Related papers: Cosmology meets cluster algebra
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; these formulas involve a family of polynomials…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal…
We present a Feynman integral representation for the general momentum-space scalar $n$-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of $n(n-3)/2$…
The Bootstrap approach to calculating cosmological correlators relies on a well motivated ansatz. It is typical in the literature to assume that correlators are rational functions as this greatly increases our constraining power. However,…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
Inertial waves in convective regions of stars exhibit topological properties linked to a Chern number of 1. The first of these is a unique, unidirectional, prograde oscillation mode within the cavity, which propagates at arbitrarily low…
Based on a closed formula for a star product of Wick type on $\CP^n$, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the…
We consider the moduli space of holomorphic principal bundles for reductive Lie groups over Riemann surfaces (possibly with boundaries) and equipped with meromorphic connections. We associate to this space a point-wise notion of quantum…
The Fomin-Zelevinsky Laurent phenomenon states that every cluster variable in a cluster algebra can be expressed as a Laurent polynomial in the variables lying in an arbitrary initial cluster. We give representation-theoretic formulas for…
We study cluster algebras that are associated to unpunctured surfaces with coefficients arising from boundary arcs. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of…
Topological structure has been extensively studied and confirmed in highly correlated condensed matter physics. We explore the gravitational waves emitted from binary neutron star mergers using the pseudoconformal model for dense nuclear…
Recent theoretical work has revealed that basic observables of quantum field theory in de Sitter space, known as in-in or cosmological correlators, exhibit surprisingly simple mathematical structure reminiscent of scattering amplitudes in…
Cosmological correlators capture the spatial fluctuations imprinted during the earliest episodes of the universe. While they are generally very non-trivial functions of the kinematic variables, they are known to arise as solutions to…
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we…
Power-law cosmologies, in which the cosmological scale factor evolves as a power law in the age, $a \propto t^{\alpha}$ with $\alpha \ga 1$, regardless of the matter content or cosmological epoch, is comfortably concordant with a host of…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
(abridged) We use a theoretical model to predict the clustering properties of galaxy clusters. Our technique accounts for past light-cone effects on the observed clustering and follows the non-linear evolution of the dark matter correlation…
Upcoming multi-wavelength astronomical surveys will soon discover all massive galaxy clusters and provide unprecedented constraints on cosmology and cluster astrophysics. In this paper, we investigate the constraining power of the…