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Warm Dark Matter Cosmology in the Nonlinear Domain: Warm Dark Matter Katarina Markoviˇc M¨unchen 2012 Cosmology in the Nonlinear Domain: Warm Dark Matter Katarina Markoviˇc Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Katarina Markoviˇc aus Ljubljana, Slowenien M¨unchen, den 17.12.2012 Erstgutachter: Prof. Dr. Jochen Weller Zweitgutachter: Prof. Dr. Andreas Burkert Tag der m¨undlichen Pr¨ufung:01.02.2013 Abstract The introduction of a so-called dark sector in cosmology resolved many inconsistencies be- tween cosmological theory and observation, but it also triggered many new questions. Dark Matter (DM) explained gravitational effects beyond what is accounted for by observed lumi- nous matter and Dark Energy (DE) accounted for the observed accelerated expansion of the universe. The most sought after discoveries in the field would give insight into the nature of these dark components. Dark Matter is considered to be the better established of the two, but the understanding of its nature may still lay far in the future. This thesis is concerned with explaining and eliminating the discrepancies between the current theoretical model, the standard model of cosmology, containing the cosmological constant (Λ) as the driver of accelerated expansion and Cold Dark Matter (CDM) as main source of gravitational effects, and available observational evidence pertaining to the dark sector. In particular, we focus on the small, galaxy-sized scales and below, where N-body simulations of cosmological structure in the ΛCDM universe predict much more structure and therefore much more power in the matter power spectrum than what is found by a range of different observations. This discrepancy in small scale power manifests itself for example through the well known \dwarf-galaxy problem" (e.g. Klypin et al., 1999), the density profiles and concentrations of individual haloes (Donato et al., 2009) as well as the properties of voids (Tikhonov et al., 2009). A physical process that would suppress the fluctuations in the dark matter density field might be able to account for these discrepancies. Free-streaming dark matter particles dampen the overdensities on small scales of the initial linear matter density field. This corresponds to a suppression of power in the linear matter power spectrum and can be modeled relatively straightforwardly for an early decoupled thermal relic dark matter particle. Such a particle would be neutrino-like, but heavier; an example being the gravitino in the scenario, where it is the Lightest Supersymmetric Particle and it decouples much before neutrinos, but while still relativistic. Such a particle is not classified as Hot Dark Matter, like neutrinos, because it only affects small scales as opposed to causing a suppression at all scales. However, its free-streaming prevents the smallest structures from gravitationally collapsing and does therefore not correspond to Cold Dark Matter. The effect of this Warm Dark Matter (WDM) may be observable in the statistical properties of cosmological Large Scale Structure. The suppression of the linear matter density field at high redshifts in the WDM scenario can be calculated by solving the Boltzmann equations. A fit to the resulting linear matter power spectrum, which describes the statistical properties of this density field in the simple thermal relic scenario is provided by Viel et al.(2004). This linear matter power spectrum must then be corrected for late-time non-linear collapse. This is rather difficult already in the standard cosmological scenario, because exact solutions the the evolution of the perturbed density field in the nonlinear regime cannot be found. The widely used approaches are to the i Abstract halofit method of Smith et al.(2003), which is essentially a physically motivated fit to the results of numerical simulations or using the even more physical, but slightly less accurate halo model. However, both of these non-linear methods were developed assuming only CDM and are therefore not necessarily appropriate for the WDM case. In this thesis, we modify the halo model (see also Smith & Markoviˇc, 2011) in order to better accommodate the effects of the smoothed WDM density field. Firstly, we treat the dark matter density field as made up of two components: a smooth, linear component and a non-linear component, both with power at all scales. Secondly, we introduce a cut-off mass scale, below which no haloes are found. Thirdly, we suppress the mass function also above the cut-off scale and finally, we suppress the centres of halo density profiles by convolving them with a Gaussian function, whose width depends on the WDM relic thermal velocity. The latter effect is shown to not be significant in the WDM scenario for the calculation of the non-linear matter power spectrum at the scales relevant to the present and near future capabilities of astronomical surveys in particular the Euclid weak lensing survey. In order to determine the validity of the different non-linear WDM models, we run cosmo- logical simulations with WDM (see also Viel et al., 2012) using the cutting edge Lagrangian code Gadget-2 (Springel, 2005). We provide a fitting function that can be easily applied to approximate the non-linear WDM power spectrum at redshifts z = 0:5 − 3:0 at a range of scales relevant to the weak lensing power spectrum. We examine the simple thermal relic scenario for different WDM masses and check our results against resolution issues by varying the size and number of simulation particles. We finally briefly discuss the possibility that the effects of WDM on the matter power spec- trum might resemble the analogous, but weaker and larger scale effects of the free-streaming of massive neutrinos. We consider this with the goal of re-examining the Sloan Digital Sky Survey data (as in Thomas et al., 2010). We find that the effects of the neutrinos might just differ enough from the effects of WDM to prevent the degeneracy of the relevant parameters, namely the sum of neutrino masses and the mass of the WDM particle. ii Zusammenfassung Mit der Einf¨uhrung eines so genannten \dunklen Sektors" in der Kosmologie konnten zwar Ungereimtheiten zwischen kosmologischer Theorie und Beobachtungen gel¨ostwerden - er wirft allerdings auch viele neue Fragen auf. Dunkle Materie (DM), erkl¨artgravitative Ef- fekte, die nicht durch die beobachtete leuchtende Materie verursacht werden k¨onnen. Dun- kle Energie (DE) erkl¨artdie beobachtete beschleunigte Expansion des Universums. Zu den begehrenswertesten Entdeckungen des gesamten Feldes geh¨orenjene, die unser Verst¨andnis bez¨uglich der Dunklen Materie und Dunklen Energie erweitern. Obwohl die Dunkle Materie die etabliertere der beiden Theorien ist, steckt unser Verst¨andnis auch ihrbez¨uglich noch in den Kinderschuhen. Diese Doktorarbeit befasst sich mit der Erkl¨arungund Beseitigung von Unstimmigkeiten zwischen dem g¨angigentheoretischem Modell, dem ΛCDM-Modell - welches die kosmologische Konstante (Λ) als Ursache f¨urdie beschleunigte Ausbreitung des Universums und kalte dun- kle Materie (CDM) als die Quelle f¨urGravitationseffekte beinhaltet - und den verf¨ugbaren Beobachtungsdaten ergeben. Dabei wird der Schwerpunkt auf kleine Maßst¨abe - Galax- iengr¨oßeund kleiner - gelegt, wo N-Teilchensimulationen der kosmologischen Strukturbildung im ΛCDM-Modell viel mehr Struktur und folglich viel mehr Leistung im Materieleistungsspek- trum voraussagten, als viele andere Beobachtungen. Diese Unstimmigkeiten im Leistungspek- trum auf kleinen Maßst¨aben ¨außernsich zum Beispiel im so genannten Zwerggalaxienproblem (z.B. Klypin et al., 1999), in der Konzentration und den Dichteprofilen individueller Halos (Donato et al., 2009) und auch in den Eigenschaften so genannter Voids, großer Leerr¨aumeim Universum. (Tikhonov et al., 2009). Diese Ungereimtheiten k¨onnten durch einen physikalis- chen Prozess erkl¨artwerden, welcher die Schwankungen des DM-Dichtefeldes zu unterdr¨ucken vermag. Frei str¨ohmendedunkle Materieteilchen d¨ampfen auf kleinen Abst¨andendas urspr¨ungliche lineare Materiedichtefeld. Dies deckt sich mit einer Unterdr¨uckung der der Leistung im Leis- tungsspektrum und erlaubt eine relativ einfache Erstellung von Modellen von fr¨uhabgekoppel- ten thermischen Reliktteilchen. Solche Teilchen w¨arenneutrino¨ahnlich, allerdings schwerer. Ein Beispiel w¨aredas Gravitino in einem Szenarium wo es das leichteste supersymmetrische Teilchen ist und sich viel fr¨uherabkoppelte als Neutrinos, aber noch w¨ahrendes sich in einem relativistischen Zustand befand. Diese Teilchen k¨onnennicht wie Neutrinos als heiße dunkle Materie klassifiziert werden, da sie nur auf kleinen und nicht auf allen Abst¨andeneinen Ein- fluss auf das Leistungsspektrum haben. Allerdings bewahrt das freie Str¨omendieser Teilchen die kleinsten Strukturen vom Gravitationskollaps, womit sie auch nicht in die Kategorie der kalten dunklen Materie fallen k¨onnen.Der Einfluss dieser warmen dunklen Materie kann in den statistischen Eigenschaften von kosmologischen Strukturen beobachtet werden. Die Unterdr¨uckung des linearen Materiedichtefeldes bei hohen Rotverschiebungen im WDM- Szenarium kann durch L¨osender Boltzmann-Gleichungen berechnet werden. Ein Fit an das iii Zusammenfassug resultierende lineare Materieleistungsspektrum, welches die statistischen Eigenschaften dieses Materiedichtefeldes im einfachen thermischen Reliktszenarium beschreibt, wird von Viel et al. (2004) bereitgestellt. Dieses lineare Materieleistungsspektrum muss als n¨achstes korrigiert werden um die nichtlineare Strukturbildung
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