  We explore a broad class of three-parameter inflationary models, called the
$\Lambda$-inflation, and its observational predictions: high abundance of
cosmic gravitational waves consistent with the Harrison-Zel'dovich spectrum of
primordial cosmological perturbations, the non-power-law wing-like spectrum of
matter density perturbations, high efficiency of these models to meet current
observational tests, and others. We show that a parity contribution of the
gravitational waves and adiabatic density perturbations into the large-scale
temperature anisotropy, T/S $\sim 1$, is a common feature of
$\Lambda$-inflation; the maximum values of T/S (basically not larger than 10)
are reached in models where (i) the local spectrum shape of density
perturbations is flat or slightly red ($n_S{}_\sim^< 1$), and (ii) the residual
potential energy of the inflaton is near the GUT scale ($V_0^{{1/4}} \sim
10^{16} GeV$). The conditions to find large T/S in the paradigm of cosmic
inflation and the relationship of T/S to the ratio of the power spectra, $r$,
and to the inflationary $\gamma$ and Hubble parameters, are discussed. We argue
that a simple estimate, T/S$\simeq 3r\simeq 12\gamma \simeq (\frac{H}{6\times
10^{13}{\rm GeV}})^2$, is true for most known inflationary solutions and allows
to relate straightforwardly the important parameters of observational and
physical cosmology.
