In this paper, we examine a static gravitational field with axial symmetry over probe particles in the Solar system. Using the Weyl conformastatic solution as a model, we find a non-standard expression to perihelion advance due to the constraints imposed by the topology of the local gravitational field. We show that the application of the slow motion condition to the geodesic equations without altering Einstein's equations does not necessarily lead to the Newtonian limit; rather it leads to an intermediate nearly Newtonian gravitational stage, which can be applied to astrophysical problems in Solar system scale. We apply the model to the perihelion advance of inner planets and minor objects (NEO asteroids and the comets). As a result, we obtain an expression of a non-standard relativistic precession that reveals a close agreement to observational data calibrated with the Ephemerides of the Planets and the Moon (EPM2011) (Pitjeva & Pitjev; Pitjev & Pitjeva). The study of perihelion advance of eight small celestial bodies (asteroids and comets) is also considered.

The cosmic acceleration problem remains one of the most significant challenges in cosmology. One of the proposed solutions to this problem is the modification of gravity on large scales. In this paper, we explore the well-known μ-Σ parametrization scenarios and confront them with observational data, including the cosmic microwave background (CMB) radiation from the Wilkinson Microwave Anisotropy Probe (WMAP), Atacama Cosmology Telescope (ACT), and South Pole Telescope (SPT), as well as large-scale structure data from the Sloan Digital Sky Survey (SDSS: BAO+RSD) and Pantheon Supernovae (SN) catalog. We employ a Bayesian framework to constrain the model parameters and discuss the implications of our results on the viability of modified gravity theories. Our analysis reveals the strengths and limitations of the μ-Σ parametrization and provides valuable insights into the nature of gravity on cosmological scales. From the joint analysis of the ACT + WMAP + SDSS + SN, we find μ₀ − 1 = 0.02 ± 0.19 and Σ₀ − 1 = 0.021 ± 0.068 at 68% CL. In light of the SPT + WMAP + SDSS + SN, we find μ₀ − 1 = 0.07 ± 0.18 and |$\Sigma _0 -1 = -0.009^{+0.078}_{-0.11}$| at 68% CL. In all the analyses carried out, we do not find any deviations from the theory of general relativity. Our results represent an observational update on the well-known μ-Σ parameterization in view of current CMB data, independent and competitive with the constraints obtained with the Planck data.

We study the possibility that Universe is subjected to a deformation, besides its expansion described by Friedmann's equations. The concept of smooth deformation of a riemannian manifold associated with the extrinsic curvature is applied to the standard Friedmann–Lemaître–Robertson–Walker cosmology. Starting from the resulting modified Friedman's equation we study two possible solutions with six models for each one in low redshift. In order to constrain the models, we calculate the main cosmic parameters (Hubble parameter H(z), deceleration parameter q(z) and jerk parameter j(z)) compared with different data sets as the latest Baryons Acoustic Oscillations/Cosmic Microwave Background + SNla constraints, SuperNova Legacy Survey Type Ia supernova (SNIa), X-ray galaxy clusters and the gold sample (SNIa). As a result, we obtain a set of proper models compatible with the current observational data.

In this work, we examine the orbit equations originated from Zipoy’s oblate metric. Accordingly, the solution of Einstein’s vacuum equations can be written as a linear combination of Legendre...

In this work, we apply the smooth deformation concept in order to obtain a modification of Friedmann's equations. It is shown that the cosmic coincidence can be at least alleviated using the dynamical properties of the extrinsic curvature. We investigate the transition from nucleosynthesis to the coincidence era obtaining a very small variation of the ratio that compares the matter energy density to extrinsic energy density, compatible with the known behavior of the deceleration parameter. We also show that the calculated 'equivalence' redshift matches the transition redshift from a deceleration to accelerated phase and the coincidence ceases to be. The dynamics on r is also studied based on Hubble parameter observations as the latest Baryons Acoustic Oscillations/Cosmic Microwave Background Radiation (BAO/CMBR) + SNIa.