Scale invariance, unimodular gravity and dark energy (0809.3395v2)

Abstract: We demonstrate that the combination of the ideas of unimodular gravity, scale invariance, and the existence of an exactly massless dilaton leads to the evolution of the universe supported by present observations: inflation in the past, followed by the radiation and matter dominated stages and accelerated expansion at present. All mass scales in this type of theories come from one and the same source.

• The paper introduces a no-scale scenario in which a singlet scalar field dynamically generates all mass scales, including Newton's constant.
• It employs unimodular gravity to convert the cosmological constant into an evolving integration constant that drives both inflation and late-time cosmic acceleration.
• The study addresses quantum challenges in maintaining scale invariance, suggesting novel renormalization techniques aligned with observed dark energy behavior.

Scale Invariance, Unimodular Gravity, and Dark Energy

The paper by Mikhail Shaposhnikov and Daniel Zenhäusern presents an exploration of the theoretical implications of combining unimodular gravity with scale invariance and the presence of a massless dilaton in cosmological models. This approach aims to provide a coherent explanation of cosmological phenomena such as inflation and the current accelerated expansion of the universe, often attributed to dark energy.

Key Concepts and Theoretical Framework

The authors investigate the potential of having all mass scales, including Newton’s gravitational constant and particle masses, originate from a single source within a cosmological framework. The conventional separation of these mass scales between the vacuum expectation value of the Higgs field, the QCD scale, and Newton's constant poses a fundamental question in high-energy physics. To address this, the authors propose the "no-scale scenario," where these scales emerge from the dynamics of a new singlet scalar field $\chi$, in conjunction with the Standard Model extended by the Neutrino Minimal Standard Model ($\nu$MSM).

The discussion incorporates unimodular gravity (UG), a variant of Einstein's general relativity where the determinant of the metric is fixed, eliminating a cosmological constant as a fundamental parameter. Instead, the cosmological constant emerges as an integration constant determined by initial conditions, which, in a scale-invariant theory, evolves into a run-away effective potential for the dilaton field. The massless dilaton, a hypothetical particle associated with the spontaneous breaking of dilatational symmetry, plays a crucial role as a candidate for dynamical dark energy.

Cosmological Implications

The paper asserts that incorporating UG and scale invariance leads naturally to a cosmological model accommodating early universe inflation and late-time acceleration. The model dictates that:

1. Inflation: The interplay between the Higgs field and the singlet $\chi$ potentially drives early inflation following a chaotic inflation scenario. The non-minimal coupling of the Higgs field with gravity suggests it as the inflaton, consistent with previous hypotheses that the Standard Model Higgs fluctuations could induce inflationary dynamics.
2. Dark Energy and Cosmic Acceleration: Unlike fixed cosmological constants, the scalar field dynamics offer a variable dark energy model. For $\Lambda > 0$ (derived from UG's initial conditions), the Higgs and $\chi$ fields evolve over time, naturally introducing a form of dark energy consistent with observations of low $\omega$. This model proposes a slow-changing equation of state parameter $\omega$, a quantifiable discriminator from a pure cosmological constant model ($\omega = -1$).
3. Absence of True Cosmological Constant: The scale-invariant UG model effectively removes a static cosmological constant, suggesting a universe where all masses and coupling constants dynamically rescale during cosmic evolution.

Quantum Theoretical Considerations

Addressing the transition from classical to quantum theories, the authors emphasize the challenges in maintaining the scale invariance on the quantum level. Achieving a theory consistent with observed low-energy phenomena requires that all dimensionful parameters adapt dynamically along a flat direction of the quantum potential, a formidable challenge given the theory's inherent non-renormalizability. This consideration leads to the necessity of novel renormalization techniques to maintain a dilatationally invariant quantum field theory that is also consistent with the observed cosmological progressions.

Conclusion

The paper proposes that integrating unimodular gravity with scale invariance could explain several cosmic-scale phenomena without the need for fine-tuning or introducing complex new physics beyond the Standard Model and its minimal extensions. While the theoretical model is compelling, its predictions, particularly regarding the parameter $\omega$ for dark energy, invite further experimental scrutiny and offer potential avenues for distinguishing it from alternative dark energy models.

These theoretical insights suggest future research directions on developing explicit quantum scale-invariant models, understanding their phenomenological implications, and testing these predictions against empirical cosmic observational data. The work stands as a thoughtful contribution to the discourse on fundamental symmetries and their role in shaping the universe's large-scale structure and evolution.