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The status of searches for possible variation in the constants of nature from astronomical observation of molecules is reviewed, focusing on the dimensionless constant representing the proton-electron mass ratio $mu=m_p/m_e$. The optical detection of H$_2$ and CO molecules with large ground-based telescopes (as the ESO-VLT and the Keck telescopes), as well as the detection of H$_2$ with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope is discussed in the context of varying constants, and in connection to different theoretical scenarios. Radio astronomy provides an alternative search strategy bearing the advantage that molecules as NH$_3$ (ammonia) and CH$_3$OH (methanol) can be used, which are much more sensitive to a varying $mu$ than diatomic molecules. Current constraints are $|Deltamu/mu| < 5 times 10^{-6}$ for redshift $z=2.0-4.2$, corresponding to look-back times of 10-12.5 Gyrs, and $|Deltamu/mu| < 1.5 times 10^{-7}$ for $z=0.88$, corresponding to half the age of the Universe (both at 3$sigma$ statistical significance). Existing bottlenecks and prospects for future improvement with novel instrumentation are discussed.
Absorption lines of H$_2$ and HD molecules observed at high redshift in the line of sight towards quasars are a test ground to search for variation of the proton-to-electron mass ratio $mu$. For this purpose, results from astronomical observations ar
We review the variety of new singularities in homogeneous and isotropic FRW cosmology which differ from standard Big-Bang and Big-Crunch singularities and suggest how the nature of these singularities can be influenced by the varying fundamental constants.
[Abridged] Observations of molecular gas at all redshifts are critical for measuring the cosmic evolution in molecular gas density and understanding the star-formation history of the Universe. The 12CO molecule (J=1-0 transition = 115.27 GHz) is the
We discuss minisuperspace models within the framework of varying physical constants theories including $Lambda$-term. In particular, we consider the varying speed of light (VSL) theory and varying gravitational constant theory (VG) using the specific
Varying fundamental constants (VFC) [e.g., the fine-structure constant, $alpha_{rm EM}$] can arise in numerous extended cosmologies. Through their effect on the decoupling of baryons and photons during last scattering and reionisation, these models c