A general myth created by the Chaotic Inflation, that `` T/S is negligible for the Harrison--Zel'dovich spectrum'', proved to be an artifact of the model, namely, the -potential-choice there (the power-law inflation has demonstrated the consistency with the myth displaying that large can be obtained only while rejecting from the HZ-slope of density perturbations, ). The reason is that the CI-models generate cosmological-scale-perturbations only for (as the process of inflation is to be intrinsicly stopped at ) so, the remains always there. At the same time, smooth -potentials produce ``red'' HZ spectra of scalar perturbations, which is also a general property of CI. Although both properties, small T/S and , originate from a single condition -- the inflation, -- the latter is not a general case for inflationary process at all. More of that, the relationship between T/S and is not confirmed (in particular, it is violated when the slow-roll approximation is broken). Instead, the connection of T/S to seems a fundamental one (see below).
Obviously, it is clear that T/S becomes large if the cosmological perturbations are generated at . In this case the inflation must continue to smaller . This possibility is realised for a rather general class of the fundamental inflations with one scalar field and the effective -term (Lukash & Mikheeva (1996)):
The vacuum density () should be metastable (otherwise inflation will proceed infinitely) and decay at some . The mechanism of the decay may be arbitrary and is not fixed in this simple model (as an example of -decay see hybrid inflation, Linde (1994)).
Regarding that the inflation proceeds up to small , eq(2) can be relevantly understood as the decomposition of near the local-minimum-point .
Figure 1: The spectra of scalar () and tensor () metric perturbations in the model (2) with in arbitrary normalisation. In the ``blue'' asymptotic .
Another important parameter of the model (besides ) is where . For
the process of the inflation is dominated by the -term. Such a stage, being impossible in the chaotic inflation, brings about the generation of ``blue'' spectra of S-perturbations. Taking into account that for the spectrum is ``red'', we come to very generic properties of the S and T spectra in the models with -term.
Figure 2: T/S ratio for the model (2) with .
Figure 3: The slices for T/S.
Figure 1 presents S and T perturbation spectra (dashed and solid lines, respectively) and a ratio between them (dotted line). The gauge-invariant metric perturbations generated in the inflation, are determined in the synchronous reference system comoving to the -field in large scales ():
where and are random Gaussian functions of spatial coordinates, ,
For HZ-spectra and would be -independent ( and , respectively). The normalisation of both spectra is arbitrary and can be calculated exactly after defining .
For the case , , T/S was calculated by the authors for the following model parameters: , (Figure 2). Figure 3 shows the same two-parametric function T/S as a set of the slices of constant T/S values. We see that the probability to find in the model plane is roughly 50%.
As the ``blue'' S-spectra appearing naturally in the -dominated inflation models have important implications for LSS formation theories, below we write down explicitly ().
For the dimensionless power spectrum of density perturbations is as follows: