Sarma, MaharshiMarinoni, ChristiaKalbouneh, BasheeClarkson, ChrisMaartens, Roy2026-06-232026-06-232026Sarma, M., Marinoni, C., Kalbouneh, B., Clarkson, C. and Maartens, R., 2026. Covariant cosmography in the presence of local structures: comparing exact solutions and perturbation theory. Journal of Cosmology and Astroparticle Physics, 2026(04), p.069.10.1088/1475-7516/2026/04/069https://hdl.handle.net/10566/24697Recent observational evidence of axially symmetric anisotropies in the local cosmic expansion rate motivates an investigation of whether they can be accounted for within the Lemaître– Tolman-Bondi (LTB) framework with an off-center observer. Within this setting, we compute the exact relativistic luminosity distance via the Sachs equation and compare it with the approximate expression obtained from the covariant cosmographic approach (including Hubble, deceleration, jerk and curvature parameters). This comparison allows us to identify the regimes in which the covariant cosmographic method remains reliable. In addition, we compare the LTB relativistic distance for small inhomogeneities with the corresponding result derived from linear perturbation theory (LPT) in the standard cosmological model. This analysis establishes a precise correspondence between the LTB and LPT approaches, offering a consistent dictionary for the interpretation of the observed anisotropies of the large-scale gravitational field. We test luminosity distance reconstructions in a spherically symmetric overdensity with an off-center observer. For moderate central density contrasts (δc ≲ 1), LPT reproduces the exact distance within 10% for observers inside the typical size of the structure. However, Covariant Cosmography (CC) extends this regime of validity upto δc ≲ 2.5. At larger radii, the situation reverses: for observers at three times the characteristic size, LPT remains accurate up to δc ≲ 3, while CC already exceeds 10% error for δc ≳ 1.5. At sufficiently large distances from the structure, both methods converge to the exact solution. Thus, CC is essential for accurate distance estimates near dense regions, while LPT remains reliable at larger separations. This analysis will be instrumental in interpreting expansion-rate anisotropies, facilitating investigations of the local Universe beyond the FLRW framework with a fully non-perturbative metric approach.encosmological perturbation theoryCosmological perturbation theory in GR and beyondexact solutionArticle