Elementos Tangibles

the current value for the scale factor is taken to be one,a(t0) =1.

As mentioned before, the gravitational dynamics in the weak field can be well described by the Poisson Equation. The equation can be solved given the matter distribution of the baryonic and dark matter contributions. Commonly, the dark matter is modelled as a spherical mass distribution following what is known in the literature as the Navarro-Frenk-White or NFW profile (Navarro et al., 1997; Zhao, 1996),

ρN F W(r) = ρs € r rs Š € 1+ _rr s Š2 (1.20)

where ρ_s and r_s are the halo scale density and radius. Although the NFW density profile is written in terms of these two parameters, it is common in the literature to use different param- eters to define them, mainly the total enclosed mass atr =r₂₀₀, M₂₀₀, and the concentration parameter at this radius, c200. The radius r200 is defined to be the point where the average

density equals 200 times the critical density of the Universe and usually defines the edge of the halo. The concentration parameter is defined asc200=r200/rs.

1.3

Is

ΛCDM Entirely Successful?

Although the ΛCDM model has enjoyed a vast amount of success, there are still questions which need to be answered. Firstly, why, after many efforts, has cold dark matter not been detected? Secondly, what is the nature of dark energy? These are question which cannot be answered at this stage. Aside from these two questions, so far only the success of theΛCDM model has been outlined, but does it have weaknesses? That is the topic of this section, looking at theoretical and observational challenges which the standard model still struggles to explain. This discussion will be split into two broad sections; 1) issues with dark matter and 2) issues with the cosmological constant.

1.3.1

Issues with Cold Dark Matter

Although cold dark matter can produce the observed flat rotation curves in galaxies,ΛCDM simulations have shown discrepancies with observations. The three big issues, which seem to be persistent, are; the “too big to fail" problem, “missing satellite problem” and the “cuspy-core” problem (e.g. Walker & Peñarrubia, 2011; Dubinski & Carlberg, 1991; de Blok, 2010; Klypin et al., 1999; Moore et al., 1999; Boylan-Kolchin et al., 2012, 2011; Pawlowski et al., 2012).

Chapter 1. Introduction

These will be outlined with proposed solutions and outstanding concerns. Also outlined in this section, and perhaps the most worrying issue, is the lack of a direct detection dark matter. Finally, an issue on the larger, galaxy cluster scale will be discussed regarding the so-called “Trainwreck" cluster"

Missing Satellites

As mentioned previously, simulations of theΛCDM paradigm predict dark haloes around galax- ies, but also smaller, sub-haloes. These sub-haloes span a range of masses and sizes and should form the satellite galaxies. Satellite galaxies are observed around our galaxy, but there is a problem. The number of simulated haloes, around a Milky Way-like object, does not reflect the amount of satellite galaxies which are observed. There too many simulated haloes(e.g. Klypin et al., 1999; Moore et al., 1999). This in known as the missing satellite problem.

The missing satellites problem does not rule out cold dark matter completely however. There could be other explanations for the discrepancy. One explanation involves tidal stripping of the dwarf satellite galaxies during their evolution, thus failing to become galaxies (Brooks et al., 2013). However, it has been argued that some of the predicted sub-haloes should be too large to fail as galaxies, see Section 1.3.1.

Other attempts to counter the missing satellites problem involve switching from a cold dark matter universe to a warm dark matter universe (e.g. Polisensky & Ricotti, 2011). The greater speed, at the time of decoupling, of the warm dark matter particle reduces the number of simulated satellite galaxies compared to the cold dark matter simulations. Changing the type of dark matter changes the galaxy structure formation. This can put observational constraints on the types dark matter particle allowed. For example, it was found that the number of simulated satellite galaxies decreased with mass of the dark matter particle (Kennedy et al., 2014). So the number of satellites can constrain the dark matter candidates. Also, it was shown that if the Milky Way is smaller than_≈1.2_×1012M then warm dark matter is ruled out at 95% confidence.

Too Big to Fail

1.3. IsΛCDM Entirely Successful?

Boylan-Kolchin et al., 2012, 2011). The gravitational potential of the dark matter should be enough to bind the baryonic matter. There have been studies which claim that the introduction of baryonic processes can resolve this problem inΛCDM processes (e.g. Sawala et al., 2014), but have been contested (Pawlowski et al., 2015).

Cuspy-Core Problem

Further to the previous two issues, the distribution of dark matter also shows an inconsistency. As discussed previously, galaxy dark matter tends to be modelled with an NFW profile, which was derived from N-body simulations (Navarro et al., 1997). This profile predicts a very steep central dark matter density (1/r) profile. This is the preferred profile for ΛCDM physics as it matches well with simulations. However, observations seem to prefer a shallower, almost constant density core. This is known as the cuspy-core problem (Walker & Peñarrubia, 2011; Dubinski & Carlberg, 1991). Again, this is argued to be alleviated with the introduction of baryons and including physical processes such as supernova feedback (e.g. Governato et al., 2012).

No Detection

Despite many detection efforts, dark matter has yet to be discovered directly. Not only this, as the field of detection evolves, the parameter space where dark matter may exist is being ruled out. The question of whether dark matter will ever be detected is a worrying one. Just as, or even more worryingly, what if dark matter is detected, but it is inconsistent with current candidate predictions? The entire standard model rests on the fact that dark matter both exists and is cold enough that galaxies can form. The phrase “putting all the eggs in one basket" might apply to the standard model. Having said this, the author attended a workshop9 where the question of “what if dark matter is never detected?” was asked. The result of the poll showed that the lack of detection would not affect the majority of people’s view of the standard model. Perhaps no detection will not cause a scientific revolution.

Trainwreck Cluster

The Trainwreck cluster (cluster A520), like the Bullet cluster, is a galaxy cluster which has un- dergone an interaction. It is aptly named as the system is very complex and has been described

Chapter 1. Introduction

as ‘chaotic’. Unlike the bullet cluster, the distribution of dark matter, inferred from weak lens- ing, contradicts any prediction which can be made under that dark matter paradigm. There should exists a vast amount of dark matter where there are no galaxies (Mahdavi et al., 2007). Remember that in the discussion of the bullet cluster, the galaxies followed the dark matter through the interaction. This is a mystery which has yet to be solved.

1.3.2

Issues with the Cosmological Constant

The cosmological constant (CC) as a solution to the expansion of the universe has been remark- ably successful. It has surpassed many observational tests from Type Ia supernova data, the Baryonic acoustic oscillations and the power spectrum of the cosmic microwave background.

The main issue with the CC is the inability to understand it from a theoretical point of view. The CC, so far, is a finely tuned value which seems to agree with the data. However, when trying to understand this from a theoretical point of view, the predicted vacuum energy density is approximately 120 orders of magnitude different from that estimated from observation (see section 4 of Carroll (2001)). This is known as the cosmological constant problem and is yet to be explained.