The Physics OF The Early Universe

Introduction

Cosmology is a field that has worried humanity for millenia, trying to find answers to the questions about the origin, evolution and fate of the universe. Although in the beginning this could only be theorical, the development of new technologies has given us a way to probe these theories experimentally. This article is a review about how distant supernovae are used as standard candles, enabling us to measure the history of cosmic expansion. Given the current theories, the universe was known to be expanding, but this expansion was expected to be slowing down due to gravity. However, by using these new data provided by type Ia supernovae a surprising result was obtained, the expansion is accelerating. This unexpected outcome means that something is missing in our fundamental knowledge of physics and, therefore, further investigation is needed.

Standard candles

The main goal of cosmology is determining the expansion history of the universe. In order to do this, standard candles can be used. A standard candle is a class of astrophyisical objects that have a known absolute magnitude. Due to the expansion of the universe, the wavelength of the light travelling from these sources is stretched and, when it reaches the Earth, it has been redshifted by the same factor by which the cosmos has expanded in that time interval: z ≡ ∆λ/λ. The distance to these standard candles can be calculated from the apparent magnitude comparing to a standard of the class. If several different objects are identified over a wide distance range, their relationships between distance (or magnitude) and redshift can be used to determine the expansion history of the universe.

Throughout astronomy history, different standard candles have been used for different purposes. When he dis- covered the expansion of the universe, Edwin Hubble used galaxies but, as they are not easy to compare against a standard and they can change a lot with time, a better standard candle was needed for cosmology research. In 1938 Baade and Zwicky proposed supernovae for this purpose, since they have a uniform peak brightness and they can be seen from very large distances due to a high intrinsic brightness.

Supernovae

Supernovae were initially divided into two groups: type I, presenting no hydrogen features in their spectra, and type II, with hydrogen. However, they were still a quite heterogeneous group, and this made it difficult to work with them and match them against a standard. This was solved some years later with a new subclassification. In addition to the already existing classification, type I supernovae could be classified as type Ia, if they presented a silicon feature, or type Ib, with no silicon.

The study of type Ia supernovae showed a promising uniformity in their spectra, that became even clearer when examining the spectra in detail as they evolved in time. This uniformity meant that all type Ia supernovae have the same physical origin: a white dwarf in a binary system with a large star. This star keeps losing material that falls onto the white dwarf until it eventually reaches the Chandrasekhar limit and explodes. The second consequence of the uniformity is that a standard spectra and light curve templates can be used to compare the different observations.

Further studies with these templates allowed researchers to identify outliers, supernovae with peak brightness different from the norm and with a spectrum that did not match the template. Their light curves were also different from expected, but a tendency was found, when they faded faster, supernovae showed a lower peak brightness, while slower supernovae were brighter at the peak. This result could be used to recalibrate the few outliers found, and this, together with the uniformity observed from the beginning, made type Ia supernovae excellent standard candles to measure the expansion history of the universe. Figure 1 shows these light curves before and after the recalibration.

Cosmological distances

Given the advantages of using type Ia supernovae as standard candles, their possible uses were many. These included measuring the Hubble constant, H0, with a few 100 million years old supernovae, and, with farther supernovae, measure the expansion of the universion billions of years ago, showing the expected deceleration rate due to gravity. However, although they were bright enough to be seen from large distances, there were still some issues to solve before using type Ia supernovae for cosmological purposes.

Due to its specific physical origin, type Ia supernova explosions are rare and random. Moreover, they have to be discovered promptly in order to observe their peak brightness. For these reasons, prescheduling time at telescopes was not an easy task, as this usually requires requesting time in advance and guaranteeing the observation. Apart from this, some other aspects have to be taken into account when observing supernovae, such as the K-correction, to compare objects with different redshifts, or the possibility of dust dimming the light of the supernova. These problems were solved by researchers by using methods that included taking images of sky showing more than 10000 galaxies at different points in time, so that they could assure the observation of a few supernovae when applying for telescope time. All these led to the development and progress of the field of supernovae, with the creation of two groups devoted to their study, Supernova Cosmology Project (SCP, one of whose members is the author of the paper) and High-z Supernova Search. Both groups worked hard competing and collaborating in the search of new type Ia supernovae until finding enough to draw conclusions about the history of the universe. The result, confirmed by both groups and shown in Figure 2, was a problem for the physics of the moment since, according to the data of the supernovae, the universe not only is not decelerating its expansion, but it is accelerating.

Analysis of results

By the time this was discovered, the simplest cosmological models included only a dominant mass energity density driving the expansion history. However, the results shown in Figure 2 imply that these models are too simple, given that even in an empty universe (ρm ∼ 0) the high-z supernovae observed should be brighter. The only solution to fit the data well was introducing a cosmological constant, Λ, in these models, so that the best fit to the data is:

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ΩΛ ≡ ρΛ/ρc ' 0.7

Ωm ≡ ρm/ρc ' 0.3

Despite this, there were still some issues that made researchers reluctant to the cosmological constant. First, this was not in perfect agreement with the standard model of particle physics, which would predict a vacuum energy times greater than the required by astrophysical data, and even with symmetries cancelling this value, there should be a remainer of precisely one part in 10120. The second coincidence is that, while ρm decreases with the expansion of the universe, ρΛ stays constant, but at present the relationship between them is ρΛ ∼ 2ρm. This suggests that something is missing in the standard model, and raises the need for new models.

Checking the results

In the theoretical aspect, the results implied the development of a new model. However, in the experimental aspect, the results could mean something wrong or unknown in the observations that should be checked. First of all, the high level of agreement between both teams gave confidence in the results, but there still remained important systematic uncertainties. By performing color measurements it was shown that the faintness of the supernovae could not be caused by dust, and spectral comparisons rejected the hypothesis of supernovae being intrinsically fainter in the past.

These results could be confirmed by observing even farther supernovae, from when the mass energy density dominated and the expansion was decelerating These results may be compared with other independent observations, such as the cosmic microwave background (CMB), which confirmed the flatness of the universe, and studies of galaxy clusters to estimate ρm. Figure 3 shows the agreement between the three different types of measurements in the already mentioned region ΩΛ = 0.3 and Ωm = 0.3.

Dark energy models

Since the acceleration of the universe’s expansion is driven by an unknown energy, this has been called dark energy, and different models have been proposed to describe it. These are all characterized by the parameter w = P/ρ, called the equation-of-state parameter. The equation that describes the expansion of the universe is the following (Friedmann acceleration equation), where R is the scale factor from where it can be seen that the expansion is accelerated if w < −1/3. This parameter presents different values for the different components of the universe:

• Nonrelativistic matter: w = 0
• Relativistic matter and radiation: w = 1/3
• Dark energy: w = −1

For each component, its energy density decreases as R−3(1+w) with the expansion, meaning that radiation will fall faster than the other components and, in the current universe, nonrelativistic matter and dark energy dominate.

Knowing that the relationship between these two at present is ρΛ ∼ 2ρm, the only constraint on w is w < −1/2. These results are the only ones that can be obtained with the current data, so in order to distinguish between different dark energy models more measurements of type Ia supernovae are needed, and these have to be more accurate and more distant in time.

Conclusion

This paper shows what could be done with a first series of supernovae measurements. The existing cosmological models were proven to be too simple, with the major component of the universe being almost completely unknown at the moment. New theoretical models in agreement with the observations need to be developed, and new observations need to be made in order to test them. The next generation of supernovae projects, including more telescopes and prescheduled time, must reduce to the minimum the systematic uncertainties, and will try to make clear some aspects of the nature of dark energy, such as its variation with time (if it is not constant). The results shown are as surprising as promising, since they mean that so much more research is needed in the field of cosmology. This, together with the rise of new cosmological observational techniques, makes cosmology a rising field, that will draw the attention of the scientific community during the next years in the hope of answering the fundamental questions of the origin, evolution and fate of the universe.