Varying constants, Gravitation and Cosmology

Abstract: Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

• The paper's main contribution is proposing that nearly massless scalar fields induce variations in typically invariant fundamental constants.
• It employs high-precision methods, including atomic clock comparisons and quasar absorption studies, to constrain these potential variations.
• The findings imply necessary modifications to gravitational theory and hint at a coupling between varying constants and dark energy in cosmological evolution.

Essay: Varying Constants, Gravitation, and Cosmology

The paper "Varying Constants, Gravitation and Cosmology" explores the concept that fundamental constants of nature, which traditionally are considered invariant, might actually vary in time and/or space. This idea prompts a profound reconsideration of the underlying laws of physics, especially in the context of gravitational theory and cosmology, where it suggests the presence of new fields and interactions. The scientific inquiry into varying fundamental constants dates back to Dirac's Large Numbers Hypothesis, which stimulated numerous theoretical investigations and empirical tests over the decades.

One cornerstone of the paper is the potential existence of almost massless scalar fields that could couple to matter, leading to a spatial or temporal variation in these constants. Such scenarios could have profound implications, notably violating the universality of free fall, a fundamental tenet of general relativity, thereby necessitating modifications to our current understanding of gravitational laws. The paper conducts a thorough examination of the relationships among fundamental constants, their potential variability, and the resultant theoretical frameworks.

Experimental and Observational Constraints

The paper scrutinizes an array of empirical systems that have been leveraged to place constraints on the variation of fundamental constants. These include atomic clocks, the Oklo natural nuclear reactor, solarsystem observations, meteorite dating, and the absorption spectra of distant quasars. Each system is considered for its dependence on the constants and the methodologies employed to isolate potential variations.

For instance, atomic clocks allow for high-precision tests due to their diverse dependence on constants like the fine-structure constant (α) and the electron-to-proton mass ratio (μ). Studies using atomic clock comparisons between diverse elements point to constraints on the time variation of these constants down to parts-per-trillion levels annually. Similarly, quasar absorption lines provide constraints over cosmological timescales by examining shifts in spectral lines due to varying α.

Models of fundamental constant variations heavily involve scalar fields, as illustrated through scalar-tensor theories. These fields potentially couple to the electromagnetic Faraday tensor, impacting constants like the fine-structure constant. A consistent theme in theoretical models is the appeal to higher-dimensional theories or string theory, which naturally introduce scalar degrees of freedom (e.g., dilatons) capable of affecting physical constants.

Theoretical Frameworks and Implications

The varying constant hypothesis introduces significant implications for both general relativity and cosmology. The paper discusses theoretical models where such variations could arise, often within the context of higher-dimensional theories or string theory. In string theory, the vacuum expectation values of scalar fields such as the dilaton influence low-energy constants, where the challenge is to reconcile these with observed constraints.

Scalar-tensor theories illustrate how introducing an additional scalar degree of freedom affects the gravitational coupling, leading to theoretical deviations from standard Einsteinian gravity. These changes are often parameterized in terms of post-Newtonian parameters which in practice necessitate comparably small variations to remain in concordance with precision Solar System tests and cosmic microwave background (CMB) observations.

Moreover, these theoretical explorations touch upon potential links between varying constants and dark energy; hypothesizing that the dynamics of scalar fields might simultaneously drive the variation of constants and cosmic acceleration. This avenue offers a speculative yet tantalizing route to integrate cosmic evolution with fundamental physics.

Conclusion

The inquiry into varying constants straddles an interplay between cutting-edge theoretical physics and high-precision observational techniques. While empirical data steadily anchors the invariability of these constants, the scope remains for new physics to emerge that elegantly unites gravitation, cosmology, and quantum field theory under scenarios that admit slowly varying constants as remnants of high-energy, underlying dynamics. Continuous advancements in observational precision, alongside robust theoretical frameworks, remain pivotal in this profound quest.

The theoretical positions described in this paper pave the way for further research that can progress by either strengthening the constraints on constant invariance or unearthing the subtle whisper of new physics contained within the smallest permissible variations in these fundamental cornerstones of nature.