The standard model of physics is built on the fundamental constants of nature, but it does not provide an explanation for their values, nor require their constancy over space and time.Here we set a limit on a possible cosmological variation of the proton-to-electron mass ratio m by comparing transitions in methanol observed in the early universe with those measured in the laboratory. From radio-astronomical observations of PKS1830-211, we deduced a constraint of ∆m/m = (0.0 T 1.0) × 10 −7 at redshift z = 0.89, corresponding to a look-back time of 7 billion years. This is consistent with a null result. T he standard model of particle physics, the theory describing symmetries and forces of nature at the deepest level, does not provide an intrinsic explanation for the values of the fundamental coupling constants, nor does it prohibit that the fundamental constants depend on time and space. In contrast, Einstein's equivalence principle, a basic assumption of general relativity, assumes that the laws of nature, and hence the fundamental constants are independent of a local reference system. Some cosmological scenarios aimed at explaining the fine-tuning between fundamental constants sketch an evolving mechanism, where minimally varying constants are crucial for reaching the present state of complexity in the universe (1). Theoretical approaches involving additional scalar fields have imposed bounds on varying constants through tests of the weak equivalence principle (2). In the past decade the search for small variations of dimensionless fundamental constants over cosmological time scales has become an active experimental endeavor, in particular because accurate measurements of spectral lines of atoms at high redshift have provided indication for a possible variation of the fine structure constant a, either temporally (3, 4) or spatially (5, 6).A second dimensionless fundamental constant m, representing the proton-to-electron mass ratio m p /m e , probes the cosmological evolution of the nuclear versus the electroweak sector in the standard model. A search for a possible drift of m has been made operational by comparing observations of spectral lines of the hydrogen molecule (H 2 ) in distant galaxies with accurate laboratory measurements (7). These investigations, based on observations with the world's largest optical telescopes, have yielded a limit at the level of ∆m/m < 10 −5 for look-back times of 12 billion years (8, 9).Inversion transitions of ammonia (NH 3 ) were found to be~100 times more sensitive to m-variation than H 2 transitions (10, 11). Astronomical observations of NH 3 , in the microwave or radio range of the electromagnetic spectrum, led to stringent 1s constraints at the level of (1.0 T 4.7) × 10 −7(12) and (-3.5 T 1.2) × 10 −7 (13). This has shifted the paradigm for probing m-variation from optical to radio astronomy. Here we use the extreme sensitivity of methanol (CH 3 OH) (14, 15) to probe the variation of the proton-to-electron mass ratio m over cosmic time.Methanol (Fig. 1A) is the simplest a...
We report Karl G. Jansky Very Large Array (VLA) absorption spectroscopy in four methanol (CH 3 OH) lines in the z = 0.88582 gravitational lens towards PKS1830−211. Three of the four lines have very different sensitivity coefficients K µ to changes in the proton-electron mass ratio µ; a comparison between the line redshifts thus allows us to test for temporal evolution in µ. We obtain a stringent statistical constraint on changes in µ by comparing the redshifted 12.179 GHz and 60.531 GHz lines, [∆µ/µ] 1.1 × 10 −7 (2σ) over 0 < z 0.88582, a factor of ≈ 2.5 more sensitive than the best earlier results. However, the higher signal-to-noise ratio (by a factor of ≈ 2) of the VLA spectrum in the 12.179 GHz transition also indicates that this line has a different shape from that of the other three CH 3 OH lines (at > 4σ significance). The sensitivity of the above result, and that of all earlier CH 3 OH studies, is thus likely to be limited by unknown systematic errors, probably arising due to the frequency-dependent structure of PKS1830−211. A robust result is obtained by combining the three lines at similar frequencies, 48.372, 48.377 and 60.531 GHz, whose line profiles are found to be in good agreement. This yields the 2σ constraint [∆µ/µ] 4 × 10 −7 , the most stringent current constraint on changes in µ. We thus find no evidence for changes in the proton-electron mass ratio over a lookback time of ≈ 7.5 Gyrs.
Rovibronic molecular hydrogen (H 2 ) transitions at redshift z abs 2.659 towards the background quasar B0642−5038 are examined for a possible cosmological variation in the proton-to-electron mass ratio, µ. We utilise an archival spectrum from the Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a signal-to-noise ratio of ∼35 per 2.5-km s −1 pixel at the observed H 2 wavelengths (335-410 nm). Some 111 H 2 transitions in the Lyman and Werner bands have been identified in the damped Lyman α system for which a kinetic gas temperature of ∼84 K and a molecular fraction log f = −2.18 ± 0.08 is determined. The H 2 absorption lines are included in a comprehensive fitting method, which allows us to extract a constraint on a variation of the proton-electron mass ratio, ∆µ/µ, from all transitions at once. We obtain ∆µ/µ = (17.1 ± 4.5 stat ± 3.7 sys ) × 10 −6 . However, we find evidence that this measurement has been affected by wavelength miscalibration errors recently identified in UVES. A correction based on observations of objects with solar-like spectra gives a smaller ∆µ/µ value and contributes to a larger systematic uncertainty: ∆µ/µ = (12.7 ± 4.5 stat ± 4.2 sys ) × 10 −6 .
The A 1 − X 1 + band system of carbon monoxide, which has been detected in six highly redshifted galaxies (z = 1.6-2.7), is identified as a probe method to search for possible variations of the proton-electron mass ratio (μ) on cosmological time scales. Laboratory wavelengths of the spectral lines of the A − X (v,0) bands for v = 0-9 have been determined at an accuracy of λ/λ = 1.5 × 10 −7 through VUV Fourier-transform absorption spectroscopy, providing a comprehensive and accurate zero-redshift data set. For the (0,0) and (1,0) bands, two-photon Doppler-free laser spectroscopy has been applied at the 3 × 10 −8 accuracy level, verifying the absorption data. Sensitivity coefficients K μ for a varying μ have been calculated for the CO A − X bands so that an operational method results to search for μ variation.
An overview is presented of the H 2 quasar absorption method to search for a possible variation of the proton-electron mass ratio µ = mp/me on a cosmological time scale. The method is based on a comparison between wavelengths of absorption lines in the H 2 Lyman and Werner bands as observed at high redshift with wavelengths of the same lines measured at zero redshift in the laboratory. For such comparison sensitivity coefficients to a relative variation of µ are calculated for all individual lines and included in the fitting routine deriving a value for ∆µ/µ. Details of the analysis of astronomical spectra, obtained with large 8-10 m class optical telescopes, equipped with high-resolution echelle grating based spectrographs, are explained. The methods and results of the laboratory molecular spectroscopy of H 2 , in particular the laser-based metrology studies for the determination of rest wavelengths of the Lyman and Werner band absorption lines, are reviewed. Theoretical physics scenarios delivering a rationale for a varying µ will be discussed briefly, as well as alternative spectroscopic approaches to probe variation of µ, other than the H 2 method. Also a recent approach to detect a dependence of the proton-to-electron mass ratio on environmental conditions, such as the presence of strong gravitational fields, will be highlighted. Currently some 56 H 2 absorption systems are known and listed. Their usefulness to detect µvariation is discussed, in terms of column densities and brightness of background quasar sources, along with future observational strategies. The astronomical observations of ten quasar systems analyzed so far set a constraint on a varying proton-electron mass ratio of |∆µ/µ| < 5 × 10 −6 (3-σ), which is a null result, holding for redshifts in the range z = 2.0 − 4.2. This corresponds to look-back times of 10-12.4 billion years into cosmic history. Attempts to interpret the results from these 10 H 2 absorbers in terms of a spatial variation of µ are currently hampered by the small sample size and their coincidental distribution in a relatively narrow band across the sky.PACS numbers: 06.20.Jr, 95.85.Mt, 98.80.Es,
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