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Inflationary cosmology represents a well-studied framework to describe the expansion of space in the early universe, as it explains the origin of the large-scale structure of the cosmos and the isotropy of the cosmic microwave background radiation. The recent detection of the Higgs boson renewed research activities based on the assumption that the inflaton could be identified with the Higgs field. At the same time, the question whether the inflationary potential can be be extended to the electroweak scale and whether it should be necessarily chosen ad hoc in order to be physically acceptable are at the center of an intense debate. Here, we perform the slow-roll analysis of the so-called Massive Natural Inflation (MNI) model which has three adjustable parameters, the explicit mass term, a Fourier amplitude u, and a frequency parameter $beta$, in addition to a constant term of the potential. This theory has the advantage to present a structure of infinite non-degenerate minima and is amenable to an easy integration of high-energy modes. We show that, using PLANCK data, one can fix, in the large $beta$-region, the parameters of the model in a unique way. We also demonstrate that the value for the parameters chosen at the cosmological scale does not influence the results at the electroweak scale. We argue that other models can have similar properties both at cosmological and electroweak scales, but with the MNI model one can complete the theory towards low energies and easily perform the integration of modes up to the electroweak scale, producing the correct order-of-magnitude for the Higgs mass.
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We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on $r$ and $n_S$, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95% confidence out by current data. If we assume protracted reheating characterized by $overline{w}>1/3,$ Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inflation into the 68% confidence region requires values of $T_{mathrm{re}}$ below the scale of electroweak symmetry breaking. The addition of a SHOES prior on the Hubble Constant $H_0$ only worsens the fit.
We consider natural inflation in a warm inflation framework with a temperature-dependent dissipative coefficient $Gamma propto T^3$. Natural inflation can be compatible with the Planck 2018 results with such warm assistance. With no a priori assumptions on the dissipative effects magnitude, we find that the Planck results prefer a weak dissipative regime for our benchmark scale $f=5 M_{rm pl}$, which lies outside the $2sigma$ region in the cold case. The inflation starts in the cold regime and evolves with a growing thermal fluctuation that dominates over quantum fluctuation before the end of the inflation. The observed spectral tilt puts stringent constraints on the models parameter space. We find that $f< 1 M_{rm pl}$ is excluded. A possible origin of such dissipative coefficient from axion-like coupling to gauge fields and tests of the model are also discussed.
The simplest two-field completion of natural inflation has a regime in which both fields are active and in which its predictions are within the Planck 1-$sigma$ confidence contour. We show this for the original model of natural inflation, in which inflation is achieved through the explicit breaking of a U(1) symmetry. We consider the case in which the mass coming from explicit breaking of this symmetry is comparable to that from spontaneous breaking, which we show is consistent with a hierarchy between the corresponding energy scales. While both masses are comparable when the observable modes left the horizon, the mass hierarchy is restored in the last e-foldings of inflation, rendering the predictions consistent with the isocurvature bounds. For completeness, we also study the predictions for the case in which there is a large hierarchy of masses and an initial period of inflation driven by the (heavy) radial field.
We study the Hybrid Natural Inflation (HNI) model and some of its realisations in the light of recent CMB observations, mainly Planck temperature and WMAP-9 polarization, and compare with the recent release of BICEP2 dataset. The inflationary sector of HNI is essentially given by the potential $V(phi) = V_0(1+acos (frac{phi}{f} ) )$, where $a$ is a positive constant smaller or equal to one and $f$ is the scale of (pseudo Nambu-Goldstone) symmetry breaking. We show that to describe the HNI model realisations we only need two observables; the spectral index $n_s$, the tensor-to-scalar ratio, and a free parameter in the amplitude of the cosine function $a$. We find that in order to make the HNI model compatible with the BICEP2 observations, we require a large positive running of the spectra. We find that this could over-produce primordial black holes in the most consistent case of the model. This situation could be aleviated if, as recently argued, the BICEP2 data do not correspond to primordial gravitational waves.
We study the generation of magnetic field in Higgs-inflation models where the Standard Model Higgs boson has a large coupling to the Ricci scalar. We couple the Higgs field to the Electromagnetic fields via a non- renormalizable dimension six operator suppressed by the Planck scale in the Jordan frame. We show that during Higgs inflation magnetic fields with present value $10^{-6}$ Gauss and comoving coherence length of $100 kpc$ can be generated in the Einstein frame. The problem of large back-reaction which is generic in the usual inflation models of magneto-genesis is avoided as the back-reaction is suppressed by the large Higgs-curvature coupling.
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