Where did we come from? How did the Universe develop? These questions have been intriguing astronomers and physicists for years and years. Even though scientists still do not have a clear answer, at least we have gained a better understanding of our place in the Universe. 

From the beginning of the twentieth century, when scientists were observing the universe, they found a problem. When Fritz Zwicky(1937) was looking at the coma cluster and studying the Hubble observation, he found that by using the method of measuring the luminosity to the mass of the cluster and calculating the velocity of galaxies via Doppler shifts, the calculation did not match up with the actual data he observed. The error bar was out of the range of the systematic error bar. Moreover, Zwicky suggested that the large velocity of galaxies he observed in the Coma cluster of galaxies required the existence of dark matter since the total cluster mass determined from the observed velocities exceeded the total baryonic mass of the individual galaxy members. Additionally, if there were not any invisible matter present to hold the galaxy cluster together, the gravitational effect from the galaxies would cause the galaxies to scatter apart. Thus, Zwicky proposed that there must be an invisible matter - a dark matter that presents and dominate the galaxy cluster. 

However, scientists were not quite convinced until in the 1970s. When scientists measure the luminous mass velocity of an object in a galaxy, if the mass is all luminous and concentrated in the central region, then the velocity of the region outside should be inversely proportional to the square root of the radius (which the velocity should decrease from the center). However, when scientists actually measured the galaxies, the results they got were quite different from what they calculated: the rotation curve of the galaxy remains flat from the center, meaning the luminous mass velocity stays constant instead of decreasing. Vera Rubin and Kent Fund (1980) first measured the rotation curves of the M31( Andromeda) galaxy. In her experiment, Rubin used radio telescopes to measure the neutral hydrogen gas disk’s orbiting galaxy M31, which is similar to the high HI rotation curve by van de Hulst. This measurement indicated that the rotation speed of galaxies remains constant rather than declining. To find out what caused this flatness in velocity, Vera Rubin (1970) performed another experiment. In their paper, it presents that for certain optical galaxies, there must contain non-luminous matter surrounding the galaxies. Nowadays, with the aid of more advanced instruments and Rubin’s discoveries, scientists have measured the presence of dark halo from galaxies.  

Nevertheless, the debate of dark matter did not end here. Rubin’s discovery caught the attention of other scientists. In fact, the measurement of the flat rotation curves of galaxies let many scientists realize that the understanding of dark matter would be not only crucial to the structure of galaxies, but also to the entire universe. Faber and Gallagher  in their paper Masses and Mass-To-Light Ratios of Galaxies stated that “It is likely that the discovery of invisible matter will endure as one of the major conclusions of modern astronomy.” In the 1980s, most astronomers were convinced that there was dark matter present in the galaxies and clusters, even though there was still ambiguity about dark matter, scientists started to classify and unveil the mysterious dark matter. In the 1980s, scientists tried to classify dark matter to be “hot”, meaning the size of the particles which make up the dark matter with respect to a protogalaxy(from the early universe and can form dwarf galaxies) rather than the temperature of the particles. In this case, the Hot Dark Matter (HDM) particle would be very light particles with high FSLs (free streaming length - how far the particles can travel before the expansion from the cosmic expansion slow them down); thus, neutrinos were considered to have a great possibility to be the candidate for HDM. However, scientists quickly ruled out neutrinos or HDM to be the classification for dark matter. In a paper by White, S. D. M., Frenk, C. S., & Davis, M. they indicated that the discrepancy between the large coherence length of the neutrino dominated universe and small scale of observed galaxy clustering makes it unlikely that neutrino provided the missing mass (White et al.). Because the neutrinos have extremely high velocities, which smooth out the density fluctuations in the universe, meaning that the neutrinos can stream through any area with uneven density in the universe, and the density fluctuation would only appear after neutrinos slow down, this means that neutrinos cannot form galaxies from this very smooth state; therefore HDM was ruled out completely. After ruling out HDM, scientists found a new flavor of dark matter: Cold Dark Matter (CDM). In 1982, James Peebles proposed the CDM theory in his paper. In his paper, he assumed that the universe is dominated by very massive, weakly interacting particles, meaning that they are heavy and have relatively slow speed with respect to light, with these properties, they have the ability to cause fluctuations in density(Peebles, P. J. E.). From Blumenthal, Faber, Primack, & Rees, they made simulations where they had the mass of cold dark matter 10 times more than the baryonic matter, and it fitted the observable universe quite well; it was very consistent with superclusters, voids, and larger-scale clustering. Also, in their research, they could correctly use CDM to predict the masses of the galaxies(Blumenthal et al.).  From their research, it seems that CDM is probably the answer that scientists were looking for. Given the reason that CDM is closely linked to the early universe that scientists are trying to understand, with more and more discoveries, scientists furthermore confirmed the idea of CDM from the perspective of Cosmic Microwave Background(CMB). As aforementioned, the density from the CMB can cause density fluctuations, thus, only with particles with relatively larger mass and velocity can cause the perturbations, which can cause small ripples in the CMB to form the galaxies and other objects we see today. 

With the majority of scientists accepting CDM, many theories used CDM to describe and understand the universe. In the 1980s, scientists were trying to focus on CDM with critical density. However, to make this model work, the Hubble constant would be required to be lower than observed, and the model would predict way too many galaxies and clusters than observed. On the other hand, in many models, Lambda Cold Dark Matter (ΛCDM), is the most accepted by many scientists. The letter Λ represents the cosmological constant, the energy density of space, which is used to explain the accelerating expansion of the universe because it has negative pressure which contributes to the stress-density tensor. The CDM, aforementioned, is responsible for the gravitational effect observed in very large-scale structures. ΛCDM is the mathematical parameterization of Big Bang cosmology, as described by General Relativity and the Friedman-Lemaître-Roberson-Walker (FLRW) equations. ΛCDM assumes that the universe is composed of photons, neutrinos, ordinary matter (baryons, electrons) and cold (non-relativistic) dark matter, which only interacts gravitationally, plus "dark energy", which is responsible for the observed acceleration in the Hubble expansion. Dark energy is assumed to take the form of a constant vacuum energy density, referred to as the cosmological constant (Λ). Standard (6 parameters) ΛCDM further imposes the constraint that space is flat (Euclidean). (NASA LAMBDA Archive Team). 

ΛCDM can explain and describe our universe very well, such as the existence and structure of the cosmic microwave background, the large-scale structure in the distribution of galaxies, the abundances of hydrogen (including deuterium), helium, and lithium, and the accelerating expansion of the universe observed in the light from distant galaxies and supernovae. With this easy yet powerful model, scientists have successfully predicted many observations. With the help of ΛCDM, scientists discovered the polarization of the CMB. In 2002, Kovac et.al. reported the usage of Degree Angular Scale Interferometer (DASI) and the detection of the anisotropy polarization of the CMB. In their report, they also did a likelihood ratio test which is used to demonstrate the agreement of the observed CMB temperature and polarization anisotropy signals with a concordance ΛCDM model, and strongly rejects models without CMB polarization (Kovac et al. Detection of polarization in the cosmic microwave background using DASI). In 2013, from the Planck observations, Ade, P. A. R., et al found that the temperature and polarization power spectra matched their observations with the six parameters of the ΛCDM. Because of the spatial curvature of our universe, they added a tensor component which is the extension of the ΛCDM to find an upper limit on the tensor-to-scalar ratio that consistent with the Planck 2013 results and Planck (BKP) data. In addition, when they combined Planck data with other astrophysical data, including Type Ia supernovae (type of supernovae with no hydrogen emission line in their spectra that is the explosion of carbon-oxygen white dwarf in a binary system, which go over the Chandrasekhar limit) and the equation for dark energy, they found that the standard Big Bang nucleosynthesis predictions for the helium and deuterium abundances for the ΛCDM cosmology matched the observations extremely well, and their data were consistent with the Standard Model of particle physics and WMAP polarization measurements. Also, the Planck results for ΛCDM agreed with Baryon Acoustic Oscillation (density fluctuation of baryonic matter in the early universe that caused by acoustic sound waves in the prodromal plasma) data and the sample of Type Ia supernovae(Ade et al.). 

Based on these accurate scientific research and observations, ΛCDM seems to be the perfect match and solution for our understanding of the universe and its history. However, this model still faces many challenges. From the Planck observation,  Ade, P. A. R., et al, in their research, they used the 2013 analysis, and they found at the amplitude of the fluctuation spectrum did not quite match with some rich cluster counts and gravitational lensing. In this case, they think that these problems cannot be solved just by modifying ΛCDM. However, this is not the only scenario that ΛCDM cannot match some details of this big puzzle of understatement of the universe. From some observation of the sub-galaxies scale, the prediction from ΛCDM shows way too many dwarf galaxies than there really are, which is called “the small-scale crisis” by many scientists. Also, there are many theories that hold alternative views with ΛCDM, like the modified Newtonian gravity, decaying dark matter, and other theories. 

Even though there are many disagreements towards ΛCDM, none of them are convincing enough to overthrow ΛCDM. Still, ΛCDM is not perfect, it needs more evidence from scientists; although it has already given scientists insights about the universe and its history. Scientists are now investing in more programs, experiments, and satellites to help to provide evidence for ΛCDM. From the Large Hadron Collider (LHC), scientists are trying to create dark matter particles, even though dark matter particles are very light; however, if they are leaving the LHC, scientists would notice their momentum they bring out with themselves. Also, from NASA’s Fermi Gamma-ray Space Telescope, there is indirect evidence that indicates the signal of DM, and it can unveil more about both the Milky Way and Andromeda galaxies. However, we still have too many questions and unknowns about dark matter, galaxies, and the universe. ΛCDM, as a really useful tool, can give us some really inspiring insights, but there are still lots in the universe for us to explore. 

Work Cited 

[1] Zwicky, F. “On the Masses of Nebulae and of Clusters of Nebulae.” The Astrophysical Journal, vol. 86, 1937, p. 217., doi:10.1086/143864.

[2] Rubin, Vera C., and W. Kent Jr. Ford. “Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions.” The Astrophysical Journal, vol. 159, 1970, p. 379., doi:10.1086/150317.

[3] Rubin, V. C., et al., “Rotational Properties of 21 SC Galaxies with a Large Range of Luminosities and Radii, from NGC 4605 /R = 4kpc/ to UGC 2885 /R = 122 Kpc/.” The Astrophysical Journal, vol. 238, 1980, p. 471., doi:10.1086/158003.

[4]Faber, S. M., and J. S. Gallagher. “Masses and Mass-To-Light Ratios of Galaxies.” Annual Review of Astronomy and Astrophysics, vol. 17, no. 1, 1979, pp. 135–187., doi:10.1146/annurev.aa.17.090179.001031.

[5] White, S. D. M., et al., “Clustering in a Neutrino-Dominated Universe.” The Astrophysical Journal, vol. 274, 1983, doi:10.1086/184139.

[6] Peebles, P. J. E. “Large-Scale Background Temperature and Mass Fluctuations Due to Scale-Invariant Primeval Perturbations.” The Astrophysical Journal, vol. 263, 1982, doi:10.1086/183911.

[7] Blumenthal, G., Faber, S., Primack, J. et al. Formation of galaxies and large-scale structure with cold dark matter. Nature 311, 517–525 (1984) doi:10.1038/311517a0

[8] NASA LAMBDA Archive Team. “LAMBDA - Introduction.” NASA, NASA, 2016, lambda.gsfc.nasa.gov/education/graphic_history/.

[9] Kovac, J. M., et al, “Detection of Polarization in the Cosmic Microwave Background Using DASI.” Nature, vol. 420, no. 6917, 2002, pp. 772–787., doi:10.1038/nature01269.

[10] Ade, P. A. R., et al. “Planck2015 Results.” Astronomy & Astrophysics, vol. 594, 2016, doi:10.1051/0004-6361/201525830.