Maartens, RoyClarkson, ChrisKalbouneh, Basheer2025-07-302025-07-302025Kalbouneh, B., Santiago, J., Marinoni, C., Maartens, R., Clarkson, C. and Sarma, M., 2025. Expanding covariant cosmography of the local universe: incorporating the snap and axial symmetry. Journal of Cosmology and Astroparticle Physics, 2025(02), p.076.https://doi.org/10.1088/1475-7516/2025/02/076https://hdl.handle.net/10566/20632Studies show that the model-independent, fully non-perturbative covariant cosmographic approach is suitable for analyzing the local Universe (z ≲ 0.1). However, accurately characterizing large and inhomogeneous mass distributions requires the fourth-order term in the redshift expansion of the covariant luminosity distance dL (zn ). We calculate the covariant snap parameter S and its spherical harmonic multipole moments using the matter expansion tensor and the evolution equations for lightray bundles. The fourth-order term adds 36 degrees of freedom, since the highest independent multipole of the snap is the 32-pole (dotriacontapole) (ℓ=5). Including this term helps to de-bias estimations of the covariant deceleration parameter. Given that observations suggest axially symmetric anisotropies in the Hubble diagram for z ≲ 0.1 and theory shows that only a subset of multipoles contributes to the signal, we demonstrate that only 12 degrees of freedom are needed for a model-independent description of the local universe. We use an analytical axisymmetric model of the local Universe, with data that matches the Zwicky Transient Facility survey, in order to provide a numerical example of the amplitude of the snap multipoles and to forecast precision.enCosmic flowsCosmological parameters from LSSCosmological simulationsAxial symmetryCovariant decelerationArticle