Natural inflation: Particle physics models, power-law spectra for large-scale structure, and constraints from the Cosmic Background Explorer

Particle Physics and Cosmology Intertwined

While the standard model accurately describes data at the electroweak scale without the inclusion of gravity, beyond the standard model, physics is increasingly intertwined with gravitational phenomena and cosmology. Thus, the gravity-mediated breaking of supersymmetry in supergravity models leads to sparticle masses, which are gravitational in origin, observable at TeV scales and testable at the LHC, and supergravity also provides a candidate for dark matter, a possible framework for inflationary models and for models of dark energy. Further, extended supergravity models and string and D-brane models contain hidden sectors, some of which may be feebly coupled to the visible sector, resulting in heat exchange between the visible and hidden sectors. Because of the couplings between the sectors, both particle physics and cosmology are affected. The above implies that particle physics and cosmology are intrinsically intertwined in the resolution of essentially all of the cosmological phenomena, such as dark matter and dark energy, and in the resolution of cosmological puzzles, such as the Hubble tension and the EDGES anomaly. Here, we give a brief overview of the intertwining and its implications for the discovery of sparticles, as well as the resolution of cosmological anomalies and the identification of dark matter and dark energy as major challenges for the coming decades.

Strong Backreaction Regime in Axion Inflation

We study the nonlinear dynamics of axion inflation, capturing for the first time the inhomogeneity and full dynamical range during strong backreaction, till the end of inflation. Accounting for inhomogeneous effects leads to a number of new relevant results, compared to spatially homogeneous studies: (i) the number of extra efoldings beyond slow-roll inflation increases very rapidly with the coupling, (ii) oscillations of the inflaton velocity are attenuated, (iii) the tachyonic gauge field helicity spectrum is smoothed out (i.e., the spectral oscillatory features disappear), broadened, and shifted to smaller scales, and (iv) the nontachyonic helicity is excited, reducing the chiral asymmetry, now scale dependent. Our results are expected to impact strongly on the phenomenology and observability of axion inflation, including gravitational wave generation and primordial black hole production.

Enhanced Gravitational Waves from Inflaton Oscillons

In broad classes of inflationary models the period of accelerated expansion is followed by fragmentation of the inflaton scalar field into localized, long-lived, and massive oscillon excitations. We demonstrate that matter dominance of oscillons, followed by their rapid decay, significantly enhances the primordial gravitational wave (GW) spectrum. These oscillon-induced GWs, sourced by second-order perturbations, are distinct and could be orders of magnitude lower in frequency than the previously considered GWs associated with oscillon formation. We show that detectable oscillon-induced GW signatures establish direct tests independent from cosmic microwave background radiation for regions of parameter space of monodromy, and logarithmic and pure natural (plateau) potential classes of inflationary models, among others. We demonstrate that oscillon-induced GWs in a model based on pure natural inflation could be directly observable with the Einstein Telescope, Cosmic Explorer, and DECIGO. These signatures offer a new route for probing the underlying inflationary physics.

Inflation in Supergravity from Field Redefinitions

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by G ( T i , T ¯ i ) = K + log | W | 2 , where K is a real Kähler potential, and W is a holomorphic superpotential. A field redefinition T i → f 1 ( T i ) changes neither the theory nor the Kähler geometry. Similarly, the Kähler transformation, K → K + f 2 + f ¯ 2 , W → e − f 2 W where f 2 is holomorphic and leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in K ( T i , T ¯ i ) → K ( f ( T i ) , f ( T ¯ i ) ) , while keeping the same superpotential W ( T i ) , we get a different theory, as G is not invariant under such a transformation while maintaining the same Kähler geometry. This freedom of choosing f ( T i ) allows construction of an infinite number of new theories given a fixed Kähler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of W. In particular, it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat Kähler geometry and an originally renormalizable superpotential W. The models are in accord with current observations and predict r ∈ [ 10 − 6 , 0.06 ] spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with T R ∼ O ( 10 7 G e V ) .

Can the Inflaton Also Be a Weakly Interacting Massive Particle?

We propose a class of models in which a stable inflaton is produced as a thermal relic in the early Universe and constitutes the dark matter. We show that inflaton annihilations can efficiently reheat the Universe, and identify several examples of inflationary potentials that can accommodate all cosmic microwave background observables and in which the inflaton dark matter candidate has a weak scale mass. As a simple example, we consider annihilations that take place through a Higgs portal interaction, leading to encouraging prospects for future direct detection experiments.

Spinodal instabilities and super-Planckian excursions in natural inflation

Models such as Natural Inflation that use pseudo-Nambu-Goldstone bosons as the inflaton are attractive for many reasons. However, they typically require trans-Planckian field excursions ΔΦ>MPl, due to the need for an axion decay constant f>MPl to have both a sufficient number of e-folds and values of ns,r consistent with data. Such excursions would in general require the addition of all other higher dimension operators consistent with symmetries, thus disrupting the required flatness of the potential and rendering the theory nonpredictive. We show that in the case of Natural Inflation, the existence of spinodal instabilities (modes with tachyonic masses) can modify the inflaton equations of motion to the point that versions of the model with f<MPl can still inflate for the required number of e-folds. The instabilities naturally give rise to two separate phases of inflation with different values of the Hubble parameter H, one driven by the zero mode, the other by the unstable fluctuation modes. The values of ns and r typically depend on the initial conditions for the zero mode, and, at least for those examined here, the values of r tend to be unobservably small.

Inflation from broken scale invariance

We construct a model of inflation based on a low-energy effective theory of spontaneously broken global scale invariance. This provides a shift symmetry that protects the inflaton potential from quantum corrections. Since the underlying scale invariance is noncompact, arbitrarily large inflaton field displacements are readily allowed in the low-energy effective theory. A weak breaking of scale invariance by almost marginal operators provides a nontrivial inflaton minimum, which sets and stabilizes the final low-energy value of the Planck scale. The underlying scale invariance ensures that the slow-roll approximation remains valid over large inflaton displacements, and yields a scale invariant spectrum of perturbations, as required by the cosmic microwave background observations.

Non-Gaussianity in axion N-flation models

We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter f{NL} may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation.

A natural framework for chaotic inflation

We show that inflation with a quadratic potential occurs naturally in theories where an axionlike field mixes with a 4-form. Such an axion is massive, with the mass which arises from the mixing being protected by the axion shift symmetry. The 4-form backgrounds break this symmetry spontaneously and comprise a minilandscape, where their fluxes can change by emission of membranes. Inflation can begin when the 4-form dominates the energy density. Eventually, this energy is reduced by membrane emission, and the axion can roll slowly towards its minimum, as in the simplest version of chaotic inflation.

Temperature of the inflaton and duration of inflation from Wilkinson microwave anisotropy probe data

If the initial state of the inflaton field is taken to have a thermal distribution instead of the conventional zero particle vacuum state then the curvature power spectrum gets modified by a temperature dependent factor such that the fluctuation spectrum of the microwave background radiation is enhanced at larger angles. We compare this modified cosmic microwave background spectrum with Wilkinson microwave anisotropy probe data to obtain an upper bound on the temperature of the inflaton at the time our current horizon crossed the horizon during inflation. We further conclude that there must be additional -foldings of inflation beyond what is needed to solve the horizon problem.

Extranatural inflation

We present a new model of inflation in which the inflaton is the extra component of a gauge field in a 5D theory compactified on a circle. The chief merit of this model is that the potential comes only from nonlocal effects so that its flatness is not spoiled by higher-dimensional operators or quantum gravity corrections. The model predicts a red spectrum (n approximately 0.96) and a significant production of gravitational waves (r approximately 0.11). We also comment on the relevance of this idea to quintessence.