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It has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter β, which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.

The Generalized Uncertainty Principle (GUP) naturally emerges in several quantum gravity models, predicting the existence of a minimal length at Planck scale. Here, we consider the quadratic GUP as a semiclassical approach to thermodynamic gravity and constrain the deformation parameter by using observational bounds from Big Bang Nucleosynthesis and primordial abundances of the light elements 4He,D,7Li. We show that our result fits with most of existing bounds on β derived from other cosmological studies.

Modified Friedmann equations have been recently derived by implementing the gravity-thermodynamics conjecture in Kaniadakis statistics, which is a relativistic self-consistent generalization of the classical Boltzmann–Gibbs theory. The ensuing cosmological scenario exhibits new extra corrections depending on the model parameter K. In this work we apply Kaniadakis statistics to the horizon entropy of the FRW Universe and explore implications on baryogenesis and primordial Lithium abundance problems. This framework is motivated by the fact that physics of the early Universe is fundamentally relativistic, suggesting that a relativistic description might also involve the statistical properties of horizon degrees of freedom. By requiring consistency with observational data on baryogenesis and Lithium abundance, we constrain the Kaniadakis parameter. We also speculate on the possibility that a running K be allowed to trace the usual thermal history of the Universe in Kaniadakis statistics.

Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

We study quantum corrections at the horizon scale of a black hole induced by a Generalized Uncertainty Principle (GUP) with a quadratic term in the momentum. The interplay between quantum mechanics and gravity manifests itself into a non-zero uncertainty in the location of the black hole radius, which turns out to be larger than the usual Schwarzschild radius. We interpret such an effect as a correction which makes the horizon disappear, as it happens in other models of quantum black holes already considered in literature. We name this kind of horizonless compact objects GUP stars . We also investigate some phenomenological aspects in the astrophysical context of binary systems and gravitational wave emission by discussing Love numbers, quasi-normal modes and echoes, and studying their behavior as functions of the GUP deformation parameter. Finally, we preliminarily explore the possibility to constrain such a parameter with future astrophysical experiments.

Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermality of Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters sinθ and Δm. As opposed to bosons, we find q>1, which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

Kaniadakis statistics is a widespread paradigm to describe complex systems in the relativistic realm. Recently, gravitational and cosmological scenarios based on Kaniadakis (κ -deformed) entropy have been considered, leading to generalized models that predict a richer phenomenology comparing to their standard Maxwell–Boltzmann counterparts. The purpose of the present effort is to explore recent advances and future challenges of Gravity and Cosmology in Kaniadakis statistics. More specifically, the first part of the work contains a review of κ -entropy implications on Holographic Dark Energy, Entropic Gravity, Black hole thermodynamics and Loop Quantum Gravity, among others. In the second part, we focus on the study of Big Bang Nucleosynthesis in Kaniadakis Cosmology. By demanding consistency between theoretical predictions of our model and observational measurements of freeze-out temperature fluctuations and primordial abundances of 4He and D, we constrain the free κ -parameter, discussing to what extent the Kaniadakis framework can provide a successful description of the observed Universe.

We exhibit a theoretical calculation of the parameter \\[ \\] appearing in the generalized uncertainty principle (GUP) with only a quadratic term in the momentum. A specific numerical value is obtained by comparing the GUP-deformed Unruh temperature with the one predicted within the framework of Caianiello’s theory of maximal acceleration. The physical meaning of this result is discussed in connection with constraints on \\[ \\] previously fixed via both theoretical and experimental approaches.

In this paper we show that Modified Inertia, i.e., the modification of inertia predicted by some alternative theories of gravity at cosmic scales, can be naturally derived within the framework of the extended uncertainty principle (EUP). Specifically, we consider two possible extensions of the Heisenberg uncertainty principle (HUP), corresponding to two different deformations of the fundamental commutator: the first one provides the natural generalization of the HUP to the (anti)-de Sitter spacetime and is endowed with only a quadratic correction in the uncertainty position. On the other hand, the second model contains both linear and quadratic extra terms. We prove that modified inertia is a direct consequence of the minimal acceleration experienced by any body due to the cosmic expansion. The obtained results are then discussed in connection with the empirical predictions of Modified Newtonian dynamics (MoND). The requirement of consistency between the two approaches allows us to fix the adjustable constant which marks the transition between the Newtonian and deep-MoND regimes.

We show that the implications of the generalized uncertainty principle (GUP) in the black hole physics are consistent with the predictions of the corpuscular theory of gravity, in which a black hole is conceived as a Bose–Einstein condensate of weakly interacting gravitons stuck at the critical point of a quantum phase transition. In particular, we compute such characteristic thermodynamic quantities as the temperature and the evaporation rate of a black hole. By comparing the results obtained in the two scenarios, we are able to estimate the GUP deformation parameter \\[ \\], which turns out to be of order unity, in agreement with the expectations of some models of string theory. We also comment on the sign of \\[ \\], exploring the possibility of having a negative deformation parameter when a corpuscular quantum description of the gravitational interaction is assumed to be valid.