An interesting feature of the normal branch is the ‘degravitation’ property, i.e., that is effectively
screened by 5D gravity effects. This follows from rewriting the modified Friedmann equation (432
) in
standard general relativistic form, with
Perturbations in the normal branch have the same structure as those in the self-accelerating branch,
with the same regimes – i.e., below the Vainshtein radius (recovering a GR limit), up to the
Hubble radius (Brans–Dicke behaviour), and beyond the Hubble radius (strongly 5D behaviour).
The quasistatic approximation and the numerical integrations can be simply repeated with the
replacement (and the addition of
to the background). In the sub-Hubble regime, the
effective Brans–Dicke parameter is still given by Equations (425
) and (426
), but now we have
– and this is consistent with the absence of a ghost. Furthermore, a positive Brans–Dicke
parameter signals an extra positive contribution to structure formation from the scalar degree of
freedom, so that there is less suppression of structure formation than in LCDM – the reverse of
what happens in the self-accelerating DGP. This is confirmed by computations, as illustrated in
Figure 25
.
The closed normal DGP models fit the background expansion data reasonably well, as shown in
Figure 25. The key remaining question is how well do these models fit the large-angle CMB
anisotropies, which is yet to be computed at the time of writing. The derivative of the ISW
potential
can be seen in Figure 25
, and it is evident that the ISW contribution is negative
relative to LCDM at high redshifts, and goes through zero at some redshift before becoming
positive. This distinctive behaviour may be contrasted with the behaviour in
models
(see Figure 26
): both types of model lead to less suppression of structure than LCDM, but
they produce different ISW effects. However, in the limit
, normal DGP tends to
ordinary LCDM, hence observations which fit LCDM will always just provide a lower limit for
.
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