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The contribution of cosmological perturbations to the time drift of the cosmological redshift is derived. It is shown that the dominant correction arises from the local acceleration of both the emitter and the observer. The amplitude of this effect is estimated to be of the order of 1% of the drift signal at z=2-4, but can easily be lowered down to 0.1% by using many absorption lines and quasars.
The cosmological redshifts z in the frequencies of spectral lines from distant galaxies as compared with their values observed in terrestrial laboratories, which are due to the scale factor a(t), frequently are interpret as a special-relativistic Dop
We propose and apply a new test of Einsteins Equivalence Principle (EEP) based on the gravitational redshift induced by the central super massive black hole of quasars in the surrounding accretion disk. Specifically, we compare the observed gravitati
In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective optimizati
We solve a min-max problem in a robust exploratory mean-variance problem with drift uncertainty in this paper. It is verified that robust investors choose the Sharpe ratio with minimal $L^2$ norm in an admissible set. A reinforcement learning framewo
We demonstrate that observations lacking reliable redshift information, such as photometric and radio continuum surveys, can produce robust measurements of cosmological parameters when empowered by clustering-based redshift estimation. This method in