Dark balloon

The previous post discussed of dark matter that appears to have gravity effect to hold galaxy clusters together. However, in the larger scale the universe is expanding and galaxy clusters are moving away from us. In 1998, the red shift measurement from the distant galaxies revealed that the rate of expansion is accelerating. According to the general relativity, the matter content of the universe curves all spacetime causing a global gravitational effect, which would decelerate the expansion. Thus something must counteract and win the gravitation. Currently, dark energy has been the most accepted premise to account for the accelerated expansion and is a part of the standard cosmological lamda-CDM model. Cosmologists' well-tested standard model assumes that 68% of the content of the universe is dark energy. However, the origin and composition of dark energy is one of the biggest mysteries.

The simplest explanation for the dark energy is the cosmological constant, representing a constant vacuum energy density filling space homogeneously. In 1917, Einstein extended the field equations with the cosmological constant (lamda) to counterbalance the effect of gravity and achieve a static universe. Later he abandoned it as his "biggest blunder" when Hubble observed that the universe expands. However, in the dynamic universe, the cosmological constant is valid. Moreover, the accelerating expansion requires a strictly positive constant that settled in the cosmological standard model. A cosmological constant is associated with negative pressure producing repulsive force, in contrast to matter density causing positive pressure and attractive force. You can think an inflating balloon that increases in volume while it is filled by dark energy with constant density and pressure. Basically, new space with energy is created constantly everywhere inside the balloon. While the volume increases overall density of any matter inside decreases. If there are dots painted on the balloon representing matter, their distance increases during inflating. 

The energy density represented by the cosmological constant is extremely low compared to matter (5.96 x 10^-27 kg/m³). Although it permits throughout the entire universe, within galaxies or in the close vicinity of organized matter generally, a cosmological constant has no effect. However, by the huge volume of the universe, the repulsive force becomes dominant and overcomes the gravity. The more there is empty space between two galaxies the more there is force to accelerate them to escape each other. However, the cosmological constant cannot tear the existing structures imprisoned by the gravity. On the other hand, quantum field theories predict zero-point energy for the quantum vacuum. The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift. However, the measured cosmological constant is much smaller than this by a factor of ~10¹²⁰. This extreme discrepancy is called the cosmological constant problem. From the quantum field theory point of view, the question is what renders the cosmological constant to be so small. If it had been bigger the universe enabling life we experience would not exist.

The cosmological constant is only one explanation for the dark energy. In quintessence models of dark energy, the observed acceleration is caused by the potential energy of a dynamical field, referred to as quintessence field. Quintessence differs from the cosmological constant in that it can vary in space and time. It is a scalar field with an equation of state (w) that is the pressure divided by density, given by potential energy. In the case of the cosmological constant, the pressure is exactly the negative of the energy density resulting in w=-1. Many quintessence models have a tracker behavior that partially solves the cosmological constant problem and sets the low energy scale for dark energy. The energy density of the field tracked the radiation density of the universe until the matter-radiation equality, which triggered its nature of dark energy when the universe was 50 000 years old. This enabled time for creation of matter structures before the dark energy finally won the gravity pull approximately after seven billion years. After finding dark energy much research was done to measure the state parameter w, which appeared to be close to -1. In 2002, the physicist Robert Caldwell calculated that if w is less than -1 even infinitesimally, the energy density will increase as universe expands, which will lead to over exponential expansion that eventually tears the entire universe in its smallest scale apart in finite time (Big Rip scenario). He labeled this special type of quintessence as "phantom dark energy". In some models the state variable has evolved below the critical value -1 already in the past but we have not received any information of it yet. 

In 1980 Alan Guth et.al. proposed that a field with negative pressure drove cosmic inflation, which lead to enormous exponential expansion of the universe during the fraction of the first second. Although it's unclear if there is any relation, dark energy appears similarly but at much lower energy scale. In widely accepted models the cosmic inflation was driven by a scalar field like it's the case with quintessence. This field had much higher energy density than is dark energy. It is possible that the field experienced a phase transition while it found a lower energy state by the end of the cosmic inflation and a false vacuum became the current true vacuum. Higgs field is the only scalar field proven to exist and it is possible to be in charge of all expansion periods of the universe. The Standard Model Higgs non-minimally coupled to gravity could be responsible for the symmetry properties of the universe at large scales and for the generation of the primordial spectrum of curvature perturbations seeding structure formation.

Distances of galaxies are measured from certain type supernovae that have well predicted properties and thus they are called as standard candles. Nowadays, the expansion rate of the universe, the Hubble constant, has been calculated with quite good precision to be 74 km/s/megaparsec. However, the measurements of the cosmic microwave background (CMB) seem to convergence to a different value 67 km/s/megaparsec that is clearly beyond the error margin of the supernovae measurements. Of course there is a chance of systematic errors that explains this discrepancy but it is possible that the acceleration rate has just increased from the early times when CMB became visible. If that is the case the expansion could be driven by quintessence rather than the cosmological constant. Moreover, if the density of dark energy increases it can easily lead to the Big Rip scenario. Whatever is the truth, the discrepancy of the expansion rates has lead to crisis in cosmology and furthermore challenges the cosmological constant.

Only thing we actually know about the dark energy is that it is expanding the universe or, more precisely, it has negative pressure. If the pressure of some weird substance can be negative, it would cancel out the impact of its mass on the curvature of the spacetime resulting in repulsive net gravitational effect. Thus there is no need for substance with negative mass, even though that is theorized in some models. A positive cosmological constant, gives empty spacetime positive constant curvature, ie de Sitter geometry. However, in the spatial dimensions the universe has been measured to be flat without curvature with quite good precision. Taking the time dimension into account the universe might have intrinsic positive curvature that explains the accelerated expansion without any mystic ever increasing substance. Instead, we need to understand spacetime itself better. The curvature may have changed over the time of the universe and may be coupled to global quintessence field potential. Moreover, it can also vary between the patches of the universe. The cosmological constant is the simplest modification to the general relativity, whereas other proposed modifications would have more implications on the universe, how its structures have evolved and light gets lensed in vacuum. On the other hand, some theories relying purely on the general relativity omit dark energy proposing that the universe's acceleration could be driven by variations, or inhomogeneities, in its density. Starting this year Euclid starship is producing scientific data hopefully helping us to find the right direction in research.