Low Scale Inflation Research Articles

Higgs-dilaton model revisited: Can a dilaton act as a QCD axion?

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be included in the fundamental principle of the ultimate theory of Nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field -- the dilaton. We explore the scenario in which this field is capable of solving the strong CP-problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to non-perturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realising the axion-like dilaton dark matter production compatible with the CMB data.

Axions in string theory — slaying the Hydra of dark radiation

It is widely believed that string theory easily allows for a QCD axion in the cosmologically favored mass range. The required small decay constant, fa ≪ MP, can be implemented by using a large compactification volume. This points to the Large Volume Scenario which in turn makes certain cosmological predictions: first, the closed string axion behaves similarly to a field-theoretic axion in the pre-inflationary scenario, i.e. the initial value can be tuned but one is constrained by isocurvature fluctuations. In addition, the volume represents a long-lived modulus that may lead to an early matter-dominated phase. Finally, the decay of the volume modulus to its own axion tends to overproduce dark radiation. In this paper we aim to carefully analyze the cosmology by studying models that not only allow for a QCD axion but also include inflation. Quite generally, limits on isocurvature fluctuations restrict us to relatively low-scale inflation, which in the present stringy context points to Kähler moduli inflation. As a novel feature we find that the lightest (volume) modulus couples strongly to the Higgs. It hence quickly decays to the SM, thus resolving the original dark radiation problem. This decay is much faster than that of the inflaton, implying that reheating is determined by the inflaton decay. The inflaton could potentially reintroduce a dark radiation problem since it decays to lighter moduli and their axions with equal rates. However, due its mixing with the QCD-saxion, the inflaton has also a direct decay rate to the SM, enhanced by the number of SM gauge bosons. This results in an amount of dark radiation that is consistent with present limits but potentially detectable in future measurements.

Beating the Lyth Bound by Parametric Resonance during Inflation.

We propose a novel mechanism for enhancing primordial gravitational waves without significantly affecting the curvature perturbations produced during inflation. This is achieved due to nonlinear sourcing of resonantly amplified scalar field fluctuations. Our result is an explicit scale-dependent counterexample of the famous Lyth bound, which opens up a promising perspective of producing detectable inflationary tensor modes with low-scale inflation and a sub-Planckian field excursion. We explicitly demonstrate the testability of our mechanism with upcoming cosmic microwave background B-mode observations.

The stochastic axiverse

In addition to spectacular signatures such as black hole superradiance and the rotation of CMB polarization, the plenitude of axions appearing in the string axiverse may have potentially dangerous implications. An example is the cosmological overproduction of relic axions and moduli by the misalignment mechanism, more pronounced in regions where the signals mentioned above may be observable, that is for large axion decay constant. In this work, we study the minimal requirements to soften this problem and show that the fundamental requirement is a long period of low-scale inflation. However, in this case, if the inflationary Hubble scale is lower than around O(100) eV, no relic DM axion is produced in the early Universe. Cosmological production of some axions may be activated, via the misalignment mechanism, if their potential minimum changes between inflation and today. As a particular example, we study in detail how the maximal-misalignment mechanism dilutes the effect of dangerous axions and allows the production of axion DM in a controlled way. In this case, the potential of the axion that realises the mechanism shifts by a factor ∆θ = π between the inflationary epoch and today, and the axion starts to oscillate from the top of its potential. We also show that axions with masses ma ∼ O(1 − 100) H0 realising the maximal-misalignment mechanism generically behave as dark energy with a decay constant that can take values well below the Planck scale, avoiding problems associated to super-Planckian scales. Finally, we briefly study the basic phenomenological implications of the mechanism and comment on the compatibility of this type of maximally-misaligned quintessence with the swampland criteria.

TwInflation

The general structure of Hybrid Inflation remains a very well-motivated mechanism for lower-scale cosmic inflation in the face of improving constraints on the tensor-to-scalar ratio. However, as originally modeled, the “waterfall” field in this mechanism gives rise to a hierarchy problem (η−problem) for the inflaton after demanding standard effective field theory (EFT) control. We modify the hybrid mechanism and incorporate a discrete “twin” symmetry, thereby yielding a viable, natural and EFT-controlled model of non-supersymmetric low-scale inflation, “Twinflation”. Analogously to Twin Higgs models, the discrete exchange-symmetry with a “twin” sector reduces quadratic sensitivity in the inflationary potential to ultra-violet physics, at the root of the hierarchy problem. The observed phase of inflation takes place on a hilltop-like potential but without fine-tuning of the initial inflaton position in field-space. We also show that all parameters of the model can take natural values, below any associated EFT-cutoff mass scales and field values, thus ensuring straightforward theoretical control. We discuss the basic phenomenological considerations and constraints, as well as possible future directions.

On hybrid monodromy inflation — hic sunt dracones

We revisit two-field hybrid inflation as an effective field theory for low-scale inflation with sub-Planckian scalar field ranges. We focus on a prototype model by Stewart because it allows for a red spectral tilt, which still fits the current data. We describe the constraints on this model imposed by current CMB measurements. We then explore the stability of this model to quantum corrections. We find that for relevant, marginal, and at least a finite set of irrelevant operators, some additional mechanism is required to render the model stable to corrections from both quantum field theory and quantum gravity. We outline a possible mechanism by realizing the scalars as compact axions dual to massive 4-form field strengths, and outline how natural hybrid inflation may be supported by strong dynamics in the dual theory.

Opening the 1 Hz axion window

An axion-like particle (ALP) with mass mϕ ∼ 10−15 eV oscillates with frequency ∼1 Hz. This mass scale lies in an open window of astrophysical constraints, and appears naturally as a consequence of grand unification (GUT) in string/M-theory. However, with a GUT-scale decay constant such an ALP overcloses the Universe, and cannot solve the strong CP problem. In this paper, we present a two axion model in which the 1 Hz ALP constitutes the entirety of the dark matter (DM) while the QCD axion solves the strong CP problem but contributes negligibly to the DM relic density. The mechanism to achieve the correct relic densities relies on low-scale inflation (mϕ ≲ Hinf ≲ 1 MeV), and we present explicit realisations of such a model. The scale in the axion potential leading to the 1 Hz axion generates a value for the strong CP phase which oscillates around {overline{theta}}_{mathrm{QCD}}sim {10}^{-12} , within reach of the proton storage ring electric dipole moment experiment. The 1 Hz axion is also in reach of near future laboratory and astrophysical searches.

The cosmological heavy ion collider: Fast thermalization after cosmic inflation

Heavy-ion colliders have revealed the process of “fast thermalization”. This experimental break-through has led to new theoretical tools to study the thermalization process at both weak and strong coupling. We apply this to the reheating epoch of inflationary cosmology, and the formation of a cosmological quark gluon plasma (QGP). We compute the thermalization time of the QGP at reheating, and find it is determined by the energy scale of inflation and the shear viscosity to entropy ratio η/s; or equivalently, the tensor-to-scalar ratio and the strong coupling constant at the epoch of thermalization. Thermalization is achieved near-instantaneously in low-scale inflation and in strongly coupled systems, and takes of order or less than a single e-fold of expansion for weakly-coupled systems or after high-scale inflation. We demonstrate that the predictions of inflation are robust to the physics of thermalization, and find a stochastic background of gravitational waves at frequencies accessible by interferometers, albeit with a small amplitude.

Reheating-induced axion dark matter after low scale inflation

A kinetic mixing between the axion and the inflaton allows for a production of axion dark matter even if the inflationary Hubble scale is smaller than the zero-temperature axion mass. We analyze the axion dynamics in this recently discovered “inflaxion” frame- work, and present a new cosmological scenario where the axion drifts away from its vacuum during the reheating epoch, giving rise to the observed dark matter abundance. We discuss the implications for both the QCD axion and axion-like particles.

Inflaxion dark matter

A new mechanism for producing axion dark matter is proposed. By invoking low-scale inflation and a kinetic mixing between the axion and the inflaton, it is shown that the axion is driven to a field point slightly displaced from the potential minimum, which can give rise to the observed dark matter abundance. In this framework, different combinations of the axion and inflaton fields play various cosmological roles, including generating the cosmological perturbations, reheating the universe, and serving as dark matter. The kinetic mixing also relates the dark matter lifetime with the reheating temperature. The mechanism tames axions that would otherwise overdominate the universe, and thus opens up new windows in the axion parameter space, including decay constants at the GUT scale and higher.

Relaxing the cosmological moduli problem by low-scale inflation

We show that the cosmological abundance of string axions is much smaller than naive estimates if the Hubble scale of inflation, Hinf , is sufficiently low (but can still be much higher than the axion masses) and if the inflation lasts sufficiently long. The reason is that the initial misalignment angles of the string axions follow the Bunch-Davies distribution peaked at the potential minima. As a result, the cosmological moduli problem induced by the string axions can be significantly relaxed by low-scale inflation, and astrophysical and cosmological bounds are satisfied over a wide range of the mass without any fine-tuning of the initial misalignment angles. Specifically, the axion with its decay constant fϕ = 1016 GeV satisfies the bounds over 10−18 eV ≲ mϕ ≲ 10 TeV for Hinf ≲ 10 keV-106 GeV. We also discuss cases with multiple axions and the QCD axion.

Super-cool Dark Matter

In dimension-less theories of dynamical generation of the weak scale, the Universe can undergo a period of low-scale inflation during which all particles are massless and undergo super-cooling. This leads to a new mechanism of generation of the cosmological Dark Matter relic density: super-cooling can easily suppress the amount of Dark Matter down to the desired level. This is achieved for TeV-scale Dark Matter, if super-cooling ends when quark condensates form at the QCD phase transition. Along this scenario, the baryon asymmetry can be generated either at the phase transition or through leptogenesis. We show that the above mechanism takes place in old and new dimension-less models.

QCD axion window and low-scale inflation

We show that the upper bound of the classical QCD axion window can be significantly relaxed for low-scale inflation. If the Gibbons-Hawking temperature during inflation is lower than the QCD scale, the initial QCD axion misalignment angle follows the Bunch-Davies distribution. The distribution is peaked at the strong CP conserving minimum if there is no other light degree of freedom contributing to the strong CP phase. As a result, the axion overproduction problem is significantly relaxed even for an axion decay constant larger than $10^{12}$GeV. We also provide concrete hilltop inflation models where the Hubble parameter during inflation is comparable to or much smaller than the QCD scale, with successful reheating taking place via perturbative decays or dissipation processes.

Observational signatures of the parametric amplification of gravitational waves during reheating after inflation

We study the evolution of Gravitational Waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass $m_g$ that depends either on the inflaton field $\phi$ or on its time derivative $\dot{\phi}$, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinsky's $R^2$ inflation model with a $\phi$-dependent $m_g$ and the second is a low-energy-scale inflation model with a $\dot{\phi}$-dependent $m_g$. We compute the energy density spectrum $\Omega_{\rm GW}(k)$ today of the GW background. In the Starobinsky's model, we show that the GWs can be amplified up to the detectable ranges of both CMB and DECIGO, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential $V(\phi)=M^2 \phi^2/2$ around $\phi \approx M_{\rm pl}$ (where $M_{\rm pl}$ is the reduced Planck mass), we find that the peak position of $\Omega_{\rm GW}(k)$ induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies.

Electroweak vacuum metastability and low-scale inflation

We study the stability of the electroweak vacuum in low-scale inflation models whose Hubble parameter is much smaller than the instability scale of the Higgs potential. In general, couplings between the inflaton and Higgs are present, and hence we study effects of these couplings during and after inflation. We derive constraints on the couplings between the inflaton and Higgs by requiring that they do not lead to catastrophic electroweak vacuum decay, in particular, via resonant production of the Higgs particles.

Gravitational Waves from Oscillons after Inflation.

We investigate the production of gravitational waves during preheating after inflation in the common case of field potentials that are asymmetric around the minimum. In particular, we study the impact of oscillons, comparatively long lived and spatially localized regions where a scalar field (e.g., the inflaton) oscillates with large amplitude. Contrary to a previous study, which considered a symmetric potential, we find that oscillons in asymmetric potentials associated with a phase transition can generate a pronounced peak in the spectrum of gravitational waves that largely exceeds the linear preheating spectrum. We discuss the possible implications of this enhanced amplitude of gravitational waves. For instance, for low scale inflation models, the contribution from the oscillons can strongly enhance the observation prospects at current and future gravitational wave detectors.

Low scale inflation at high energy colliders and meson factories

Inflation occurring at energy densities less than (10$^{14}$ GeV)$^4$ produces tensor perturbations too small to be measured by cosmological surveys. However, we show that it is possible to probe low scale inflation by measuring the mass of the inflaton at low energy experiments. Detection prospects and cosmological constraints are determined for low scale quartic hilltop models of inflation paired with a curvaton field, which imprints the spectrum of scalar perturbations observed in large scale structure and on the cosmic microwave background. With cosmological constraints applied, low scale quartic inflation at energies GeV--PeV, can be mapped to an MeV--TeV mass inflaton resonance, discoverable through a Higgs portal coupling at upcoming collider and meson decay experiments. It is demonstrated that low scale inflatons can have detectably large couplings to Standard Model particles through a Higgs portal, permitting prompt reheating after inflation, without spoiling, through radiative corrections to the inflaton's self-coupling, the necessary flatness of a low scale inflationary potential. A characteristic particle spectrum for a quartic inflaton-curvaton pair is identified: to within an order of magnitude, the mass of the curvaton can be predicted from the mass of the inflaton, and vice-versa. Low scale inflation Higgs portal sensitivity targets are found for experiments like the LHC, SHiP, BEPC, and KEKB.

High-scale SUSY from anR-invariant new inflation in the landscape

We provide an anthropic reason that the supersymmetry breaking scale is much higher than the electroweak scale as indicated by the null result of collider experiments and observed 125 GeV Higgs boson. We focus on a new inflation model as a typical low-scale inflation model that may be expected in the string landscape. In this model, the R-symmetry is broken at the minimum of the inflaton potential and its breaking scale is related to the reheating temperature. Once we admit that the anthropic principle requires thermal leptogenesis, we obtain a lower bound on gravitino mass, which is related to R-symmetry breaking scale. This scenario and resulting gravitino mass predict the consistent amplitude of density perturbations. We also find that string axions and saxions are consistently implemented in this scenario.

On the initial conditions for inflation with plateau potentials: the R+R2 (super)gravity case

We discuss the initial conditions problem for inflation driven by the vacuum energy of a plateau potential, and in particular the Starobinsky inflation. We show that the supergravity embedding of the R+R2 theory naturally decreases the size of the acausal homogeneity, required for the low-scale inflation to occur, thanks to the presence of the dynamical pure supergravitational ``auxiliary'' fields. We examine the evolution of the R+R2 fields within a FLRW Universe. We also find a dependence of the initial conditions problem on the background spatial curvature.

Gravitational waves in bigravity cosmology

In this paper we study gravitational wave perturbations in a cosmological setting of bigravity which can reproduce the ΛCDM background and large scale structure. We show that in general gravitational wave perturbations are unstable and only for very fine tuned initial conditions such a cosmology is viable. We quantify this fine tuning. We argue that similar fine tuning is also required in the scalar sector in order to prevent the tensor instability to be induced by second order scalar perturbations. Finally, we show that due to this power law instability, models of bigravity can lead to a large tensor to scalar ratio even for low scale inflation.