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The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, as it allows us to study particles with much higher energies and travelling much longer distances than possible in terrestrial experiments, but more progress is needed on several fronts. A thorough appraisal of current strategies and experimental frameworks, regarding quantum gravity phenomenology, is provided here. Our aim is twofold: a description of tentative multimessenger explorations, plus a focus on future detection experiments. As the outlook of the network of researchers that formed through the COST Action CA18108 "Quantum gravity phenomenology in the multi-messenger approach (QG-MM)", in this work we give an overview of the desiderata that future theoretical frameworks, observational facilities, and data-sharing policies should satisfy in order to advance the cause of quantum gravity phenomenology., Comment: Submitted to CQG for the Focus Issue on "Quantum Gravity Phenomenology in the Multi-Messenger Era: Challenges and Perspectives". Please contact us to express interesst of endorsement of this white paper

We investigate the quasinormal modes of a massless scalar field in a Schwarzschild black hole, which is deformed due to noncommutative corrections. We introduce the deformed Schwarzschild black hole solution, which depends on the noncommutative parameter $\Theta$. We then extract the master equation as a Schr\"odinger-like equation, giving the explicit expression of the effective potential which is modified due to the noncommutative corrections. After that, we solve the master equation numerically. The significance of these results is twofold. Firstly, our results can be related to the detection of gravitational waves by the near future gravitational wave detectors, such as LISA, which will have a significantly increased accuracy. In particular, these observed gravitational waves produced by binary strong gravitational systems have oscillating modes which can provide valuable information. Secondly, our results can serve as an additional tool to test the predictions of GR, as well as to examine the possible detection of this kind of gravitational corrections., Comment: 15 pages, 7 figures

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers., Comment: This review was written by participants of the COST Action CA18108. Further information on the review can be found at https://qg-mm.unizar.es/review/, updated to published version

We extract observational constraints on $f(T)$ gravity, using the recently proposed statistical method which is not affected by the value of $H_0$ and thus it bypasses the problem of the disagreement in its exact numerical value between Planck and direct measurements. We use direct measurements of the Hubble parameter with the corresponding covariance matrix, and for completeness we perform a joint analysis using the latest data from Supernovae type Ia based on JLA sample, quasi-stellar objects, and Cosmic Microwave Background shift parameter from Planck. We analyze a large family of $f(T)$ models, and we compare the fitting results with $\Lambda$CDM cosmology using the AIC statistical test. Utilizing only the Hubble parameter data we find that in the case of the power-law $f(T)$ model a small but non-zero deviation from $\Lambda$CDM cosmology is slightly favored at 1-$\sigma$, nevertheless the corresponding AIC value shows a statistical equivalence with it. Finally, the join analysis reveals that all $f(T)$ models are very efficient and in very good agreement with observations., Comment: 23 pages, 5 figures, accepted for publication in JCAP

We use BBN observational data on primordial abundance of ${}^4He$ to constrain f(T) gravity. The three most studied viable $f(T)$ models, namely the power law, the exponential and the square-root exponential are considered, and the BBN bounds are adopted in order to extract constraints on their free parameters. For the power-law model, we find that the constraints are in agreement with those acquired using late-time cosmological data. For the exponential and the square-root exponential models, we show that for realiable regions of parameters space they always satisfy the BBN bounds. We conclude that viable f(T) models can successfully satisfy the BBN constraints., Comment: 10 pages, 1 figure

We investigate the Einstein static universe (ESU) and the emergent universe scenario in the framework of Ho\v{r}ava-Lifshitz-like $F(R)$ gravity. We first perform a dynamical analysis in the phase space, and amongst others we show that a spatially open universe filled with matter satisfying the strong energy condition can exhibit a stable static phase. Additionally, we examine the behavior of the scenario under scalar perturbations and extract the conditions under which it is free of perturbative instabilities, showing that the obtained background ESU solutions are free of such instabilities. However, in order for the Einstein static universe to give rise to the emergent universe scenario we need to have an exotic matter sector that can lead the universe to depart from the stable static state and enter into its usual expanding thermal history., Comment: 9 pages, 2 figures

Spherically symmetric solutions for f(T) gravity models are derived by the so called Noether Symmetry Approach. First, we present a full set of Noether symmetries for some minisuperspace models. Then, we compute analytical solutions and find that spherically symmetric solutions in f(T) gravity can be recast in terms of Schwarzschild-like solutions modified by a distortion function depending on a characteristic radius. The obtained solutions are more general than those obtained by the usual solution methods., Comment: 10 pages, to appear in Phys. Rev. D

We investigate the cosmological predictions of several $f(T)$ models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric supernovae type Ia, cosmic microwave background and baryonic acoustic oscillation and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance $\Lambda$ cosmology at the background level. In addition we constrain the growth index $\gamma$ predicted in the context of these models using the latest perturbation growth data in the context of three parametrizations for $\gamma$. The evolution of the best fit effective Newton constant, which incorporates the $f(T)$-gravity effects, is also obtained along with the corresponding $1\sigma$ error regions. We show that all the viable parameter sectors of the $f(T)$ gravity models considered practically reduce these models to $\Lambda$CDM. Thus, the degrees of freedom that open up to $\Lambda$CDM in the context of $f(T)$ gravity models are not utilized by the cosmological data leading to an overall disfavor of these models., Comment: 16 pages, 9 figures, changes match published version

We investigate general braneworld models, with a non-minimally coupled phantom bulk field and arbitrary brane and bulk matter contents. We show that the effective dark energy of the brane-universe acquires a dynamical nature, as a result of the non-minimal coupling which provides a mechanism for an indirect "bulk-brane interaction" through gravity. For late-time cosmological evolution and without resorting to special ansatzes or to specific areas of the parameter space, we show that the -1-crossing of its equation-of-state parameter is general and can be easily achieved. As an example we provide a simple, but sufficiently general, approximate analytical solution, that presents the crossing behavior., Comment: 11 pages, 2 figures

We examine quintom dark energy models, produced by the combined consideration of a canonical and a phantom field, with nearly flat potentials and dark energy equation-of-state parameter $w_{DE}$ close to -1. We find that all such models converge to a single expression for $w_{DE}(z)$, depending only on the initial field values and their derivatives. We show that this quintom paradigm allows for a description of the transition through -1 in the near cosmological past. In addition, we provide the necessary conditions for the determination of the direction of the -1-crossing., Comment: 7 pages, 3 figures, version to appear in Phys. Rev. D

In the present work we investigate the cosmological implications of holographic dark energy density in the Gauss-Bonnet framework. By formulating independently the two cosmological scenarios, and by enforcing their simultaneous validity, we show that there is a correspondence between the holographic dark energy scenario in flat universe and the phantom dark energy model in the framework of Gauss-Bonnet theory with a potential. This correspondence leads consistently to an accelerating universe. However, in general one has not full freedom of constructing independently the two cosmological scenarios. Specific constraints must be imposed on the coupling with gravity and on the potential., Comment: 10 pages, no figures. Has been accepted for publication in Physics Letters B

We investigate canonical, phantom and quintom models, with the various fields being non-minimally coupled to gravity, in the framework of holographic dark energy. We classify them and we discuss their cosmological implications. In particular, we examine the present value of the dark energy equation-of-state parameter and the crossing through the phantom divide, and we extract the conditions for a future cosmological singularity. The combined scenarios are in agreement with observations and reveal interesting cosmological behaviors., Comment: 9 pages, 5 figures, version published in Phys. Lett. B

We investigate the quintom model of dark energy in the generalized case where the corresponding canonical and phantom fields possess O($N$) symmetries. Assuming exponential potentials we find that this O$(N)$ quintom paradigm exhibits novel properties comparing to the simple canonical and phantom scenarios. In particular, we find that the universe cannot result in a quintessence-type solution with $w>-1$, even in the cases where the phantom field seems to be irrelevant. On the contrary, there are always late-time attractors which correspond to accelerating universes with $w<-1$ and with a recent crossing of the phantom divide, and for a very large area of the parameter space they are the only ones. This is in contrast with the previous simple-quintom results, where an accelerating universe is a possible late-time stable solution but it is not guaranteed., Comment: 13 pages, no figure

We investigate the phase-space structure of the quintom paradigm in the framework of a spatially flat, open, or closed isotropic and homogeneous universe. We examine the dynamical evolution under the assumption of late-time dark energy domination, without specifying the explicit quintom potential form. The obtained cosmological behavior is qualitatively different than that acquired from the single phantom model., Comment: 9 pages, version published at Int. J. Mod. Phys. D

We investigate quintom cosmology in FRW universes using isomorphic models consisting of three coupled oscillators, one of which carries negative kinetic energy. In particular, we examine the cosmological paradigms of minimally-coupled massless quintom, of two conformally-coupled massive scalars and of conformally-coupled massive quintom, and we obtain their qualitative characteristics as well as their quantitative asymptotic behavior. For open or flat geometries, we find that, independently of the specific initial conditions, the universe is always led to an eternal expansion., Comment: 11 pages, no figures

We apply bulk holographic dark energy in general braneworld models with a Gauss-Bonnet term in the bulk and an induced gravity term and a perfect fluid on the brane. Without making any additional assumptions we extract the Friedmann equation on the physical brane and we show that a $\rho$-$\rho_\Lambda$ coupling arises naturally by the full 5D dynamics. The low-energy (late-time) evolution reveals that the effective 4D holographic dark energy behaves as ``quintom'', that is it crosses the phantom divide $w=-1$ during the evolution. In particular, the Gauss-Bonnet contribution decreases the present value of $w_\Lambda$, while it increases the growing rate of $w_\Lambda(z)$ with $z$, in comparison with the case where such a term is absent., Comment: 16 pages, version published in Phys. Lett. B

We apply the bulk holographic dark energy in general 5D two-brane models. We extract the Friedmann equation on the physical brane and we show that in the general moving-brane case the effective 4D holographic dark energy behaves as a quintom for a large parameter-space area of a simple solution subclass. We find that $w_\Lambda$ was larger than -1 in the past while its present value is $w_{\Lambda_0}\approx-1.05$, and the phantom bound $w_\Lambda=-1$ was crossed at $z_{p}\approx0.41$, a result in agreement with observations. Such a behavior arises naturally, without the inclusion of special fields or potential terms, but a fine-tuning between the 4D Planck mass and the brane tension has to be imposed., Comment: 15 pages, 2 figures, version published in JCAP

We present a generalized version of holographic dark energy arguing that it must be considered in the maximally subspace of a cosmological model. In the context of brane cosmology it leads to a bulk holographic dark energy which transfers its holographic nature to the effective 4D dark energy. As an application we use a single-brane model and we show that in the low energy limit the behavior of the effective holographic dark energy coincides with that predicted by conventional 4D calculations. However, a finite bulk can lead to radically different results., Comment: 11 pages, version published in Phys. Lett. B

We investigate the full 5D dynamics of general braneworld models. Without making any further assumptions we show that cyclic behavior can arise naturally in a fraction of physically accepted solutions. The model does not require brane collisions, which in the stationary case remain fixed, and cyclicity takes place on the branes. We indicate that the cosmological constants play the central role for the realization of cyclic solutions and we show that its extremely small value on the observable universe makes the period of the cycles and the maximum scale factor astronomically large., Comment: 17 pages, 1 figure, version published in Nucl. Phys. B

We investigate the dynamics of the critical isoscalar condensate, formed during heavy-ion collisions. Our analysis is based on a simplified model where the sigma and the pions are the only degrees of freedom. In field description, both in physical and momentum space, we find that the freeze-out profile presents a structure which reveals clear traces of the critical fluctuations in the sigma-component. In particle representation, using Monte-Carlo simulations and factorial moment analysis, we show that signatures of the initial criticality survive at the detected pions. We propose the distribution of suitably defined intermittency indices, incorporating dynamical effects due to sigma-pion interaction, as the basic observable for the exploration of critical fluctuations in heavy-ion collision experiments., Comment: 22 pages, 8 figures, version published at Phys. Rev. C

We investigate the physically accepted solutions of general Braneworld scenarios, scanning uniformly the associated parameter space. Without making any further assumptions we find that solutions which give "small" Hubble parameters on the physical brane, and therefore "small" effective cosmological constants on the 4D Universe, are far more probable than those with "large" ones. Eventually, their distribution tends to the $\delta$-function in the limit of continuous covering of the parameter space., Comment: 6 pages, 6 figures, version published in JCAP

We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the distribution of isoscalar particles (sigmas) in configuration space. Non-equilibrium dynamics is induced through a sudden symmetry breaking leading gradually to the deformation of the initial fractal geometry. After constructing an ensemble of configurations describing the initial state of the isoscalar field we solve the equations of motion and show that remnants of the critical state and the associated fractal geometry survive for time scales larger than the time needed for the mass of the isoscalar particles to reach the two-pion threshold. This result is more transparent in an event-by-event analysis of the phenomenon. Thus, we conclude that the initial fractal properties can eventually be transferred to the observable pion-sector through the decay of the sigmas even in the case of a quench., Comment: 12 pages, 9figures, version published at Nuclear Physics A

We consider the classical evolution of a lattice of non-linear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular we show that traces of the critical fractal measure can sustain for large times and we extract the properties of the chain which determine the associated time-scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges in time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry broken phase., Comment: 15 pages, 15 figures, version publiced at Physical Review E

It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing down). On the other hand the dynamics in the order parameter space is simplified significantly in this case due to the onset of self-similarity in the associated fluctuation patterns. As a consequence the effective action at the critical point obtains a very simple form. In the present work we show that this simplified action can be used in order to simulate efficiently the statistical properties of a macroscopic system exactly at the critical point. Using the proposed algorithm we generate an ensemble of configurations resembling the characteristic fractal geometry of the critical system related to the self-similar order parameter fluctuations. As an example we simulate the one-component real scalar field theory at the transition point $T=T_c$ as a representative system belonging to the $3-D$ Ising universality class., Comment: 10 pages, 6 figures, submitted for publication to Journal of Computational Physics

We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of non-equilibrium evolution., Comment: 13 pages, 13 figures, version published at Int. J. Mod. Phys. A

We demonstrate that energy can be transferred very rapidly from the bulk to the brane through parametric resonance. In a simple realization, we consider a massless bulk field that interacts only with fields localized on the brane. We assume an initial field configuration that has the form of a wave-packet moving towards the brane. During the reflection of the wave-packet by the brane the localized fields can be excited through parametric resonance. The mechanism is also applicable to bulk fields with a potential. The rapid energy transfer can have important cosmological and astrophysical implications., Comment: 12 pages, 4 figures, accepted for publication in Phys. Lett. B

Within the context of the linear $\s$-model for two flavours, we investigate non-equilibrium phenomena that may occur during the QCD chiral phase transition in heavy-ion collisions. We assume that the chiral symmetry breaking is followed by a rapid quench so that the system falls out of thermal equilibrium. We study the mechanism for the amplification of the pion field during the oscillations of the $\s$-field towards and around its new minimum. We show that the pion spectrum develops a characteristic pronounced peak at low momenta., Comment: 14 pages, 8 figures, RevTex4