiscale correction to the ordinary result, getting the absolute upper bound $t_*<10^{-23}\,{\rm s}$. For the natural choice $α_0=1/2$ of the fractional exponent in the measure, this bound is strengthened to $t_*<10^{-29}\,{\rm s}$, corresponding to $\ell_*<10^{-20}\,{\rm m}$ and $E_*>28\,{\rm TeV}$. Stronger bounds are obtained from the measurement of the fine-structure constant. (ii) In the theory with $q$-derivatives, considering the muon decay rate and the Lamb shift in light atoms, we obtain the independent absolute upper bounds $t_* < 10^{-13}{\rm s}$ and $E_*>35\,\text{MeV}$. For $α_0=1/2$, the Lamb shift alone yields $t_*<10^{-27}\,{\rm s}$, $\ell_*<10^{-19}\,{\rm m}$ and $E_*>450\,\text{GeV}$.

hep-th↗

arXiv2016

Cosmic microwave background and inflation in multi-fractional spacetimes

We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with $q$-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.

hep-th↗

arXiv2016

What gravity waves are telling about quantum spacetime

We discuss various modified dispersion relations motivated by quantum gravity which might affect the propagation of the recently observed gravitational-wave signal of the event GW150914. We find that the bounds set by the data on the characteristic quantum-gravity mass scale $M$ are too weak to constrain these scenarios and, in general, much weaker than the expected $M> 10^4\,\text{eV}$ for a correction to the dispersion relation linear in $1/M$. We illustrate this issue by giving lower bounds on $M$, plus an upper bound coming from constraints on the size of a quantum ergosphere. We also show that a phenomenological dispersion relation $ω^2 = k^2(1+αk^n/M^n)$ is compatible with observations and, at the same time, has a phenomenologically viable mass $M>10\,\text{TeV}$ only in the quite restrictive range $0<n<0.68$. Remarkably, this is the domain of multiscale spacetimes but not of known quantum-gravity models.

gr-qc↗

arXiv2016

Quantum spectral dimension in quantum field theory

We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension $d_s$ of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension $D$. In particular, in the presence of higher momentum powers it changes with the scale, dropping from $D$ in the infrared (IR) to a value $d_s^{\rm UV}\leq D$ in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value $d_s^{\rm UV}=2$ for any dimension $D$.

hep-th↗

arXiv2016

ABC of multi-fractal spacetimes and fractional sea turtles

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with $q$-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

hep-th↗

arXiv2016

Particle-physics constraints on multifractal spacetimes

We study electroweak interactions in the multiscale theory with $q$-derivatives, a framework where spacetime has the typical features of a multifractal. In the simplest case with only one characteristic time, length and energy scale $t_*$, $\ell_*$, and $E_*$, we consider (i) the muon decay rate and (ii) the Lamb shift in the hydrogen atom, and constrain the corrections to the ordinary results. We obtain the independent absolute upper bounds (i) $t_* < 10^{-13}{\rm s}$ and (ii) $E_*>35\,\text{MeV}$. Under some mild theoretical assumptions, the Lamb shift alone yields the even tighter ranges $t_*<10^{-27}\,{\rm s}$, $\ell_*<10^{-19}\,{\rm m}$, and $E_*>450\,\text{GeV}$. To date, these are the first robust constraints on the scales at which the multifractal features of the geometry can become important in a physical process.

hep-th↗

arXiv2015

Nonlocal quantum gravity and M-theory

We construct a ultraviolet completion of the bosonic sector of 11-dimensional supergravity motivated by string field theory. We start from a general class of theories characterized by an entire nonpolynomial form factor which allows one to avoid new poles in the propagator and improves the high-energy behavior of the loops amplitudes. Comparing these models with effective string field theory, a unique form factor is selected out. In view of this, we modify 10-dimensional supergravity and finally get a ultraviolet completion of 11-dimensional supergravity by an oxidation process. The result is a candidate for a finite and unitary particle-field limit of M-theory.

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