[Paper Review] Neutralino Relic Density Enhancement in Non-Standard Cosmologies

Stefano Profumo, Piero Ullio|arXiv (Cornell University)|Apr 20, 2004

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper demonstrates that non-standard cosmologies—such as those with a quintessence scalar field or primordial anisotropies—can enhance the thermal relic density of neutralinos by up to six orders of magnitude, enabling supersymmetric models with large annihilation cross sections to account for the observed cold dark matter abundance while predicting strong indirect detection signals.

ABSTRACT

The thermal relic abundance of species critically depends on the assumed underlying cosmological model. In the case of neutralinos, freeze-out takes place long before Big Bang Nucleosynthesis, which provides the strongest constraint on the evolution of the Hubble parameter in the Early Universe. We show that non-standard cosmologies, such as models featuring a quintessential scalar field or primordial anisotropies, can lead to large enhancements in the neutralino relic abundance, up to six orders of magnitudes. Within these scenarios, supersymmetric models with large neutralino annihilation cross sections may account for the whole inferred amount of cold dark matter, yielding on the other hand large indirect detection rates.

Motivation & Objective

• To investigate how non-standard cosmological models affect the thermal relic abundance of neutralinos.
• To determine whether cosmological enhancements can reconcile supersymmetric models with large annihilation cross sections to the observed cold dark matter density.
• To assess the implications for indirect dark matter detection in scenarios where standard relic abundance calculations fail.
• To explore the role of dynamical scalar fields (quintessence) and primordial anisotropies in modifying the Hubble expansion rate during neutralino freeze-out.
• To quantify the maximum possible enhancement of the neutralino relic density under Big Bang Nucleosynthesis (BBN) constraints.

Proposed method

• Uses the Boltzmann equation for comoving number density evolution, incorporating the effective annihilation rate and Hubble expansion rate.
• Modifies the Friedmann equation to include additional energy components, such as a quintessence scalar field with an exponential potential $ V( heta) = M_{\text{Pl}}^4 \exp(-\lambda \theta / M_{\text{Pl}}) $.
• Introduces the parameter $ \xi_X = \rho_X / \rho_r $ at freeze-out temperature to quantify the relative energy density of non-standard components.
• Analyzes the mAMSB (minimal Anomaly Mediated SUSY Breaking) scenario to study relic density enhancement across varying neutralino masses and $ \xi_\phi $ values.
• Considers alternative cosmologies such as scalar-tensor theories and Bianchi-I anisotropic models, where shear energy density $ \rho_s \sim a^{-6} $ can dominate at freeze-out.
• Compares results with the standard $ \Lambda $CDM model and uses the WMAP-recommended $ \Omega_{\chi}h^2 \approx 0.11 $ range as a benchmark.

Experimental results

Research questions

• RQ1 To what extent can non-standard cosmologies, such as those with a quintessence field, enhance the neutralino relic density beyond the standard $ \Lambda $CDM prediction?
• RQ2 What is the maximum possible enhancement of the neutralino relic abundance compatible with Big Bang Nucleosynthesis constraints?
• RQ3 How do primordial anisotropies or shear-dominated cosmologies affect the freeze-out dynamics and final relic density of neutralinos?
• RQ4 Can supersymmetric models with large neutralino annihilation cross sections still yield the observed cold dark matter abundance in non-standard cosmologies?
• RQ5 What are the implications for indirect dark matter detection in scenarios where relic density is enhanced via cosmological mechanisms?

Key findings

• Non-standard cosmologies, particularly those with a quintessence scalar field, can enhance the neutralino relic density by up to six orders of magnitude, reaching $ \Delta\Omega \sim 10^6 $.
• In the mAMSB model, the relic density enhancement scales as $ \sqrt{\xi} $, allowing wino-like neutralinos to satisfy the WMAP-observed $ \Omega_{\chi}h^2 $ range across a wide mass range.
• The maximal enhancement compatible with BBN constraints is $ \Delta\Omega \sim 10^6 $, achieved for specific $ \lambda $ and $ H_i $ values in the quintessence model.
• In anisotropic cosmologies (e.g., Bianchi-I), shear energy density $ \rho_s \sim a^{-6} $ can dominate at freeze-out, leading to significant relic density enhancements quantified by $ \xi $.
• Models with low relic density in $ \Lambda $CDM—especially wino- and higgsino-like neutralinos—can achieve the correct $ \Omega_{\chi}h^2 $ in non-standard cosmologies, enabling strong indirect detection signals.
• The study shows that indirect detection rates scale linearly with $ \langle\sigma_{\text{eff}}v\rangle $, so enhanced relic densities allow large-annihilation-cross-section models to remain viable while predicting observable signals.