Yasunori Fujii

Re/Os constraint on the time variability of the fine-structure constant

We argue that the accuracy by which the isochron parameters of the decay 187Re-->187Os are determined by dating iron meteorites may constrain the possible time dependence of the decay rate and hence of the fine-structure constant alpha, not directly but only in a model-dependent manner. From this point of view, some of the attempts to analyze the Oklo constraint and the results of the quasistellar-object absorption lines are reexamined.

On the Analogy between Strong Interaction and Electromagnetic Interaction

According to Sakatas composits hypothesis of heavy particles, the fundamental particles do not change their kind through strong interactions. A formulation of these interactions is given which requires invariance under the gauge transformation of the first kind for each baryon field. Assuming the phase function depends on the spacetime coordinate, this leads to the existence of a neutral vector meson analogous to the electromagnetic field, the mass of which need not always vanish. Its consequences are examined and found to be quite favorable for the interpretation of the strong interaction. In particular, it leads to the conservation law of parity in strong interactions and the condition for the existence of the composite state.

Attractor Universe in the Scalar-Tensor Theory of Gravitation

In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant (or a vacuum energy) behave as attractors independently of the initial values. We develop a general formulation in terms of two-dimensional phase space, mainly according to the Brans-Dicke model requiring the scalar field decoupled from the matter Lagrangian in the Jordan frame. We show that there are two kinds of fixed points, one of which is an attractor depending on the coupling constant and equation of state. We find that the static universe in the Jordan frame is an attractor in the presence of a cosmological constant for some range of the coupling constant. We extend our analysis to a power-law potential, finding a new type of power-law inflation caused by the coupling to the matter fluid, also as an attractor.

An Approach toward the Laboratory Search for the Scalar Field as a Candidate of Dark Energy

The observed accelerating universe indicates the presence of Dark Energy which is probably interpreted in terms of an extremely light gravitational scalar field. We suggest a way to probe this scalar field which contributes to optical light-by-light scattering through the resonance in the quasi-parallel collision geometry. As we find, the frequency-shifted photons with the specifically chosen polarization state can be a distinct signature of the scalar-field-exchange process in spite of the extremely narrow width due to the gravitationally weak coupling to photons. Main emphasis will be placed in formulating a prototype theoretical approach, then showing how the weak signals from the gravitational coupling are enhanced by other non-gravitational effects at work in laser experiments.

Mass of the Dilaton and the Cosmological Constant

One might raise the question if the gravitational scalar field (dilaton) mediates a finiterange force between local objects that behaves globally like a massless field in conformity with the scenario of a decaying cosmological constant. We obtain a non-negative answer to this question by carrying out a detailed analysis of the field-theoretical quantization procedure taking into account the observationally required suppression of the vacuum energy which constitutes a part of the cosmological constant. The gravitational scalar field, sometimes called the dilaton, which likely has its origin in string theory, has been a focus of attempts to understand the small but nonzero cosmological constant. 1) A rapidly decaying potential, like an exponential or inverse-power type, has been favored both in phenomenological analyses 2) and as models of theoretical interest. 3)–6) In particular, we have studied an exponential potential in the context of the scalar-tensor theory with the constant Λ included. 7),8) It seems agreed that the global behavior of a spatially uniform solution for the scalar field is consistent with the “masslessness” of the field, in the sense that its inverse “mass” is as large as the size of the visible universe. Some authors go even further, arguing that this field mediates a long-range force between the macroscopic objects, and thus can be studied in solar system experiments, and free-fall measurements above the detectable level. 5),6),9) The present author, by contrast, has emphasized that the spatially varying component more likely results in a local force with a finite and intermediate range, as also discussed in Ref. 5), not necessarily constrained by the above-mentioned experiments. 7),8) In this paper we reinforce the latter point of view, expressed rather vaguely in the middle of Chapter 6, Section 4 of Ref. 8), through a detailed analysis of the self-energy of the quantized scalar field arising from the interaction with matter fields. The root of the issue lies in the widely accepted view that, unlike a gauge field, the scalar field has no immunity against acquiring self-mass due to the interaction. We recognize, on the other hand, that the vacuum energy, in the sense of relativistic quantum field theory, yields too large a contribution to the cosmological constant, while it appears to be suppressed almost to zero from observation. We show how the latter fact is related to the present issue, also discussing what the theoretical formulation should be like in order to have the expected distinction between global and local aspects. We admit that the conclusion, partly a conjecture, is only tentative,

Time-variability of the fine-structure constant expected from the Oklo constraint and the QSO absorption lines

Abstract The data from the QSO absorption lines indicating a nonzero time-variability of the fine-structure constant has been re-analyzed on the basis of a “damped-oscillator” fit, as motivated by the same type of behavior of a scalar field, dilaton, which mimics a cosmological constant to understand the accelerating universe. We find nearly as good fit to the latest data as the simple weighted mean. In this way, we offer a way to fit the more stringent result from the Oklo phenomenon, as well.

Possible time-variability of the fine-structure constant expected from the accelerating universe

We present a theoretical calculation on the time-variability of the fine-structure constant to fit the result of the recent precise analysis of the measurement of the QSO absorption lines. We find the parameters of the scalar-tensor theory to be determined much more accurately than fitting the accelerating universe itself, but leading not to easy detections of the effect on the equation of state of the dark energy in the earlier epochs.

A possible new interpretation of the results of Δα/α from QSO absorption lines

The measurement of Δα/α from the QSO absorption lines of Fe II taken at two different redshifts (Quast et al., Levshakov et al.) is compared with the result based on the 23 data points also obtained from VLT/UVES (Chand et al.), to demonstrate that the apparent oscillatory time-dependence fitting the latter taken at face value is reinforced by the former claimed to be of much better accuracy.

Conformal Transformations in the Scalar-Tensor Theory Applied to the Accelerating Universe

The scalar-tensor theory is plagued by nagging questions if different conformal frames, in particular the Jordan and Einstein conformal frames, are equivalent to each other. As a closely related question, there are opposing views on which of the two conformal frames is physically acceptable. Reinforcing our previous claims, we offer replies based on a cosmological model of the scalar-tensor theory, believed to be a promising theory for understanding the accelerating universe, as well as today’s version of the cosmological constant problem. Exploiting the advantage that this model admits analytical asymptotic solutions, our argument does not depend on whether the underlying theory is invariant under conformal transformations. Our argument provides partial support for the claimed “equivalence”, but we also present examples that require more careful analyses exploiting field equations. We also point out that the Jordan conformal frame is suitable for an interpretation in terms of unification theories in physics, for example, string theory and the Kaluza-Klein approach, while the Einstein conformal frame may be acceptable as a physical conformal frame under two conditions: (i) the simplest constant Λ term in the Lagrangian in the Jordan conformal frame; (ii) the revised form of the conventional Brans-Dicke model based on the validity of the weak equivalence principle.

Accelerating universe and the time-dependent fine-structure constant

I start with assuming a gravitational scalar field as the dark-energy supposed to be responsible for the accelerating universe. Also from the point of view of unification, a scalar field implies a time-variability of certain “constants” in Nature. In this context I once derived a relation for the time-variability of the fine-structure constant α: Δα/α =ζ Ƶ (α/π) Δσ, where ζ and Ƶ are the constants of the order one, while σ on the right-hand side is the scalar field in action in the accelerating universe. I use the reduced Planckian units with c = ℏ = M P (=(8π G ) −1/2 )=1. I then compared the dynamics of the accelerating universe, on one hand, and Δα/α derived from the analyses of QSO absorption lines, Oklo phenomenon, also different atomic clocks in the laboratories, on the other hand. I am here going to discuss the theoretical background of the relation, based on the scalar-tensor theory invented first by Jordan in 1955.