We use the three-scale framework of Hu et al. to show how the Cosmic Microwave Background anisotropy spectrum depends on the fundamental constants. As expected, the spectrum depends only on emph{dimensionless} combinations of the constants, and we em
phasize the points that make this generally true for cosmological observables. Our analysis suggests that the CMB spectrum shape is mostly determined by $alpha^2m_e/m_p$ and the proton-CDM-particle mass ratio, $m_p/mchi$. The distance to the last-scattering surface depends on $Gm_pmchi/hbar c$, so published CMB observational limits on time variations of the constants implicitly assume the time-independence of this quantity, as well as assuming a flat-lcdm~cosmological model. On the other hand, low-redshift BAO, $H_0$ and baryon-mass-fraction measurements can be combined with the emph{shape} of the CMB spectrum to give information that is largely independent of these assumptions. In particular we show that the pre-recombination values of $Gmchi^2/hbar c$, $m_p/mchi$ and $alpha^2m_e/m_p$ are equal to their present values at a precision of $sim15%$.
The laws of physics have a set of fundamental constants, and it is generally admitted that only dimensionless combinations of constants have physical significance. These combinations include the electromagnetic and gravitational fine structure consta
nts, $alpha=e^2/4piepsilon_0hbar c$ and $alpha_G=Gm_p^2/hbar c$, along with the ratios of elementary-particles masses. Cosmological measurements clearly depend on the values of these constants in the past and can therefore give information on their time dependence if the effects of time-varying constants can be separated from the effects of cosmological parameters. The latter can be eliminated by using pairs of redundant measurements and here we show how such pairs conspire to give information only on dimensionless combinations of constants. Among other possibilities, we will use distance measurements based on Baryon Acoustic Oscillations (BAO) and on type Ia supernova. The fact that measurements yield information only on dimensionless combinations is traced to the fact that distances between co-moving points expand following the same function of time that governs the redshift of photon wavelengths.
We report a detection of the baryon acoustic oscillation (BAO) feature in the three-dimensional correlation function of the transmitted flux fraction in the Lya forest of high-redshift quasars. The study uses 48,640 quasars in the redshift range $2.1
le z le 3.5$ from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third generation of the Sloan Digital Sky Survey (SDSS-III). At a mean redshift $z=2.3$, we measure the monopole and quadrupole components of the correlation function for separations in the range $20hMpc<r<200hMpc$. A peak in the correlation function is seen at a separation equal to $(1.01pm0.03)$ times the distance expected for the BAO peak within a concordance $Lambda$CDM cosmology. This first detection of the BAO peak at high redshift, when the universe was strongly matter dominated, results in constraints on the angular diameter distance $da$ and the expansion rate $H$ at $z=2.3$ that, combined with priors on $H_0$ and the baryon density, require the existence of dark energy. Combined with constraints derived from Cosmic Microwave Background (CMB) observations, this result implies $H(z=2.3)=(224pm8){rm km,s^{-1}Mpc^{-1}}$, indicating that the time derivative of the cosmological scale parameter $dot{a}=H(z=2.3)/(1+z)$ is significantly greater than that measured with BAO at $zsim0.5$. This demonstrates that the expansion was decelerating in the range $0.7<z<2.3$, as expected from the matter domination during this epoch. Combined with measurements of $H_0$, one sees the pattern of deceleration followed by acceleration characteristic of a dark-energy dominated universe.
