Cosmological constant

Cosmological constant is constant $\Lambda$ of Einstein field equation

$R_{\mu \nu }-(R/2)g_{\mu \nu }+\Lambda g_{\mu \nu }=8\pi T_{\mu \nu }$,

where $R_{\mu \nu }$ is Ricci tensor, $R$ is its contraction, $g_{\mu \nu }$ is metric tensor of spacetime, and $T_{\mu \nu }$ is stress-energy tensor.

Einstein added this cosmological constant to his field equation to make the universe stationary (neither expanding nor contracting) which it works when the cosmological constant has so called Einstein value

$\Lambda _{E}=4\pi G\rho /c^{2}$,

where $G$ is Newtonian gravitational constant, $\rho$ is density of space, and $c$ is speed of light in vacuum.

Historical background

In 1915 Einstein introduced the field equation that placed into balance and found equal the curvature at one side and mass on the other. He hoped that the equations of general relativity would determine a single universe model without any beginning or end. For reasons he could never make clear, he found universe so conceived particulary satisfying and he managed to find a solution to his own equations that specified universe of that sort, static and unchanged forever. A.G. Riess declares that Einstein's original idea was to have constant amount of energy in the space. When in 1920s Russian mathematician A.Friedman (1924) and Belgian catholic priest and professor of physics G.Lemaître (1927) independently found that Einstein's gravitational field equations of general relativity have non-static cosmological solution implying an expanding universe or collapsing, Einstein, wishing to cancel out expansion, suggested modification to his field equations by adding a so-called cosmological term. Before long, after Hubble's interpretation of new discoveries as expanding universe in 1929, the role of cosmological constant aiming to allow static homogeneous solutions to field equations in presence of matter seemed finished. Einstein called $\Lambda$ "the biggest blunder of my life". In general, a positive $\Lambda$ causes acceleration to the universe expansion, whereas negative $\Lambda$ and ordinary matter tend to decelerate it. When the Supernova Cosmology Project Collaboration and High-Z Supernova Team Collaboration started their research at the beginning of 1990s, both prevailing mainstream cosmological models assumed decelerating universe scenarios. The processing of collected data from research observations however indicated that the universe is accelerating and requires something like non-zero cosmological constant. The first paper on new discovery was submitted in May 1998 and in December the same year the new discovery of the accelerating universe was declared to be a "breakthrough of the year" in the journal Science.

According to J.Hartnett, it would be fair to state that most cosmologist would like the requirement for cosmological constant to disappear altogether. He interprets its extremely small value as a possible evidence for fine-tuned universe. The 2011 Nobel Laureate in Physics, Brian P. Schmidt was asked in 2011 the question "what is causing the universe to expand at accelerating rate?" which he answered by words that it is a big mystery why space should have energy at all, people around the world are scratching their heads to figure out but as of today there has not been lot progress yet.

It has been however declared that Carmeli's theory which has no explicit cosmological constant implies its equivalence of $\Lambda$ = 1.934 × 10-35 s-2 and this value is supposed to be in excellent agreement with measurements. The 'force' pushing the universe apart, which invokes the ideas about dark energy is more correctly just a property of the correct metric.