The Volume element of space-time and scale invariance

Guendelman, E.I.

doi:10.1023/A:1017572522313

The Volume element of space-time and scale invariance

E.I. Guendelman
(
- Ben Gurion U. of Negev
)

Nov, 2000

21 pages

Part of Proceedings, 2nd Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields (IARD 2000) : Ramat Gan, Israel, June 26-28, 2000

Published in:

Found.Phys. 31 (2001) 1019-1037

Contribution to:

- IARD 2000

e-Print:

hep-th/0011049 [hep-th]

DOI:

10.1023/A:1017572522313

View in:

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Abstract:

Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form

S = \int L_{1} \Phi d^4x

+

\int L_{2}\sqrt{-g}d^4x

where the volume element

\Phi d^4x

is independent of the metric. For global scale invariance, a "dilaton"

\phi

has to be introduced, with non-trivial potentials

V(\phi)

=

f_{1}e^{\alpha\phi}

in

L_1

and

U(\phi)

=

f_{2}e^{2\alpha\phi}

in

L_2

. This leads to non-trivial mass generation and a potential for

\phi

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

\Phi d^4x

alone. For closed strings and branes (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.

talk: Ramat Gan 2000/06/26
gravitation: action
gravitation: induced
field theory: scalar
field equations
inflation
invariance: conformal
string model
membrane model

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