Deviations from Einstein's Gravity at Large and Short Distances 89

The absorption cross section, dened as the ratio of the absorbed energy to the
incoming ux, can be calculated thanks to an optical theorem, as proved e.g. by
Weinberg [15]. According to that theorem, the absorption cross section for a signal
of frequency ! close to !N, say, the frequency of the detector mode excited by the
incoming GW, is given by the expression

where is the linewitdh of the mode |which can be arbitrarily small, as assumed
in the previous section|, and  is the dimensionless ratio

where PGW is the energy re-emitted by the detector in the form of GWs as a
consequence of its being set to oscillate by the incoming signal. In the following I
will only consider the case PGW = Pscalartensor with [3, 2]
Pscalartensor = 2G! 6

where Qij(!) is the quadrupole moment of the hollow sphere:

and 
BD is Brans{Dicke's parameter.
An explicit calculation shows that Pscalartensor is made up of two contributions:
Pscalartensor = P00 + P20 (31)
where P00 is the scalar, or monopole contribution to the emitted power, while P20
comes from the central quadrupole mode which, as discussed in [2] and [3], is excited
together with monopole in JBD theory. One must however recall that monopole
and quadrupole modes of the sphere happen at dierent frequencies, so that cross
sections for them only make sense if dened separately. More precisely,


Abstract
In this talk I will describe some recent results on the sensitivity of resonant
mass detectors shaped as a hollow sphere to scalar gravitational radiation.
Detection of this type of gravitational radiation will signal deviations from
Einstein's gravity at large distances. I will then discuss a class of experiments
aiming at nding deviations from Einstein's gravity at distances below 1 cm. I
will review the main experimental diÆculties in performing such experiments
and evaluate the eects to be taken into account besides gravity.
Estratto
In questo colloquio descriverò alcuni risultati recenti sulla
sensibilità dei rivelatori totali sonori a forma di come sfera vuota
a radiazione gravitazionale scalare. Rilevazione di questo tipo di
salti di segnale gravitazionali di volontà di radiazione da gravità
del Einstein alle grandi distanze. Allora discuterò un codice
categoria degli esperimenti che puntano che nding le deviazioni da
gravità del Einstein alle distanze inferiore a 1 centimetro.
Rivedrò i diÆculties sperimentali principali nell' effettuazione dei
tali esperimenti e valuterò i ects di e da considerare oltre a
gravità.