Dark matter relic abundance in non-standard cosmological scenarios

Meehan, Michael Thomas (2015) Dark matter relic abundance in non-standard cosmological scenarios. PhD thesis, James Cook University.

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Abstract

The relic abundance of symmetric dark matter particles (where particle χ and antiparticle χ̅ are identical and therefore self-annihilating) and asymmetric dark matter particles (where χ ≠ χ̅) is calculated in several non-standard cosmological scenarios that predict a modified Hubble expansion rate in the pre-Big Bang Nucleosynthesis (BBN) era. The Boltzmann rate equation describing the time evolution of the dark matter number density is solved to accurately quantify the level of enhancement (or suppression) of the dark matter relic abundance with respect to the standard cosmology result. In terms of the dark matter particle interactions, we adopt a model independent approach and choose a generic form for the annihilation cross section {συ} = a+bT=mᵪ (where T is the temperature of the universe and mᵪ is the dark matter particle mass), calculating results for both the s– (b = 0) and p– (a = 0)wave annihilation cases. The solution method incorporated the numerical considerations outlined in the recent paper by Steigman et al (2012) for precise calculations of relic abundances, such as maintaining the temperature dependence of the number of entropic degrees of freedom g(*)(T). Furthermore, knowing the present dark matter density, Ω(DM)ʰ² = 0:1188±0:0010, is a precisely measured quantity, the relic abundance calculations are inverted to determine the annihilation cross section, {συ}, required to provide the observed density. A comparison of these results with observational bounds on {συ}, such those derived using the Fermi-LAT gamma ray data, enables deviations from the standard expansion history in the pre-BBN era to be constrained.

The four non-standard cosmological scenarios considered fall into two broad categories: gravity supplemented with a scalar field (kination phase quintessence dark energy and scalar-tensor gravity) and higher dimensional universe models (Randall-Sundrum type II and Gauss-Bonnet braneworlds). We find that those models that predict a faster (slower) expansion rate in the early universe lead to dark matter relic abundances that are enhanced (suppressed) by up to several orders of magnitude. More specifically, of the four models considered, three predicted faster expansion rates at early times with only the Gauss-Bonnet braneworld model admitting both faster and slower pre- BBN expansion rates. Hence, the kination phase quintessence, scalar-tensor gravity and Randall-Sundrum type II braneworld models all predicted an enhanced dark matter relic abundance whilst the Gauss-Bonnet braneworld model allowed for either enhanced or suppressed relic abundances. Furthermore, the level of enhancement (or suppression) increased with the amount of deviation from the standard expansion law at the time of dark matter decoupling so that the braneworld scenarios, which predicted the fastest expansion rates, provided the greatest levels of enhancement of the order ~ 10⁶ for particle mass mᵪ = 100 GeV. Additionally, we found that the enhancement was larger for p–wave annihilating particles since the freeze-out process occured more rapidly in this case.

We also found that previous calculations that failed to properly account for the temperature variation in the number of degrees of freedom incurred errors of up to a factor of two, with the larger errors arising for smaller particle masses (mᵪ < 10 GeV) and for those models in which the freeze-out process took longer to occur (e.g. braneworld models). Moreover, for scalar-tensor gravity, we found that, although large deviations from the standard expansion history at the time of dark matter decoupling were possible, the stringent constraints imposed by BBN calculations excluded these regions of parameter space, ensuring the modified expansion rate was nearly coincident with the standard expansion law. Accordingly, the relic abundance in these models only increased by a factor of 2–3 which is in stark contrast to the several orders of magnitude enhancement factors reported in Catena et al (2004).

The calculations for the Gauss-Bonnet braneworld model extend the study by Okada and Okada (2009) who assumed that the energy scale associated with the Gauss-Bonnet correction term, m(α), was equal to that associated with the brane tension, m(σ), so that the pre-BBN expansion rate was slower than the standard cosmological model and the relic abundance was suppressed. We consider the more plausible case m(α) ≥ m(σ) and find that the relic density is typically enhanced for m(α) > m(σ) and that, in the limit m(α) >> m(σ), the familiar Randall-Sundrum type behaviour is recovered.

The annihilation cross section required to produce the observed dark matter density was found to be enhanced by several orders of magnitude in the kination phase quintessence and braneworld scenarios, allowing current Fermi-LAT gamma ray data to directly probe significant portions of parameter space.

Finally, in the context of asymmetric dark matter models, we found that the modified decoupling predicted in non-standard cosmological models can either 'wash out' or amplify the asymmetry between the majority and minority dark matter components depending on whether the early time expansion rate is faster or slower than the standard expansion law respectively. Interestingly, in the former case, the relic density of the asymmetric dark matter species depends on the annihilation cross section, {συ}, rather than the asymmetry parameter, C, so that it behaves like symmetric dark matter in this sense. This leads to the intriguing prospect that the enhanced annihilation cross section required to provide the observed dark matter density can compensate for the suppressed abundance of the minority dark matter component and produce an observable detection signal. This result, which is contrary to the usual expectation that the asymmetric annihilation rate is negligible due to the exponentially suppressed abundance of the minority component, can be achieved for a wide range of parameter values within the kination phase quintessence and braneworld scenarios (and even for particular parameter values within the scalar-tensor gravity scenario).

The findings presented in this thesis extend, and in several cases challenge, existing results in the literature and also provide important insights for the planning and interpretation of both present and future dark matter experiments.

Item ID: 41213
Item Type: Thesis (PhD)
Keywords: braneworlds; cosmology; dark energy theory; dark matter experiments; dark matter theory; dark matter; extra dimensions; extragalactic astronomy; Gauss-Bonnet theory; gravity; Lagrange equations; Lagrangian field theory; mathematical models; Scalar field theory; Scalar-Tensor
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Publications arising from this thesis are available from the Related URLs field. The publications are:

Meehan, Michael T., and Whittingham, Ian B. (2014) Asymmetric dark matter in braneworld cosmology. Journal of Cosmology and Astroparticle Physics, 2014 (6). pp. 1-18.

Meehan, Michael T., and Whittingham, Ian B. (2014) Dark matter relic density in Gauss-Bonnet braneworld cosmology. Journal of Cosmology and Astroparticle Physics, 2014 (12). pp. 1-18.

Date Deposited: 01 Dec 2015 07:18
FoR Codes: 02 PHYSICAL SCIENCES > 0201 Astronomical and Space Sciences > 020103 Cosmology and Extragalactic Astronomy @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 100%
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