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Mauro Carfora

Publications and source records attributed to Mauro Carfora.

At least 19 recordsLinked to original sources
arXiv2025

How Dark is Dark Energy? A Lightcones Comparison Approach

We present a geometrical approach that provides a non-perturbative technique, allowing the standard FLRW observer to evaluate a measurable, scale-dependent distance functional between her idealized FLRW past light cone and the actual physical past light cone. From the point of view of the FLRW observer, gathering data from sources at cosmological redshift $\widehat{z}$, this functional generates a geometry--structure--growth contribution ${\Omega_\Lambda(\widehat{z})}$ to the FLRW cosmological constant ${\widehat\Omega_\Lambda}$. This redshift--dependent contribution erodes the interpretation of ${\widehat\Omega_\Lambda}$ as representing constant dark energy. In particular, ${\Omega_\Lambda(\widehat{z})}$ becomes significantly large at very low $\widehat{z}$, where structures dominate the cosmological landscape. At the pivotal galaxy cluster scale, where cosmological expansion decouples from the local gravitation dynamics, we get ${\Omega_\Lambda(\widehat{z})/\widehat\Omega_\Lambda}\,=\,\mathscr{O}(1)$, showing that late--epoch structures provide an effective field contribution to the FLRW cosmological constant that is of the same order of magnitude as its assumed value. We prove that ${\Omega_\Lambda(\widehat{z})}$ is generated by a scale-dependent effective field governed by structure formation and related to the comparison between the idealized FLRW past light cone and the actual physical past light cone. These results are naturally framed in the mainstream FLRW cosmology; they do not require exotic fields and provide a natural setting for analyzing the coincidence problem, leading to an interpretative shift in the current understanding of constant dark energy.

astro-ph.CO↗
arXiv2024

How Dark is Dark Energy?

The nature of dark energy is one of the fundamental problems in cosmology. Introduced to explain the apparent acceleration of the Universe's expansion, its origin remains to be determined. In this paper, we illustrate a result that may significantly impact understanding the relationship between dark energy and structure formation in the late-epoch Universe. Our analysis exploits a scale-dependent energy functional, initially developed for image visualization, to compare the physical and geometrical data that distinct cosmological observers register on their celestial spheres. In the presence of late-epoch gravitational structures, this functional provides a non-perturbative technique that allows the standard Friedmann-Lemaître-Robertson-Walker (FLRW) observer to evaluate a measurable, scale-dependent difference between the idealized FLRW past light cone and the physical light cone. From the point of view of the FLRW observer, this difference manifests itself as a redshift-dependent correction $Λ^{(corr)}(z)$ to the FLRW cosmological constant $Λ^{(FLRW)}$. At the scale where cosmological expansion couples with the local virialized dynamics of gravitational structures, we get $Λ^{(corr)}(z)\sim 10^{-52}\,m^{-2}$, indicating that the late-epoch structures induce an effective cosmological constant that is of the same order of magnitude as the assumed value of the FLRW cosmological constant, a result that may lead to an interpretative shift in the very role of dark energy.

astro-ph.CO↗
arXiv2023

A Scale-Dependent Distance Functional between Past Light Cones in Cosmology

We discuss a rigorous procedure for quantifying the difference between our past lightcone and the past lightcone of the fiducial Friedmann-Lemaitre-Robertson-Walker spacetime modeling the large-scale description of cosmological data in the standard $Λ\mathrm{CDM}$ scenario. This result is made possible by exploiting the scale-dependent distance functional between past lightcones recently introduced by us. We express this harmonic map type functional in terms of the physical quantities that characterize the actual measurements along our past lightcone, namely the area distance and the lensing distortion, also addressing the very delicate problem of the presence of lightcone caustics. This analysis works beautifully and seems to remove several of the difficulties encountered in comparing the actual geometry of our past lightcone with the geometry of the fiducial FLRW lightcone of choice. We also discuss how, from the point of view of the FLRW geometry, this distance functional may be interpreted as a scale-dependent effective field, the pre-homogeneity field, that may be of relevance in selecting the FLRW model that best fits the observational data.

gr-qc↗
arXiv2021

A comparison theorem for cosmological lightcones

Let $(M, g)$ denote a cosmological spacetime describing the evolution of a universe which is isotropic and homogeneous on large scales, but highly inhomogeneous on smaller scales. We consider two past lightcones, the first, $\mathcal{C}^-_L(p, g)$, is associated with the physical observer $p\in\,M$ who describes the actual physical spacetime geometry of $(M, g)$ at the length scale $L$, whereas the second, $\mathcal{C}^-_L(p, \hat{g})$, is associated with an idealized version of the observer $p$ who, notwithstanding the presence of local inhomogeneities at the given scale $L$, wish to model $(M, g)$ with a member $(M, \hat{g})$ of the family of Friedmann-Lemaitre-Robertson-Walker spacetimes. In such a framework, we discuss a number of mathematical results that allows a rigorous comparison between the two lightcones $\mathcal{C}^-_L(p, g)$ and $\mathcal{C}^-_L(p, \hat{g})$. In particular, we introduce a scale dependent ($L$) lightcone-comparison functional, defined by a harmonic type energy, associated with a natural map between the physical $\mathcal{C}^-_L(p, g)$ and the FLRW reference lightcone $\mathcal{C}^-_L(p, \hat{g})$. This functional has a number of remarkable properties, in particular it vanishes iff, at the given length-scale, the corresponding lightcone surface sections (the celestial spheres) are isometric. We discuss in detail its variational analysis and prove the existence of a minimum that characterizes a natural scale-dependent distance functional between the two lightcones. We also indicate how it is possible to extend our results to the case when caustics develop on the physical past lightcone $\mathcal{C}^-_L(p, g)$. Finally, we show how the distance functional is related to spacetime scalar curvature in the causal past of the two lightcones, and briefly illustrate a number of its possible applications.

gr-qc↗
arXiv2021

Ricci curvature and quantum geometry

We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum) fluctuations around a background fiducial geometry. In such a scenario, Ricci curvature with its subtle connections to diffusion, optimal transport, Wasserestein geometry, and renormalization group, features prominently.

math-ph↗
arXiv2019

Scaling and Entropy for the RG-2 Flow

Let $(\mathcal{M},g)$ be a closed Riemannian manifold. The $\textit{ second order approximation}$ to the perturbative renormalization group flow for the nonlinear sigma model (RG-2 flow) is given by : \[ \frac{\partial }{\partial t} \, g(t) \, =\, -2 \mathrm{Ric}(t) \, -\, \fracα{2} \mathrm{Rm}^2(t), \] where $ g = \mathrm{Riemannian \ metric}, \mathrm{Ric} = \mathrm{Ricci \ curvature, } \ \mathrm{Rm}^2_{ij}:=\mathrm{R}_{irmk}\mathrm{R}_j^{rmk},$ and $α\ge 0$ is a parameter. The flow is invariant under diffeomorphisms, but not under scaling of the metric. We first develop a $\textit{geometrically defined}$ coupling constant $α_g$ that leads to an equivalent, scale-invariant flow. We further find a modified Perelman entropy for the flow, and prove local existence of the resulting variational system. The crucial idea is to modify the flow by two diffeomorphisms, the first being the usual DeTurck diffeomorphism the second being strictly related to the geometrical characterization of the coupling constant $α_g$. We minimize the entropy functional so introduced to characterize a natural extension $Λ[g]$ of the Perelman's $λ(g)$--functional, and show that $Λ[g]$ is monotonic under the RG-2 flow. Although the modified Perelman entropy is monotonic, the RG-2 flow is not a gradient flow with respect this functional. We discuss this issue in detail, showing how to deform the functional in order to give rise to a gradient flow for a DeTurck modified RG-2 flow.

math.DG↗
arXiv2019

Ricci Flow from the Renormalization of Nonlinear Sigma Models in the Framework of Euclidean Algebraic Quantum Field Theory

The perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the principle of general local covariance. In particular we show in an Euclidean setting how to define Wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of Khavkine, Melati and Moretti for vector valued free fields. As a by-product of such classification, we prove that, at first order in perturbation theory, the renormalization group flow of the nonlinear Sigma model is the Ricci flow.

math-ph↗
arXiv2014

The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow

Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci flow. By exploiting the heat kernel embedding introduced by N. Gigli and C. Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between non-linear sigma models and Ricci flow theory. This approach provides a rigorous model for the embedding of Ricci flow into the renormalization group flow for non linear sigma models, and characterizes a non-trivial generalization of the Hamilton-Perelman version of the Ricci flow. We discuss in detail the monotonicity and gradient flow properties of this extended flow.

math-ph↗
arXiv2010

Ricci Flow Conjugated Initial Data Sets for Einstein Equations

We discuss a natural form of Ricci--flow conjugation between two distinct general relativistic data sets given on a compact $n\geq 3$-dimensional manifold $Σ$. We establish the existence of the relevant entropy functionals for the matter and geometrical variables, their monotonicity properties, and the associated convergence in the appropriate sense. We show that in such a framework there is a natural mode expansion generated by the spectral resolution of the Ricci conjugate Hodge--DeRham operator. This mode expansion allows to compare the two distinct data sets and gives rise to a computable heat kernel expansion of the fluctuations among the fields defining the data. In particular this shows that Ricci flow conjugation entails a form of $L^2$ averaging of one data set with respect to the other with a number of desiderable properties: (i) It preserves the dominant energy condition; (ii) It is localized by a heat kernel whose support sets the scale of averaging; (iii) It is characterized by a set of balance functionals which allow the analysis of its entropic stability.

gr-qc↗
arXiv2010

Quantum Tetrahedra

We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing. The apparent twofold nature of the 6j symbol displayed in quantum field theory and quantum computing -a quantum tetrahedron and a computational gate- is shown to merge together in a unified quantum-computational SU(2)-state sum framework.

math-ph↗
arXiv2010

Renormalization Group and the Ricci flow

We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests a natural way for extending, beyond the weak coupling regime, the embedding of the Ricci flow into the renormalization group flow.

hep-th↗
arXiv2009

The Conjugate Linearized Ricci Flow on Closed 3-Manifolds

We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three--manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which characterizes a way of Ricci flow averaging metric dependent geometrical data. We also provide an integral representation of the Ricci flow metric itself and of its Ricci tensor in terms of the heat kernel of the conjugate linearized Ricci flow. These results, which readily extend to closed n-dimensional manifolds, yield for various conservation laws, monotonicity and asymptotic formulas for the Ricci flow and its linearization.

math.DG↗
arXiv2008

On the curvature of the present-day Universe

We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day Universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question whether it is sensible to assume that curvature averages out on some scale of homogeneity, as implied by the standard concordance model of cosmology, or whether the averaged scalar curvature can be largely negative today, as required for an explanation of Dark Energy from inhomogeneities. We confront both conjectures with a detailed analysis of the kinematical backreaction term and estimate its strength for a multi-scale inhomogeneous matter and curvature distribution. Our main result is a formula for the spatially averaged scalar curvature involving quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. We propose strategies to quantitatively evaluate the formula, and pinpoint the assumptions implied by the conjecture of a small or zero averaged curvature. We reach the conclusion that the standard concordance model needs fine-tuning in the sense of an assumed equipartition law for curvature in order to reconcile it with the estimated properties of the averaged physical space, whereas a negative averaged curvature is favoured, independent of the prior on the value of the cosmological constant.

gr-qc↗
arXiv2008

Ricci flow deformation of cosmological initial data sets

Ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes. This idea has been around since the appearance of the Ricci flow on the scene, but it has been difficult to turn it into a sound mathematical procedure. In this expository talk we illustrate, how Perelman's recent results in Ricci flow theory can considerably improve on such a situation. From a physical point of view this analysis can be related to the issue of finding a constant-curvature template spacetime for the inhomogeneous Universe, relevant to the interpretation of observational data and, hence, bears relevance to the dark energy and dark matter debates. These techniques provide control on curvature fluctuations (intrinsic backreaction terms) in their relation to the averaged matter distribution.

math-ph↗
arXiv2007

BCFT and Ribbon Graphs as tools for open/closed string dualities

In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with open/closed string dualities.

hep-th↗
arXiv2007

From random Regge triangulations to open strings

We show how Boundary Conformal Field Theory deformation techniques allow for a complete characterisation of the coupling between the discrete geometry inherited uniformizing a random Regge triangulations and open string theory.

hep-th↗