### Abstract

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρΛ ∼ M^{8}/M^{4}_{p}, where M p is the Planck scale and M is the weak interaction scale. The model is based on (4 + D)-dimensional gravity, with D = 2 extra dimensions with radius b(t) curled up at the ADD length scale b_{0} = M_{p}/M^{2} ∼ 0.1 mm. Vacuum fluctuations in the compactified space perturb b_{0} very slightly, generating a small present-day cosmological constant. The radius of the compactified dimensions is predicted to be b_{0} ≈ k^{1}/^{4}0.09 mm (or equivalently M ≈ 2.4 TeV/k^{1/8}), where the Casimir energy density is k/b^{4}. Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M ∼ 10^{-17} cm, rolls down its potential to b_{0}.

Original language | English (US) |
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Pages (from-to) | 21-25 |

Number of pages | 5 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 524 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 3 2002 |

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### Keywords

- Cosmological constant
- Extra dimensions
- Inflationary cosmology

### ASJC Scopus subject areas

- Nuclear and High Energy Physics