Searcharxiv⌕ Search

arXiv subjects

Andrzej Borowiec

Publications and source records attributed to Andrzej Borowiec.

At least 19 recordsLinked to original sources
arXiv2026

Bicovariant Codifferential Calculi

We develop a technique for studying first-order codifferential calculi (FOCCs) initiated by Doi and Quillen in the context of cyclic cohomology. Their classification, for a given coalgebra, reduces to the classification of subbicomodules in the universal bicomodule. For completing this task, the role of one-dimensional generating spaces (a.k.a. singletons) is found to be useful. We are particularly interested in classifying bicovariant codifferential calculi, which we define over Hopf algebras. This, in turn, can be reduced to classifying Yetter-Drinfeld (Y-D) submodules. In fact, there are two, mutually dual, Y-D structures on arbitrary Hopf algebra: one used by Woronowicz for constructing bicovariant differential calculi, and the another used here for FOCCs and shown to be related with Woronowicz construction of quantum tangent space. This argues that such codifferential calculi are better suited to Drinfeld-Jimbo type quantized enveloping algebras, as they are dual to Woronowicz' bicovariant calculi over matrix quantum groups. Relations with quantum Lie algebras and quantum vector fields are also shown. Some classification results are presented in numerous examples.

math.QA↗
arXiv2025

The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. [Abridged]

astro-ph.CO↗
arXiv2024

Is it possible to separate baryonic from dark matter within the $Λ$-CDM formalism?

We found general solutions of matter stress-energy (non-)conservation in scalar-tensor FLRW-type cosmological models by extending the logotropic formalism to the case of non-minimal coupling between the scalar field and new dark fluid candidates. The energy conditions expressed by the generating function are introduced. Next, we investigate the possibility of separating baryonic from dark matter and explain their ratio as a chameleon effect in the presence of non-minimal coupling. To answer the question affirmatively we analyze simple extensions of the $Λ$-CDM model by adding a non-minimally coupled scalar field in the Einstein frame. Two scenarios involving either a scalaron (quintessence) or a phantom (ghost) are numerically solved and compared. As a result, it is shown that in both cases LCDM model can be reproduced with a high accuracy in the region covered by observations. We have also demonstrated the compatibility of the two models under consideration with available PPN parameters estimations. As expected, in the case of the phantom (ghost) field the Big-Bang scenario is replaced by the (matter) Bounce.

gr-qc↗
arXiv2024

On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions

In this paper, we find a class of Carrollian and Galilean contractions of (extended) BMS algebra in 3+1 and 2+1 dimensions. To this end, we investigate possible embeddings of 3D/4D Poincaré into the BMS${}_3$ and BMS${}_4$ algebras, respectively. The contraction limits in the 2+1-dimensional case are then enforced by appropriate contractions of its Poincaré subalgebras. In 3+1 dimensions, we have to apply instead the analogy between the structures of Poincaré and BMS algebra. In the case of non-vanishing cosmological constant in 2+1 dimensions, we consider the contractions of $Λ$-BMS${}_3$ algebra in an analogous manner.

hep-th↗
arXiv2022

Quantum Calculi: differential forms and vector fields in noncommutative geometry

In this paper, we revise the concept of noncommutative vector fields introduced previously in Ref. [1,2], extending the framework, adding new results and clarifying the old ones. Using appropriate algebraic tools certain shortcomings in the previous considerations are filled and made more precise. We focus on the correspondence between so-called Cartan pairs and first-order differentials. The case of free bimodules admitting more friendly "coordinate description" and their braiding is considered in more detail. Bimodules of right/left universal vector fields are explicitly constructed.

math-ph↗
arXiv2022

Scalar-tensor cosmologies in a minisuperspace formulation: a case study

We revisit a general minisuperspace (MSS) formalism for scalar-tensor (ST) FLRW type cosmological models in arbitrary frame with perfect fluid source. We discuss how to impose Cauchy data on the corresponding dynamical system in order to reconstruct standard (ΛCDM) cosmological model. So far, the integrability of such models has been extensively studied in the Einstein or Jordan frames mainly. We extend these studies to arbitrary frame taking into account non-minimal coupling between matter and gravity. To this aim we explore a gauge freedom associated with a choice of lapse function. We show that particular isothermal MSS coordinates are related with Einstein frames representing solution equivalent classes and have some invariant meaning. This provides new universal framework for investigating cosmic evolution in arbitrary frame: analytical solutions obtained in the Einstein frame can be transformed back to the physical frame by making use of a conformal transformation and field redefinition. We also show how such technique can be useful when applied to Wheeler-DeWitt quantum cosmology.

gr-qc↗
arXiv2021

Dispersion Relations in $κ$-Noncommutative Cosmology

We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist $-$giving $κ$-Minkowski spacetime in flat space$-$ in the presence of a Friedman-Lemaître-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.

gr-qc↗
arXiv2020

New class of hybrid metric-Palatini scalar-tensor theories of gravity

A class of scalar-tensor theories (STT) including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction is proposed and investigated from the point of view of their consistency with generalized conformal transformations. It is shown that every such theory can be represented on-shell by a purely metric STT possessing the same solutions for a metric and a scalar field. A set of generalized invariants is also proposed. This extends the formalism previously introduced in \cite{kozak2019}. We then apply the formalism to Starobinsky model, write down the Friedmann equations for three possible cases: metric, Palatini and hybrid metric-Palatini, and compare some inflationary observables.

gr-qc↗
arXiv2019

Interpolations between Jordanian Twists Induced by Coboundary Twists

We propose a new generalisation of the Jordanian twist (building on the previous idea from [Meljanac S., Meljanac D., Pachol A., Pikutic D., J. Phys. A: Math. Theor. 50 (2017), 265201, 11 pages]). Obtained this way, the family of the Jordanian twists allows for interpolation between two simple Jordanian twists. This new version of the twist provides an example of a new type of star product and the realization for noncommutative coordinates. Real forms of new Jordanian deformations are also discussed. Exponential formulae, used to obtain coproducts and star products, are presented with details.

math-ph↗
arXiv2019

Palatini frames in scalar-tensor theories of gravity

A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and conformal transformations. We characterize theories invariant with respect to these transformations dividing them up into solution-equivalent subclasses (group orbits). To this end, invariant characteristics have been introduced. Unlike in the metric case, it turns out that the dimension four admitting the largest transformation group is rather special for such theories. The formalism provides new frames that incorporate non-metricity. The case of Palatini F(R)-gravity is considered in more detail.

hep-th↗
arXiv2018

Galaxy Rotation Curves via Conformal Factors

We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).

gr-qc↗
arXiv2017

Observables and Dispersion Relations in k-Minkowski Spacetime

We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of k-Minkowski spacetime. The corresponding quantum Poincare'-Weyl Lie algebra of infinitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

hep-th↗
arXiv2017

Emergence of dynamical dark energy from polynomial $f(R)$ theory in Palatini formalism

We consider FRW cosmology in $f(R)= R+ γR^2+δR^3$ modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field and vanishing kinetic energy term. This potential determines the running cosmological constant term as a function of the Ricci scalar. As a result we obtain the emergent dark energy parametrization from the covariant theory. We study also singularities of the model and demonstrate that in the Einstein frame some undesirable singularities disappear.

gr-qc↗
arXiv2017

Starobinsky cosmological model in Palatini formalism

We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed in terms of geometry of a potential function if it has poles. At the sewn singularity, which is of a finite scale factor type, the singularity in the past meets the singularity in the future. We show, that such singularities appear in the Starobinsky model in $f(\hat{R})=\hat{R}+γ\hat{R}^2$ in the Palatini formalism, when dynamics is determined by the corresponding piece-wise smooth dynamical system. As an effect we obtain a degenerated singularity. Analytical calculations are given for the cosmological model with matter and the cosmological constant. The dynamics of model is also studied using dynamical system methods. From the phase portraits we find generic evolutionary scenarios of the evolution of the Universe. For this model, the best fit value of $Ω_γ=3γH_0^2$ is equal $9.70\times 10^{-11}$. We consider model in both Jordan and Einstein frames. We show that after transition to the Einstein frame we obtain both form of the potential of the scalar field and the decaying Lambda term.

gr-qc↗
arXiv2017

Twisted bialgebroids versus bialgebroids from a Drinfeld twist

Bialgebroids (resp. Hopf algebroids) are bialgebras (Hopf algebras) over noncommutative rings. Drinfeld twist techniques are particularly useful in the (deformation) quantization of Lie algebras as well as underlying module algebras (=quantum spaces). Smash product construction combines these two into the new algebra which, in fact, does not depend on the twist. However, we can turn it into bialgebroid in the twist dependent way. Alternatively, one can use Drinfeld twist techniques in a category of bialgebroids. We show that both techniques indicated in the title: twisting of a bialgebroid or constructing a bialgebroid from the twisted bialgebra give rise to the same result in the case of normalized cocycle twist. This can be useful for better description of a quantum deformed phase space. We argue that within this bialgebroid framework one can justify the use of deformed coordinates (i.e. spacetime noncommutativity) which are frequently postulated in order to explain quantum gravity effects.

math-ph↗
arXiv2016

Central tetrads and quantum spacetimes

In this paper, we perform a parallel analysis to the model proposed in [25]. By considering the central co-tetrad (instead of the central metric), we investigate the modifications in the gravitational metrics coming from the noncommutative spacetime of the $κ$-Minkowski type in four dimensions. The differential calculus corresponding to a class of Jordanian $κ$-deformations provides metrics, which lead either to cosmological constant or spatial curvature type solutions of non-vacuum Einstein equations. Among vacuum solutions, we find pp-wave type.

hep-th↗
arXiv2016

Yang-Baxter sigma models and Lax pairs arising from $κ$-Poincaré $r$-matrices

We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical $r$-matrices associated with $κ$-deformations of the Poincaré algebra. These classical $κ$-Poincaré $r$-matrices describe three kinds of deformations: 1) the standard deformation, 2) the tachyonic deformation, and 3) the light-cone deformation. For each deformation, the metric and two-form $B$-field are computed from the associated $r$-matrix. The first two deformations, related to the modified classical Yang-Baxter equation, lead to T-duals of dS$_4$ and AdS$_4$\,, respectively. The third deformation, associated with the homogeneous classical Yang-Baxter equation, leads to a time-dependent pp-wave background. Finally, we construct a Lax pair for the generalized $κ$-Poincaré $r$-matrix that unifies the three kinds of deformations mentioned above as special cases.

hep-th↗