Milky Way and Andromeda past-encounters in different gravity models: the impact on the estimated Local Group mass

The Two-body problem of $M31$ and the Milky Way (MW) galaxies with a Cosmological Constant background is studied, with emphasis on the possibility that they experienced Past Encounters. By implementing the Timing Argument (TA), it is shown that if $M{31}$ and the MW have had more than one encounter then the deduced mass of the Local Group (LG) would be larger. Past encounters are possible only for non-zero transverse velocity, and their viability is subject to observations of the imprints of such near collisions. Using a recent $Gaia$ - based measurement of the transverse velocity we show that the presence of the Cosmological Constant requires the mass for the LG to be $35\%$ higher: $3.36^{+1.14}_{-0.70} \cdot 10^{12} M_{\odot}$ with no Cosmological Constant or $4.54^{+1.20}_{-0.75} \cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. If the LG has had one past encounter, the LG mass is $9.99^{+2.22}_{-1.58}\cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. Modified Newtonian Dynamics (MOND) is studied as the accelerations of the Local Group are fully in the deep-MOND regime. MOND yields the order of magnitude for the expected baryonic mass only if at least one encounter occurred. While we only consider the LG as two point masses, our calculations provide a benchmark for future work with simulations to test Dynamical Friction and other effects. This model can be also used to test screening mechanisms and alternative theories of gravity.Comment: 16 pages. A revised versio

Decaying coupled Fermions to curvature and the H0H_0 tension

A formulation of cosmology driven by fermions $\psi$ is studied. Assumption of condensation for the spinor field simplifies the homogeneous solution of the Dirac equations and connects the spinor field with the scale parameter of the universe. With coupling between the Einstein term and spinor field, the possibility for a late time interaction emerges. In that way, the early universe agrees with $\Lambda$CDM model, but for the late universe the new integrating term dominates. From late time expansion data we obtain the $H_0$ from the SH0ES experiment. The data include the Pantheon Type Ia supernova, Quasars, Gamma Ray Bursts (for the Hubble diagram), cosmic chronometers and Byron Acoustic Oscillations. The decaying coupling reveals the capabilities of the scenario and makes it a good candidate for the description of nature. The tension can be reduced even further by including the local measurement of the Hubble constant.Comment: 5 pages, 2 figure

Unified Dark Energy and Dark Matter from Dynamical Spacetime Cosmology

A model of unified dark matter and dark energy based on a Dynamical Spacetime Theory (DST) is studied. By introducing a Dynamical Spacetime vector field $\chi_\mu$, a conservation of an energy momentum tensor $T^{\mu\nu}_{(\chi)}$ emerges. The action allows for two different potentials, while one represents a dark energy. For constant potentials, the cosmological solution yields a non singular bouncing solutions that rapidly approaches the $\Lambda$CDM model. The Dynamical Time corresponds to the cosmic time as well. The theory fits with the late time expansion data of the Universe. With higher dimensions a mechanism for inflation and compactification appears, with exponential growth for some dimensions and exponential contraction of the others. By demanding that the Dynamical Spacetime vector field be a gradient of a scalar the DST becomes a theory with diffusive interacting, which asymptotically returns to the $\Lambda$CDM model as a stable point. These formulations lead to scenarios which address our understanding about the origin of the Universe.Comment: PhD Thesi