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[371, 298]. However, Figure 24 shows that best-fit flat models, using geometric data, only admit insignificant screening . The closed models provide a better fit to the data , and can allow a bare vacuum energy term with , as shown in Figure 25. This does not address the fundamental problem of the smallness of , but is nevertheless an interesting feature. We can define an effective equation-of-state parameter via ). Furthermore, there is no “big rip” singularity in the future associated with this phantom acceleration, unlike the situation that typically arises with phantom fields. The phantom behaviour in the normal DGP model is also not associated with any ghost problem – indeed, the normal DGP branch is free of the ghost that plagues the self-accelerating DGP .
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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