The Volume Element of Space-Time and Scale Invariance

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17 Scopus citations


Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form S = ∫ L1 Φ d4x + ∫ L2 √ - g d4x where the volume element Φ d4x is independent of the metric. For global scale invariance, a "dilaton" φ has to be introduced, with non-trivial potentials V(φ) = f1 eαφ L1 and U(φ) = f2 e2αφ in L2. This leads to non-trivial mass generation and a potential for φ which is interesting for inflation. Interpolating models for natural transition from inflation to a slowly accelerated universe at late times appear naturally. This is also achieved for "Quintessential models," which are scale invariant but formulated with the use of volume element Φ d4x alone. For closed strings and brunes (including the supersymmetric cases), the modified measure formulation is possible and does not require the introduction of a particular scale (the string or brane tension) from the begining but rather these appear as integration constants.

Original languageEnglish
Pages (from-to)1019-1037
Number of pages19
JournalFoundations of Physics
Issue number7
StatePublished - 1 Jan 2001

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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