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Anthropic constraints on the cosmological constant from Sun's motion through the Milky Way

We tentatively look at anthropic constraints on the Cosmological Constant (CC) Λat galactic scales by investigating its influence on the motion of the Sun throughout the Milky Way (MW) for -4.5 <= t <=0 Gyr. In particular, we look at the Galactocentric distance at which the Sun is displaced at the end of the numerical integration of its equations of motion modified in order to include the effect of Λas well. Values of it placing our star at its birth at more than 10 kpc from the Galactic center (GC) are to be considered implausible, according to the current views on the Galactic Habitable Zone (GHZ) on the metallicity level needed for stars&#39; formation. Also values yielding too close approaches to GC should be excluded because of the risks to life&#39;s evolution coming from too much nearby supernovae (SN) explosions and Gamma Ray Bursts (GRB). We investigate the impact on our results of the uncertainties on both the MW model&#39;s parameters and the Sun&#39;s initial conditions, in particular the Hubble parameter H_0 and the Local Standard Rest (LSR) speed Θ_0 accurate at 2% and 6.2% level, respectively. While H_0=70.1 km s^-1 Mpc^-1, Θ_0=254 km s^-1 and Λ<= 10^-55 cm^-2 locates the place of birth of the Sun at 19.6 kpc from GC, the same values for H_0 and Λ, and Θ_0^max=270 km s^-1, places it at the plausible Galactocentric distance of 8.5 kpc. Λ= 10^-54 cm^-2 and Λ= 10^-53 cm^-2 place the Sun at 10.6 kpc and 18.7 kpc, respectively.