Cosmological constant

The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is a value occurring in Einstein's theory of general relativity. The units of Λ are 1/second²; its value is unknown but believed to be positive based on recent observations. The constant is proportional to the energy density of the vacuum ρ:

<math>\Lambda = {{8\pi G} \over {3c^2}} \rho</math>

where π is Pi, G is the gravitational constant and c is the speed of light in vacuum. The term can be postive, negative, or zero and can be thought of as the amount of energy that is embeded in empty space. If it is positive then the expansion of space would release more energy, whereas if it is negative the expansion of space would consume energy.

Einstein initially included the term because he was dissatisfied by the fact that his equations would not allow for a static universe. Gravity would cause a universe which was initially at rest to begin to contract. To counteract the force of gravity, Einstein added the cosmological constant which would produce a repulsive force.

However, this term did not fulfill its intended purpose. First of all, observations by Edwin Hubble indicated that the universe was not at rest but rather was expanding. Second, adding the cosmological constant to Einstein's equations would not lead to a universe at rest because a static universe would still be unstable. A universe at rest which expanded slightly would release the vacuum energy, which would cause more expansion, which would release more energy. Similarly, a universe which contracted slightly would have less energy, which would increase the rate of contraction.

Einstein abandoned the cosmological constant and called it the "biggest blunder" of his life.

The cosmological constant is still of interest, as most grand unified theories predict a non-zero cosmological constant from the energy of quantum vacuum fluctuations. In fact, one theoretical problem in these theories is that the vacuum energy they predict is huge, and would have to be countered by a similarly large negative Λ to avoid an extremely rapidly expanding universe. Some physicists such as Steven Weinberg regard the delicate balance observed as being improbable and best explained by appealing to the anthropic principle.

Moreover, observations suggest that the early universe underwent a period of rapid expansion known as inflation, which can be modelled by assuming a positive cosmological constant. Observations of an accelerating universe in the late 1990s can be explained by assuming a positive cosmological constant, and as of 2002, this is the most commonly adopted position and is favored over models which assume a type of energy known as quintessence.

The value of the cosmological constant that would explain current observations is on the order of 10^-36sec^-2. This value of the cosmological constant disturbs theorists who for reasons of symmetry are uncomfortable with an extremely small cosmological constant that is non-zero. Thus the cosmological constant may ironically turn out to be Einstein's greatest prediction.

Quaternion Alternative "Gravity" and "Cosmological Constant" Theory Alternative view of the "Constant". The Constant is not a constant but 2 times the divergence of the vector energy of space. The "Constant" is part of scalar wave equation of the Quaternion spacetime force. The quaternion scalar force is a longitudinal curvature wave as opposed to the quaternion vector force which is transverse curvature wave. The variable "L=Ls + Lv" is the quaternion called "Life", it has the units energy-distance and is related to action by L=ch, where c is the speed of light and h is action (energy-time). Using L instead of action gives consistent units of distance for spacetime rather than the mixed units of time and space reflected in Maxwell's Equations and Einstein's Photoelectric Equations. The fourth dimension of spacetime is a distance dimension, "ct"!

The Quaternion Gravity Equation containing the "Constant" is:

<math>Force = X^2L=({ \partial^2 \over c^2\partial t^2 } - \nabla^2)Ls - 2\partial / c\partial t\nabla .Lv</math>

Discussion: This equation shows that the "constant" depends on the divergence of the vector field, which could be positve, negative or zero and changes with time! Flat space occurs when the force is zero.

The "Boundary Condition" Force is given by:

<math>Force = X^2L= -({ \partial^2 \over c^2\partial t^2 } + \nabla^2)L </math>

This alternative is built on the observation that spacetime is a quaternion space, obeying quaternion rules for Physics.

References

• Sean M. Carroll: "The Cosmological Constant", http://pancake.uchicago.edu/~carroll/encyc/