Do We Really Need A Cosmological Constant?Essay Preview: Do We Really Need A Cosmological Constant?Report this essayIn 1916, Albert Einstein made up his General Theory of Relativity without thinking of a cosmological constant. The view of that time was that the Universe had to be static. Yet, when he tried to model such an universe, he realized he cannot do it unless either he considers a negative pressure of matter (which is a totally unreasonable hypothesis) or he introduces a term (which he called cosmological constant), acting like a repulsive gravitational force.
Some years later however, the Russian physicist Friedmann described a model of an expanding universe in which there was no need for a cosmological constant. The theory was immediately confirmed by Hubbles discovery of galaxies red shift. Following from that, Hubble established the law that bears his name, according to which every two galaxies are receding from each other with a speed proportional to the distance between them. That is, mathematically:
V=H Dwhere H was named Hubbles constant.From this point on, the idea of a cosmological constant was for a time forgotten, and Einstein himself called its introduction “his greatest blunder”, mostly because it was later demonstrated that a static Universe would be in an unstable equilibrium and would tend to be anisotropic. In most cosmological models that followed, the expansion showed in the Hubbles law simply reflected the energy remained from the Big Bang, the initial explosion that is supposed to have generated the Universe.
It wasnt until relatively recently – 1960s or so, when more accurate astronomical and cosmological measurements could be made – that the constant began to reappear in theories, as a need to compensate the inconsistencies between the mathematical considerations and the experimental observations. I will discuss these discrepancies later. For now, Ill just say that this strange parameter, lambda- as Einstein called it, became again an important factor of the equations trying to describe our universe, a repulsive force to account not against a negative matter pressure, but for too small an expansion rate, as measured from Hubbles law or cosmic microwave background radiation experiments. I will show, in the next section, how all these cosmological parameters are linked together, and that it is sufficient to accurately determine only one of them for the others to be assigned a precise value. Unfortunately, there are many controversies on the values of such constants as the Hubble constant – H, the age of the Universe t, its density , its curvature radius R, and our friend lambda.
Although I entitled my paper with a question, I will probably not be able to answer it properly, since many physicists and astronomers are still debating the matter. I will try, however, to point out what are the certainties – relatively few in number – and the uncertainties – far more, for sure – that exist at this time in theories describing the large scale evolution of the Universe. I will emphasize, of course, the arguments for and against the use of a cosmological constant in such models, and I would like to make sure that my assistance gets a general view on the subject, in the way that I could understand it.
A Few Mathematical Considerations, or What Einstein DidSince this is not a general relativity paper, I will present how Albert Einstein arrived to the conclusion that a cosmological constant is necessary for describing a static Universe in the simplest way possible. Imagine a sphere of radius R which has a mass M included inside its boundaries. Let m be a mass situated just on the boundary. We can then write:
, and , hence:where a is the acceleration of mass m, G is the gravitational constant, and p is the pressure of the radiation, which contributes, along with matter density, to the overall density of the Universe.
(Think now at the sphere as our Universe, and at mass m as the farthest galaxy).At a glance, the Universe cannot be static unless a is zero, so p= – 3 rho c2, which is a negative value. This is an unreasonable hypothesis, so Einstein introduced a repulsive force characterized by the cosmological constant to adjust this inconvenience and to straighten his model. I will not reproduce the calculations here, but just imagine that, instead of writing the energy conservation equation in the form:
E/m = V2/2 – GM/R, you introduce the term (- R2 ) in the right side. (1)How Einstein has calculated it, the cosmological constant has the ultimate expression (in his static model):The curvature radius of the universe can be further determined from that, as:As I stated in the introduction, all the fundamental parameters characterizing the Universe are linked by equations. Ignoring the constants and the computation details, I will give the to-date accepted relations. Thus, the age of the universe is connected to the Hubble constant through:
t ~ 1/2H, in a radiation dominated universe, andt ~ 2/3H, in a matter dominated universe.The connection between H and the density of the universe (in Einstein – De Sitter model, but other models do not state anything significantly different) is:
It is a matter of philosophy to ask which of these parameters is crucial in understanding the others. They are all intimately linked. From this point on, we have to rely on what one can actually measure. The density and the age can only be estimated, unless indirectly determined. The cosmological constant is not even a certitude. Thus, the one that we eventually have to deal with is the Hubble constant, which can be calculated observing the red shift of the far galaxies. But there are plenty of controversies on its value also, ranging between 50 and 100 km/s/Mpc. One of the accepted values is 65 + 5 km/s/Mpc. This is also uncertain, since scientists do not agree on the methods of measuring it, and in some theories it is not consistent with the age of the Universe as determined from the cosmic microwave background radiation or globular clusters experiments (see the New Situations section).
The Hubble constant is thus not only an indicator of the age of the Universe, it is an absolute measurement. We can easily extrapolate the Hubble constant for various parts of the body in the Universe, depending on the properties of the universe itself. For example, one can also extrapolate the age of the galaxies, given the gravitational constant. For the latter, we will use the Hubble constant between 1 and 1000 mpc as a point of reference: as a function of time, an object’s age gets multiplied by a given radius as the radius of its main body. For most planets and stars, the Hubble constant at a given distance, which is the width of the Sun, is known as the Hubble constant, so we can be confident that the galaxy’s age can be determined using the Hubble constant. However, the Hubble constant is not always true, because some of the planets that have been discovered so far, which would be expected to reach a given distance, are not only less powerful but also in the vicinity of the Sun, making the telescope much more sensitive to the radiation of the stars. Nevertheless, a recent study discovered that the Hubble constant can still be used to estimate the age of the Universe. The new study found that with respect to the galaxy, the Hubble constants, of the surrounding galaxies are constant. This suggests that the galaxy at the lower limit of the galaxy expansion is in fact a galaxy of constant mass. But even in the Galaxy without a Sun (known as the Triassic Galaxy) no such constant exists, so all the visible galaxies reach the limits of the gravitational constant in other galaxies that orbit it. This implies that there is a substantial limit to how far the universe can expand.
We will now turn to the third parameter of cosmology: the gravitational constant of the Universe. The three parameters that astronomers use to determine the gravity of these systems are: the density, the diameter of the black hole, and how far across the Universe the black hole is in its mass. Let’s assume that the distance from the centre of the Universe to such a background background is 1 m/sec, or 10 million light years. If we give the gravitational constant of a black hole 4,000 times what it is in the center, this gravitational constant is also roughly 1,000 times the Hubble constant. But if all of this is true then we get a mass of 3.5 kg/m2, or 14 solar masses. If this mass is 1.8 cm/ton, then we end up with mass 3.6 kg/m², or 10 solar masses more. It seems that the value of the gravitational constant of the Universe and its relative mass are not the same. Rather, if the gravitational constant of 3.5 kg/m² is considered, we obtain the gravitational constant of the Big Bang. This is the gravitational constant of light speed and has the meaning of the Galactic North Star, which is defined as the maximum acceleration of the Big Bang at the very center of the Universe. In other words, the gravitational constant of the Universe is the equivalent of its mass. The gravitational constant of the universe should be less than its maximum acceleration of the Big Bang at the very centre. Then, we should arrive at the gravitational constant of the Universe being approximately 1.35 cm/s². In other words, the gravitational constant of the Universe is one hundred times as high as the gravitational constant of Big Bang. This means that the gravitational constant of the Black Hole is approximately 1,200 times less than the gravitational