[Paper Review] Towards a UV Completion for Chameleon Scalar Theories

Kurt Hinterbichler, Justin Khoury+1 more|arXiv (Cornell University)|Dec 20, 2010

Cosmology and Gravitation TheoriesPhysics and Astronomy62 references18 citations

TL;DR

This paper proposes that the volume modulus in string theory compactifications can act as a chameleon scalar field, naturally screening its long-range fifth force in high-density environments like Earth's surface. By embedding the KKLT superpotential with a negative parameter a < 0, the model realizes a chameleon mechanism that evades experimental constraints while allowing cosmologically relevant dynamics, with viable parameter space constrained by solar system and cosmological tests of gravity.

ABSTRACT

Chameleons are scalar fields that couple directly to ordinary matter with gravitational strength, but which nevertheless evade the stringent constraints on tests of gravity because of properties they acquire in the presence of high ambient matter density. Chameleon theories were originally constructed in a bottom-up, phenomenological fashion, with potentials and matter couplings designed to hide the scalar from experiments. In this paper, we attempt to embed the chameleon scenario within string compactifications, thus UV completing the scenario. We look for stabilized potentials that can realize a screening mechanism, and we find that the volume modulus rather generically works as a chameleon, and in fact the supersymmetric potential used by Kachru, Kallosh, Linde and Trivedi (KKLT) is an example of this type. We consider all constraints from tests of gravity, allowing us to put experimental constraints on the KKLT parameters.

Motivation & Objective

• To embed chameleon scalar theories—previously constructed in a phenomenological, bottom-up manner—into a fundamental theory via string compactifications.
• To identify a UV-complete realization of the chameleon mechanism within string theory, particularly focusing on moduli fields.
• To determine whether the KKLT superpotential, a cornerstone of string landscape models, can support a chameleon field with viable phenomenology.
• To derive experimental constraints on KKLT parameters from solar system and cosmological tests of gravity, ensuring the chameleon remains hidden from detection.
• To assess the naturalness and viability of such chameleon models in the broader context of the string landscape.

Proposed method

• Analyzes the chameleon mechanism in scalar-tensor gravity, focusing on the thin-shell screening condition and effective mass dependence on ambient density.
• Identifies the volume modulus in generic dimensional reductions as a candidate chameleon field due to its density-dependent effective mass.
• Constructs a general phenomenological potential for the chameleon field that captures the essential features of moduli stabilization.
• Demonstrates that the KKLT superpotential, when parameterized with a < 0, generates a potential matching the required chameleon form.
• Applies constraints from solar system tests (e.g., PPN parameters, fifth-force limits) and cosmological observations (e.g., cosmic density) to derive bounds on KKLT parameters.
• Uses the relation between the scalar field's mass, potential curvature, and Compton wavelength to derive quantitative bounds on the chameleon's range and coupling.

Experimental results

Research questions

• RQ1 Can the volume modulus in string compactifications naturally realize a chameleon mechanism that suppresses fifth-force interactions in high-density environments?
• RQ2 Does the KKLT superpotential, with appropriate parameter choices (especially a < 0), generate a potential that supports chameleon screening via density-dependent mass?
• RQ3 What experimental constraints from gravity tests (e.g., solar system, cosmological density) can be imposed on the KKLT parameters to ensure the chameleon remains undetected?
• RQ4 How does the chameleon behavior in the KKLT model compare to the standard quadratic approximation in terms of field range and screening efficiency?
• RQ5 Is the resulting chameleon model viable in the string landscape, and how does its fine-tuning compare to other known problems like the cosmological constant problem?

Key findings

• The volume modulus in string compactifications can naturally serve as a chameleon field, with its effective mass increasing in high-density regions, thereby screening long-range fifth forces.
• The KKLT superpotential with a < 0 generates a potential that realizes the chameleon mechanism, making it a viable UV completion of chameleon theories.
• The constraint |a|σmin > 10^6 is required to ensure the chameleon is screened in the solar system, derived from the thin-shell condition and Compton wavelength limits.
• The cosmological mass of the chameleon field is bounded below by m_cosmo ≳ 10^15 H0, indicating a very light field on cosmological scales, consistent with dark energy models.
• The potential minimum must satisfy |V0| ≳ 10^{-150} M_Pl^4 to avoid overproduction of the scalar field in the early universe, derived from the cosmic density constraint.
• The model remains consistent with all current gravity tests when parameters are tuned such that the superpotential factor A ∼ e^{-10^{30}}, which is comparable in fine-tuning to the KK scale and cosmological constant problems.