arXiv subjects

Bartłomiej Sikorski

Publications and source records attributed to Bartłomiej Sikorski.

6 recordsLinked to original sources

arXiv2026

Statistical Fluctuations as Primordial Correlators in the CMB: Finite Chemical Potential Thermodynamics

Can primordial cosmological correlations originate from statistical fluctuations of an early-universe thermal system? We connect grand-canonical thermodynamics, stochastic transport, and gauge-invariant cosmological perturbations for a charged fluid at finite chemical potential. Energy-charge susceptibilities determine curvature, charge-isocurvature, and cross-correlation amplitudes, while transport sets when each mode leaves equilibrium. For an isolated, adiabatic conformal plasma with conserved charge-to-entropy ratio and power-law diffusion, diffusive freeze-out yields the universal spectrum $\mathcal P_S(k)\propto k^3$, with $n_{\rm iso}=4$, while equal-time local-equilibrium curvature-isocurvature covariance vanishes in the conformal source basis. Thus neither finite chemical potential nor replacing Hubble crossing by diffusion crossing alone yields approximate scale invariance. We evade this obstruction with an open subsystem of massless Dirac fermions during a sourced quasi-de Sitter phase. There, grand-canonical energy cumulants generate a nearly scale-invariant red curvature spectrum. A benchmark gives $\mathcal P_{ζ_X}(k_\star)=2.10\times10^{-9}$ and $n_s(k_\star)=0.9649$, stays within $0.30%$ of the fitted power law over $0.002\leq k/k_\star\leq4$, and predicts weak negative running and small positive intrinsic non-Gaussianity from higher-order cumulants, $f_{\rm NL}(k_\star)\simeq0.106$ and $g_{\rm NL}(k_\star)\simeq0.0158$. With a two-helicity vacuum tensor spectrum, the tensor-to-scalar ratio is $r_{t/s}(k_\star)=1.82\times10^{-4}$. This isolates the limitation of isolated conformal thermal seeding and the open-system ingredient needed to overcome it. Thermal energy-charge fluctuations thus provide a calculable source of realistic scalar correlations, while reservoir dynamics, equilibration, and later curvature-isocurvature transfer must come from a microscopic model.

astro-ph.CO↗

arXiv2026

Weights of strongly nilpotent special multi-flags

This paper is devoted to two distinguished families of distributions: special multi-flags and their lower-rank counterparts, Goursat distributions. It is known that these two families are weakly nilpotent but strongly nilpotent only at special points. Local classification of these objects is still open and only recently singularity classes of special multi-flags were constructed by Mormul. In this paper, we study special multi-flags in the homogeneous case, which is also strongly nilpotent. The main contribution of the present work is to show that the strongly nilpotent germs of multiflags from different singularity classes are pairwise inequivalent as the singularity type uniquely determines the weights of coordinates. In the Goursat case, explicit formulas for weights of tangential geometric classes are presented. Finally, we discuss the property of strong nilpotency among special multi-flags and state open conjectures.

math.DG↗

arXiv2026

Planck mass gravitinos in Einstein-Maxwell backgrounds

Charged massive spin-3/2 fields have long been regarded as problematic, because their coupling to electromagnetism generically leads to loss of hyperbolicity, acausal propagation and loss of unitarity. At the same time, fractionally charged supermassive gravitinos play a central role in a recent proposal of two of the present authors, where they are the only fermionic degrees of freedom beyond the Standard Model and provide novel dark matter candidates. We address this apparent tension by revisiting the result of Deser and Waldron, who showed that the inclusion of gravity can compensate the electromagnetic source of the inconsistency. For a minimally coupled Rarita-Schwinger field in an Einstein-Maxwell background, consistency requires a lower bound on the mass in terms of the charge and the cosmological constant. What is usually a severe obstruction to low-energy charged spin-3/2 phenomenology becomes an independent indication that such particles must lie close to the Planck scale, as argued by two of the present authors on other grounds. We rederive the inequality from the solvability of the Rarita-Schwinger constraints and from the characteristic determinant, emphasizing how the Einstein-Maxwell stress tensor compensates the purely electromagnetic pathology. We then reformulate the system using a Stückelberg spinor, showing that the helicity-1/2 sector reproduces the same condition. This formulation is also essential for obtaining a renormalizable propagator. We discuss this propagator and the corresponding ghost system.

hep-th↗

arXiv2024

Bessel potentials and Green functions on pseudo-Euclidean spaces

We review properties of Bessel potentials, that is, inverse Fourier transforms of (regularizations of) $\frac{1}{(m^2+p^2)^{\fracμ{2}}}$ on a pseudoEuclidean space with signature $(q,d-q)$. We are mostly interested in the Lorentzian signature $(1,d-1)$, and the case $μ=2$, related to the Klein-Gordon equation $(-\Box+m^2)f=0$. We analyze properties of various ``two-point functions'', which play an important role in Quantum Field Theory, such as the retarded/advanced propagators or Feynman/antiFeynman propagators. We consistently use hypergeometric functions instead of Bessel functions, which makes most formulas much more transparent. We pay attention to distributional properties of various Bessel potentials. We include in our analysis the ``tachyonic case'', corresponding to the ``wrong'' sign in the Klein-Gordon equation.

math-ph↗

arXiv2024

Hawking radiation far away from the event horizon

We study particle production in Vaidya spacetime. Using the WKB approximation, the distribution of Hawking radiation is calculated without the near-horizon approximation, which leads to finite corrections to the purely thermal spectrum. We extend our analysis to extremal and non-extremal Reissner-Nordström and Kerr black holes. Our results can be understood in terms of a thermodynamic toy model, where one regards Hawking radiation as Unruh radiation perceived by observers outside of the black hole. Moreover, we extend the model to incorporate the backreaction of Hawking quanta on spacetime geometry. Our study suggests that the backreaction may prevent the formation of the event horizon and spacetime singularity.

gr-qc↗

arXiv2023

Higher derivatives of the end-point map of a linear control system via adapted coordinates

We study the end-point map of a control-linear system in a neighborhood of an arbitrarily chosen trajectory. In particular, we want to calculate the $k$-th order derivative of this map in a given direction. A priori it is a solution of a quite complicated ODE depending on all derivatives of order less or equal $k$. We prove that there exists a special coordinate system adapted to the geometry of the problem, which changes the system of ODEs describing all derivatives of the end-point map up to order $k$ to equations of a control-affine (non-autonomous control-linear) system, with the direction of derivation playing the role of the new control. As an application we study controllability criteria for this system, obtaining first and second-order necessary optimality conditions of sub-Riemannian geodesics. In particular, for the case of an abnormal minimizer we can interpret \emph{Goh conditions} as non-controllability conditions of this control-affine system for $k=2$. We make a hypothesis that for higher $k$'s its non-controllability corresponds to recently obtained higher-order analogs of the Goh conditions [Boarotto, Monti, Palmurella, 2020], [Boarotto, Monti, a Socionovo, 2022].

math.OC↗