# Value of the Cosmological Constant: Theory versus Experiment

###### Abstract

The numerical value of the cosmological constant is calculated using a recently suggested cosmological model and found to be s. This value of is in excellent agreement with the measurements recently obtained by the High-Z Supernova Team and the Supernova Cosmology Project.

Department of Physics, Ben Gurion University, Beer Sheva 84105, Israel The problem of the cosmological constant and the vacuum energy associated with it is of high interest these days. There are many questions related to it at the quantum level, all of which are related to quantum gravity. Why there exists the critical mass density and why the cosmological constant has this value? Trying to answer these questions and others were recently the subject of many publications 1 ; 2 ; 4 ; 6 ; 7 ; 9 ; 10 ; 12 ; 13 ; 15 ; 16 ; 17 ; 18 .

In this paper it is shown that the recently suggested cosmological model 19 predicts the value s for the cosmological constant. This value of is in excellent agreement with the measurements recently obtained by the High-Z Supernova Team and the Supernova Cosmological Project 20 ; 21 ; 22 ; 23 ; 24 ; 25 ; 26 .

The Einstein gravitational field equations with the added cosmological term are 27 :

(1) |

where is the cosmological constant, the value of which is supposed to be determined by experiment. In Eq. (1) and are the Ricci tensor and scalar, respectively, , where is Newton’s constant and the speed of light is taken as unity.

Recently the two groups (the Supernovae Cosmology Project and the High-Z Supernova Team) concluded that the expansion of the universe is accelerating 20 ; 21 ; 22 ; 23 ; 24 ; 25 ; 26 . Both teams obtained

(2) |

and ruled out the traditional (, )=(1, 0) universe. Their value of the density parameter corresponds to a cosmological constant that is small but, nevertheless, nonzero and positive,

(3) |

In Ref. 14 a four-dimensional cosmological model was presented. The model predicts that the universe accelerates and hence it is equivalent to having a positive value for cosmological constant in it. In the framework of this model the zero-zero component of Einstein’s equations is written as

(4) |

where is the critical mass density and is Hubble’s time in the zero-gravity limit.

Comparing Eq. (4) with the zero-zero component of Eq. (1), one obtains the expression for the cosmological constant,

(5) |

To find out the numerical value of we use the relationship between and given in Ref. 14 [Eq. (5.23)]:

(6) |

where is the redshift and where 19 . (Notice that is different from the standard defined with .) The redshift parameter determines the distance at which is measured. We choose (Fig. 11 in Ref. 14) and take for

(7) |

(roughly corresponds to 0.3 in the standard theory), Eq. (6) then gives

(8) |

At the value the corresponding Hubble constant according to the latest results from HST can be taken 28 as km/s-Mpc, thus km/s-Mpc or

(9) |

and

(10) |

What is left is to find the value of . We have , where and . Thus , or

(11) |

As is seen from Eqs. (7) and (11) one has

(12) |

which means the universe is flat.

As a final result we calculate the cosmological constant according to Eq. (5). One obtains

(13) |

Our results confirm those of the supernovae experiments and indicate on existance of the dark energy as has recently received confirmation from the Boomerang cosmic microwave background experiment 29 ; 30 , which showed that the universe is flat. {references}