Cosmological complexity of the modified dispersion relation

The relational framework of canonical quantum gravity with nonultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the application of Lieb-Robinson bounds to on-shell monotonic gauge flow when there is a continuous external ``time'' parameter. An explicit Lieb-Robinson bound is derived for the differential on-shell evolution of the operator norm of the commutator of discretized Dirac observables, demonstrating how a local light conelike causal structure emerges. Ultralocal constraints do not permit such a structure to arise via Lieb-Robinson bounds. Gauge and ($3+1$)-diffeomorphism invariance of the light cone is discussed along with the issues of quantum fluctuations, the nature of the nonlocalities, the spatial continuum limit, and the possible links to noncommutative geometry.

We study effects of presence of a small amount of so-called anisotropic solid remnant in the early post-inflationary Universe dominated by radiation. This model is inspired by solid inflation and its generalizations with matter described through a triplet of fields. In our model, the internal full global Euclidean symmetry of this triplet is broken, which leads to an anisotropic expansion of the Universe. Superhorizon scalar and vector perturbations grow, while behavior of tensor perturbations remains the same as in the standard case with Universe filled with only radiation. We also find a very interesting case within the limit of a very small amount of the anisotropic solid remnant and the longest possible duration of its presence, where size of vector perturbations decreases with a different power of scale factor as in the standard scenario. The obtained results improve agreement between the observational data and the theoretical predictions of solid inflation in a case with suppressed non-linear effects.

Recent cosmological observations of unprecented accuracy, by WMAP in particular, have established a `Standard Model' of cosmology, just as LEP established the Standard Model of particle physics. Both Standard Models raise open questions whose answers are likely to be linked. The most fundamental problems in both particle physics and cosmology will be resolved only within a framework for Quantum Gravity, for which the only game in town is string theory. We discuss novel ways to model cosmological inflation and late acceleration in a non-critical string approach, and discuss possible astrophysical tests.

<sec>The black hole information paradox—a fundamental conflict between quantum unitarity and semi-classical gravity—remains unresolved within the framework of quantum gravity. This work builds a conceptual bridge between this modern dilemma and Zeno’s ancient paradox of motion, emphasizing that they all rely on <i>limit processes</i> to reconcile infinite divisibility with finite physical outcomes. Although previous researches have established information conservation in black hole evaporation by copying wormholes, this study transcends mere unitarity verification to answer a deeper question: <i>How do we quantify the statistical evolution and inherent irreversibility of Hawking radiation</i>?</sec><sec> <b>Methods</b> :</sec><sec> <b>i) Gravitational path integral formalism</b> : We compute Rényi entropies <inline-formula><tex-math id="M1">\begin{document}$ S_n = \dfrac{1}{1-n} \ln \text{Tr}(\rho^n) $\end{document}</tex-math></inline-formula> by analytic continuation <inline-formula><tex-math id="M2">\begin{document}$( n \to 1 )$\end{document}</tex-math></inline-formula>, incorporating both disconnected geometries (Hawking saddles) and connected replica wormhole saddles.</sec><sec> <b>ii) JT gravity model</b> : A two-dimensional Jackiw-Teitelboim (JT) gravity coupled to a conformal bath is analyzed, with End-of-the-World (EOW) branes modeling early Hawking radiation states.</sec><sec> <b>iii) Modular thermodynamics</b> : Modular entropy <inline-formula><tex-math id="M3">\begin{document}$ S_m $\end{document}</tex-math></inline-formula> and entanglement capacity <inline-formula><tex-math id="M4">\begin{document}$ C_n $\end{document}</tex-math></inline-formula> are defined as:</sec><sec> <inline-formula><tex-math id="M5">\begin{document}$ S_m = \log\text{Tr}(\rho^n) - n\partial_n\log\text{Tr}(\rho^n), \quad C_n = n^2\partial_n^2\log\text{Tr}(\rho^n),$\end{document}</tex-math></inline-formula>mirroring thermodynamic entropy and heat capacity.</sec><sec> <b>Key results</b> :</sec><sec> <b>i) Page curve restoration</b> : The von Neumann entropy transitions from linear growth (Hawking phase) to zero (wormhole-dominated phase) at the Page time: <inline-formula><tex-math id="M6">\begin{document}$ t_{\text{Page}} \propto {S_{\text{BH}}}/({n\kappa c}), \quad S_{\text{BH}} = {A}/({4G_N}), $\end{document}</tex-math></inline-formula>indicating faster entropy reduction for higher <i>n</i>.</sec><sec> <b>ii) Replica wormhole mechanism</b> : The gravitational path integral reveals a topological transition:</sec><sec> <inline-formula><tex-math id="M7">\begin{document}$ \text{Tr}(\rho^n) \approx \dfrac{kZ_1^n + k^n Z_n}{(kZ_1)^n} \quad \Rightarrow \quad \text{Dominance shift at } k \sim {\mathrm{e}}^{S_0}$\end{document}</tex-math></inline-formula>.</sec><sec>Quantum non-cloning constraints: A reversibility paradox arises: while <i>n</i>-copies -copies of a <i>known</i> state allow full reconstruction, the non-cloning theorem forbids replication of <i>unknown</i> states. This necessitates the <i>a priori</i> existence of multiple replicas to ensure consistency.</sec><sec> <b>iii) Connection to Zeno’s paradox</b> : The resolution of Zeno’s paradox through Newtonian limits <inline-formula><tex-math id="M9">\begin{document}$( v = \lim\limits_{\Delta t \to 0} \Delta x / \Delta t $\end{document}</tex-math></inline-formula>) parall) parallels the replica trick’s role in black hole physics:</sec><sec> <b>iv) Infinite-to-finite mapping</b> : Both employ limit operations to compress divergent processes (infinite steps or entropy growth) into finite observables.</sec><sec> <b>Discrete <i>vs</i>. continuous</b> : Challenge classical spacetime continuity, hinting at holographic or discrete quantum spacetime.</sec><sec> <b>Irreversibility and generalized second law</b> : The relative entropy <inline-formula><tex-math id="M10">\begin{document}$ S(\rho \| \sigma) $\end{document}</tex-math></inline-formula>, defined as:</sec><sec> <inline-formula><tex-math id="M11">\begin{document}$ S(\rho \| \sigma) = \text{Tr}(\rho \log \rho) - \text{Tr}(\rho \log \sigma),$\end{document}</tex-math></inline-formula>monotonically increases during the Hawking-to-wormhole transition, establishing statistical irreversibility in modular space. This generalized second law persists despite microscopic unitarity, analogous to thermodynamic irreversibility in closed systems with the formula: <inline-formula><tex-math id="Z-20250414151430">\begin{document}$ \left(S_n-S_{\rho}\right)-n\left(\left\langle H\right\rangle_n-\left\langle H\right\rangle_{\rho}\right)\geqslant 0 $\end{document}</tex-math></inline-formula>.</sec><sec> <b>Conclusion</b> :</sec><sec>Our results address the black hole information paradox and the irreversible problem through three pillars:</sec><sec> <b>i) Unitarity</b> : Replica wormholes enforce unitarity via non-perturbative spacetime topology changes.</sec><sec> <b>ii) Modular thermodynamics</b> : A framework linking entanglement entropy, relative entropy, and irreversibility.</sec><sec> <b>iii) Replica priority principle</b> : Multiple radiation replicas exist <i>a priori</i>, circumventing quantum cloning constraints.</sec><sec>This work transcends mere information conservation, advancing into the second layer of black hole physics: Characterizing the irreversible evolution of Hawking radiation in modular space.</sec>

The quest to unify quantum mechanics and general relativity remains one of the greatest challenges The quest to unify quantum mechanics and general relativity remains one of the greatest challenges in theoretical physics.While string theory and loop quantum gravity dominate current research,their reliance on abstract geometries or unobserved dimensions limits experimental accessibility.This paper introduces Membrane-Point Theory(MPsT),a paradigm grounded in spacetime-matter symbiosis,offering testable predictions and bridging quantum and classical regimes. At the same time,this research present mathematical formulations,experimental predictions,and pathways for empirical validation,inviting collaborative efforts to refine this framework.

We study black hole radiation inside black holes within the framework of quantum gravity.First, we review on our previous work of a canonical quantization for a spherically symmetric geometry where one of the spatial coordinates is treated as the time variable, since we think of the interior region of a black hole.Based on this formalism, under physically plausible assumptions, we solve the Wheeler-De Witt equation inside the black hole, and show that the mass-loss rate of an evaporating black hole due to thermal radiation is equivalent to the result obtained by Hawking in his semi-classical approach.A remarkable point is that our assumptions make the momentum constraint coincide with the Hamiltonian constraint up to an irrelevant overall factor.Furthermore, for comparison, we solve the Wheeler-De Witt equation outside the black hole as well, and see that the mass-loss rate of an evaporating black hole has the same expression.The present analysis suggests that the black hole radiation comes from the black hole singularity.We also comment on the Birkhoff theorem in quantum gravity.

Holomorphic general coordinate invariant modified measure gravitational theory

The Lanczos algorithm offers a framework for constructing wave functions in closed and open quantum systems from their Hamiltonians. Since the early universe is inherently an open system, we employ this algorithm to investigate Krylov complexity across various cosmological phases: inflation, radiation domination (RD), and matter domination (MD). Our results highlight a clear distinction in Krylov complexity between the closed- and open-system methodologies. To accurately capture the influence of potentials during RD and MD, we examine a set of inflationary potentials, including the Higgs potential, R2 inflation, and chaotic inflation, while incorporating violations of slow-roll conditions. This study is conducted in conformal time through the preheating stage. Numerically, we find that the evolution of Krylov complexity and Krylov entropy shows remarkable similarity across different potentials during RD and MD. Furthermore, we rigorously construct an open two-mode squeezed state using the second kind of Meixner polynomial. Based on this construction, we derive for the first time the evolution equations for the squeezing parameter rk and phase φk in terms of the scale factor. Our analysis indicates that dissipative effects lead to rapid decoherence-like behavior. In addition, we observe that the inflationary universe behaves as a strongly dissipative system, whereas during the RD and MD epochs the universe exhibits weak dissipative characteristics. This work opens new perspectives for studying the universe from a quantum-informational viewpoint.

Due to the quasi-exponential red-shifting which occurs during an inflationary period in the very early Universe, wavelengths which at the present time correspond to cosmological lengths are in general sub-Planckian during the early stages of inflation. This talk discusses two approaches to addressing this issue which both indicate that the standard predictions of inflationary cosmology - made using classical general relativity and weakly coupled scalar matter field theory - are not robust against changes in the physics on trans-Planckian scales. One approach makes use of modified dispersion relations for a usual free field scalar matter theory, the other uses some properties of space-time non-commutativity - a feature expected in string theory. Thus, it is possible that cosmological observations may be used as a window to explore trans-Planckian physics. We also speculate on a novel way of obtaining inflation based on modified dispersion relations for ordinary radiation.

We explore the observational implications of models of intermediate inflation\ndriven by modified dispersion relations, specifically those representing the\nphenomenon of dimensional reduction in the ultraviolet limit. These models are\ndistinct from the standard ones because they do not require violations of the\nstrong energy condition, and this is reflected in their structure formation\nproperties. We find that they can naturally accommodate deviations from exact\nscale-invariance. They also make clear predictions for the running of the\nspectral index and tensor modes, rendering the models straightforwardly\nfalsifiable. We discuss the observational prospects for these models and the\nimplications these may have for quantum gravity scenarios.\n

We show that the difference between the theoretically expected and measured by WMAP amplitude of the quadrupole fluctuations of the cosmic microwave background (CMB) can be related to the impact of the anisotropic curvature of the homogeneous universe dominated by dark energy. In such a universe the matter expansion becomes practically isotropic just after the period of inflation, and only at small redshifts is the anisotropic expansion generated again by the small curvature ${\ensuremath{\Omega}}_{K}=1\ensuremath{-}{\ensuremath{\Omega}}_{m}\ensuremath{-}{\ensuremath{\Omega}}_{\ensuremath{\Lambda}}\ensuremath{\le}{10}^{\ensuremath{-}4}$. For such models the possible deviations from the parameters derived for the standard cosmological model are evidently negligible but the correlations of large scale perturbations and distortions of their Gaussianity are possible. Such models are also compatible with the existence of a homogeneous magnetic field and matter rotation which contribute to the low $\ensuremath{\ell}$ anisotropy and can be considered as ``hidden parameters'' of the model. Their influence can be observed as, for example, special correlations of small scale fluctuations and the Faraday rotation of the CMB and radiation of the farthest quasars. However, both the magnetic field and matter rotation also require modifications of the simple models of isotropic inflation, and they change the evolutionary history of the early Universe.

A search for narrow resonances decaying to an electron and a muon is presented. The mathrm {e}{mu } mass spectrum is also investigated for non-resonant contributions from the production of quantum black holes (QBHs). The analysis is performed using data corresponding to an integrated luminosity of 19.7~text {fb}^text {-1} collected in proton-proton collisions at a centre-of-mass energy of 8~text {TeV} with the CMS detector at the LHC. With no evidence for physics beyond the standard model in the invariant mass spectrum of selected mathrm {e}mu pairs, upper limits are set at 95 % confidence level on the product of cross section and branching fraction for signals arising in theories with charged lepton flavour violation. In the search for narrow resonances, the resonant production of a mathrm {tau } sneutrino in R-parity violating supersymmetry is considered. The mathrm {tau } sneutrino is excluded for masses below 1.28~text {TeV} for couplings lambda _{132}=lambda _{231}=lambda '_{311}=0.01, and below 2.30~text {TeV} for lambda _{132}=lambda _{231}=0.07 and lambda '_{311}=0.11. These are the most stringent limits to date from direct searches at high-energy colliders. In addition, the resonance searches are interpreted in terms of a model with heavy partners of the {mathrm {Z}} boson and the photon. In a framework of TeV-scale quantum gravity based on a renormalization of Newton’s constant, the search for non-resonant contributions to the mathrm {e}{mu } mass spectrum excludes QBH production below a threshold mass M_{mathrm {th}} of 1.99~text {TeV}. In models that invoke extra dimensions, the bounds range from 2.36~text {TeV} for one extra dimension to 3.63~text {TeV} for six extra dimensions. This is the first search for QBHs decaying into the mathrm {e}{mu } final state.

In this Letter we investigate the role of regular (curvature singularity-free) black holes in the framework of UV self-complete quantum gravity. The existence of a minimal length, shielding the trans-Planckian regime to any physical probe, is self-consistently included into the black hole probe itself. In this way we obtain to slightly shift the barrier below the Planck length, with the UV self-complete scenario self-consistently confirmed.

In inflationary models with minimal amount of gravity waves, the primordial power spectrum of density fluctuations, $A_S^2(k)$, together with the basic cosmological parameters, completely specify the predictions for the cosmic microwave background (CMB) anisotropy and large scale structure. Here we show how we can strongly constrain both $A_S^2(k)$ and the cosmological parameters by combining the data from the Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow $A_S^2(k)$ to be a free function, and thus probe features in the primordial power spectrum on all scales. MAP and SDSS have scale-dependent measurement errors that decrease in opposite directions on astrophysically interesting scales; they complement each other and allow the measurement of the primordial power spectrum independent of inflationary models, giving us valuable information on physics in the early Universe, and providing clues to the correct inflationary model.

In this work we present a review of some inflationary models with departures from the near-scale-invariant-power-law spectrum in the standard slow-roll scenario. These models were analysed by the Planck Collaboration in the recent release (2015), acquiring a special interest by scheduling analysis using both the Cosmic Microwave Background (CMB) and the Large Scale Structure data (LSS). In fact, these kinds of inflationary models predict observable signatures, with respect to the current data precision, in the anisotropy temperature power spectrum of CMB map and in the matter power spectrum of galaxy survey. So, it’s very interesting to explore the prediction of these models at very different cosmological scales and the results of the future analysis will be a very important test. Finally, these will confirm if these inflationary models are to be considered competitive with respect to other near-scale-invariant-power-law spectrum inflationary models or are definitively discarded.