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

¹ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
² Ioffe Physical-Technical Institute, Polytekhnicheskaya Str. 26, 194021 St. Petersburg, Russia
e-mail: lev@astro.ioffe.rssi.ru
³ Observatoire de Paris, LERMA, CNRS, 61 Av. de l’Observatoire, 75014 Paris, France
⁴ Université de Toulouse, UPS-OMP, CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
⁵ Petersburg Nuclear Physics Institute, 188300 Gatchina, Russia
⁶ St. Petersburg Electrotechnical University “LETI”, Prof. Popov Str. 5, 197376 St. Petersburg, Russia

Received: 15 February 2012
Accepted: 15 March 2012

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] ³P₂ - ³P₁ fine-structure line towards a lensed galaxy at redshift z = 5.2 to constrain temporal variations in the constant F = α²/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.