An upper limit to the variation in the fundamental constants at redshiftz= 5.2

Abstract

Aims. We constrain a hypothetical variation in the fundamental physical constants over the course of cosmic time. Methods. We use unique observations of the CO(7-6) rotational line and the [C i] 3 P 2 − 3 P 1 fine-structure line towards a lensed galaxy at redshift z = 5.2 to constrain temporal variations in the constant F = α 2 /μ, where μ is the electron-to-proton mass ratio and α is the fine-structure constant. The relative change in F between z = 0 and z = 5.2, ΔF/F = (F obs − F lab )/F lab , is estimated from the radial velocity offset, ΔV = V rot − V fs , between the rotational transitions in carbon monoxide and the fine-structure transition in atomic carbon. Results. We find a conservative value ΔV = (1±5) km s −1 (1σ C.L.), which when interpreted in terms of ΔF/F gives ΔF/F < 2×10 −5 . Independent methods restrict the μ-variations at the level of Δμ/μ < 1 × 10 −7 at z = 0.7 (look-back time t z0.7 = 6.4 Gyr). Assuming that temporal variations in μ, if any, are linear, this leads to an upper limit on Δμ/μ < 2 × 10 −7 at z = 5.2 (t z5.2 = 12.9 Gyr). From both constraints on ΔF/F and Δμ/μ , one obtains for the relative change in α the estimate Δα/α < 8 × 10 −6 , which is at present the tightest limit on Δα/α at early cosmological epochs.

Perspective: Tipping the scales: Search for drifting constants from molecular spectra

“…Crosses, also shown in the figure, indicate sensitivity coefficients that were calculated using a full molecular Hamiltonian. 63 From the figure, it can be seen that resonances occur near A/B ∼ 25 which is close to the A/B values for the 12 13 C 16 O have a sensitivity that is almost 500 times that of a pure rotational transition. An experiment to measure these transitions in a double-resonance molecular beam machine using a two-photon microwave absorption is currently under construction in our laboratory.…”

“…While electronic transitions, including spinorbit interactions, are sensitive to α, vibrational, rotational, and tunneling modes in molecules are sensitive to μ. Hyperfine effects, such as in the Cs-atomic clock 12,13 and the 21-cm line of atomic hydrogen, 14 depend on both α and μ, as do -doublet transitions in molecules. 15 The same holds for combined high-redshift observations of a rotational transition in CO and a fine structure transition in atomic carbon, 16 placing a tight constraint on the variation of the combination α 2 μ at a redshift as high as z = 5.2. Within the framework of grand unification schemes theories have been developed that relate drifts in μ and α via…”

Limits on the spatial variations of the electron-to-proton mass ratio in the Galactic plane

“…At very high redshift, z = 5.2 (epoch 12.9 Gyr), the current limit is Δα/α < 8 × 10 −6 (1σ C.L. ), corresponding to |α/α| < 6 × 10 −16 yr −1 (Levshakov et al 2012). We recall that most stringent limits set by the Oklo fossil reactor and by terrestrial atomic clock experiments are |α/α| < 5 × 10 −17 yr −1 (Uzan 2011) and |α/α| < 4 × 10 −17 yr −1 (Rosenband et al 2008), respectively.…”

Constraints on changes in the proton–electron mass ratio using methanol lines

“…Conversely, the advantage of the cross-correlation approach is that it is non-parametric, making no assumptions about the line shapes or the number of components that must be fit to the lines (which can affect the results, especially for complex line profiles) (e.g. Kanekar et al , 2010Levshakov et al 2012).…”

“…The second approach was carried out on individual pairs of lines using two non-parametric schemes, the cross-correlation method ) and the "sliding-distance" method (Levshakov et al 2012). These yielded very similar results, so we will only discuss the cross-correlation approach in detail.…”