We have recently suggested [1,2] that Inflation could have started in a local minimum of the Higgs potential at field values of about $10^{15}-10^{17}$ GeV, which exists for a narrow band of values of the top quark and Higgs masses and thus gives ris
e to a prediction on the Higgs mass to be in the range 123-129 GeV, together with a prediction on the the top mass and the cosmological tensor-to-scalar ratio $r$. Inflation can be achieved provided there is an additional degree of freedom which allows the transition to a radiation era. In [1] we had proposed such field to be a Brans-Dicke scalar. Here we present an alternative possibility with an additional subdominant scalar very weakly coupled to the Higgs, realizing an (inverted) hybrid Inflation scenario. Interestingly, we show that such model has an additional constraint $m_H<125.3 pm 3_{th}$, where $3_{th}$ is the present theoretical uncertainty on the Standard Model RGEs. The tensor-to-scalar ratio has to be within the narrow range $10^{-4}lesssim r<0.007$, and values of the scalar spectral index compatible with the observed range can be obtained. Moreover, if we impose the model to have subplanckian field excursion, this selects a narrower range $10^{-4} lesssim r<0.001$ and an upper bound on the Higgs mass of about $m_H <124 pm 3_{th}$.
Our peculiar velocity with respect to the CMB rest frame is known to induce a large dipole in the CMB. However, the motion of an observer has also the effect of distorting the anisotropies at all scales, as shown by Challinor and Van Leeuwen (2002),
due to aberration and Doppler effects. We propose to measure independently our local motion by using off-diagonal two-point correlation functions for high multipoles. We study the observability of the signal for temperature and polarization anisotropies. We point out that Planck can measure the velocity $beta$ with an error of about 30% and the direction with an error of about 20 degrees. This method constitutes a cross-check, which can be useful to verify that our CMB dipole is due mainly to our velocity or to disentangle the velocity from other possible intrinsic sources. Although in this paper we focus on our peculiar velocity, a similar effect would result also from other intrinsic vectorial distortion of the CMB which would induce a dipolar lensing. Measuring the off-diagonal correlation terms is therefore a test for a preferred direction on the CMB sky.
