The expected improvements in the precision of inflationary physics observables including the scalar spectral index <math><msub><mi>n</mi><mi>s</mi></msub></math> and the tensor-to-scalar ratio <math><mi>r</mi></math> will reveal more than just the viability of a particular model of inflation. In the presence of a curvaton field <math><mi>χ</mi></math>, supposedly dead models of inflation can be resurrected, as these observables are affected by curvaton perturbations. For currently successful models, improved constraints will enable us to constrain the properties of extra decaying scalar degrees of freedom produced during inflation. In this work, we demonstrate these diverse uses of a curvaton field with the most recent constraints on (<math><msub><mi>n</mi><mi>s</mi></msub><mo>,</mo><mi>r</mi></math>) and two exemplary inflation models, a Starobinsky-like model and a model of new inflation. The specific models used as examples can be derived in the context of supergravity. Our analysis invokes three free parameters: the curvaton mass <math><msub><mi>m</mi><mi>χ</mi></msub></math>, its decay rate <math><msub><mi>Γ</mi><mi>χ</mi></msub></math>, and the reheating temperature <math><msub><mi>T</mi><mrow><mi>RH</mi></mrow></msub></math> produced by inflaton decays. We systematically analyze possible postinflationary era scenarios of a curvaton field. By projecting the most recent cosmic microwave background (CMB) data on (<math><msub><mi>n</mi><mi>s</mi></msub><mo>,</mo><mi>r</mi></math>) into this parameter space, we can either set constraints on the curvaton parameters from successful models of inflation (so that the success is not spoiled) or determine the parameters that are able to save a model for which <math><msub><mi>n</mi><mi>s</mi></msub></math> is predicted to be below the experimental data. We emphasize that the initial value of <math><mo>⟨</mo><msup><mi>χ</mi><mn>2</mn></msup><mo>⟩</mo><mo>∝</mo><msup><mi>H</mi><mn>4</mn></msup><mo>/</mo><msubsup><mi>m</mi><mi>χ</mi><mn>2</mn></msubsup></math> produced during inflation is determined from a stochastic approach and thus not a free parameter in our analysis. We also investigate the production of local non-Gaussianity <math><msubsup><mi>f</mi><mrow><mi>NL</mi></mrow><mrow><mo>(</mo><mi>loc</mi><mo>)</mo></mrow></msubsup></math> and apply current CMB constraints to the parameter space. Intriguingly, we find that a large value of <math><msubsup><mi>f</mi><mrow><mi>NL</mi></mrow><mrow><mo>(</mo><mi>loc</mi><mo>)</mo></mrow></msubsup></math> of <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> can be produced for both of the two representative inflation models.

United States

Gongjun Choi

Wenqi Ke

Keith A. Olive

Role of the curvaton after the last Planck dataset

We study the effects on particle production of a Planck-suppressed coupling between the inflaton and a scalar dark matter candidate, <math><mi>χ</mi></math>. In the absence of this coupling the dominant source for the relic density of <math><mi>χ</mi></math> is the long wavelength modes produced from the scalar field fluctuations during inflation. In this case, there are strong constraints on the mass of the scalar and the reheating temperature after inflation from the present-day relic density of <math><mi>χ</mi></math> (assuming <math><mi>χ</mi></math> is stable). When a coupling <math><mi>σ</mi><msup><mi>ϕ</mi><mn>2</mn></msup><msup><mi>χ</mi><mn>2</mn></msup></math> is introduced, with <math><mi>σ</mi><mo>=</mo><mover><mi>σ</mi><mo>˜</mo></mover><msubsup><mi>m</mi><mi>ϕ</mi><mn>2</mn></msubsup><mo>/</mo><msubsup><mi>M</mi><mi>P</mi><mn>2</mn></msubsup><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup><mover><mi>σ</mi><mo>˜</mo></mover></math>, where <math><msub><mi>m</mi><mi>ϕ</mi></msub></math> is the inflaton mass, the allowed parameter space begins to open up considerably even for <math><mover><mi>σ</mi><mo>˜</mo></mover></math> as small as <math><mo>≳</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math>. For <math><mover><mi>σ</mi><mo>˜</mo></mover><mo>≳</mo><mfrac><mn>9</mn><mn>16</mn></mfrac></math>, particle production is dominated by the scattering of the inflaton condensate, either through single graviton exchange or the contact interaction between <math><mi>ϕ</mi></math> and <math><mi>χ</mi></math>. In this regime, the range of allowed masses and reheating temperatures is maximal. For <math><mn>0.004</mn><mo>&lt;</mo><mover><mi>σ</mi><mo>˜</mo></mover><mo>&lt;</mo><mn>50</mn></math>, constraints from isocurvature fluctuations are satisfied, and the production from parametric resonance can be neglected.

Mexico

Marcos A. G. Garcia

France

Yann Mambrini

Sarunas Verner

Inflaton production of scalar dark matter through fluctuations and scattering

The inflationary reheating phase begins when accelerated expansion ends. As all Standard Model particles are coupled to gravity, gravitational interactions will lead to particle production. This includes the thermal bath, dark matter, and gravitational radiation. Here, we compute the spectrum of gravitational waves from the inflaton condensate during the initial phase of reheating. As particular examples of inflation, we consider the Starobinsky model and T models, all of which are in good phenomenological agreement with cosmic microwave background anisotropy measurements. The T models are distinguished by the shape of the potential about its minimum and can be approximated by <math><mrow><mi>V</mi><mo>∼</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math>, where <math><mi>ϕ</mi></math> is the inflaton. Interestingly, the shape of the gravitational wave spectrum (when observed) can be used to distinguish among the models considered. As we show, the Starobinsky model and T models with <math><mi>k</mi><mo>=</mo><mn>2</mn></math>, provide very different spectra when compared to models with <math><mi>k</mi><mo>=</mo><mn>4</mn></math> or <math><mi>k</mi><mo>&gt;</mo><mn>4</mn></math>. Observation of multiple harmonics in the spectrum can be interpreted as a direct measurement of the inflaton mass. Furthermore, the cutoff in frequency can be used to determine the reheating temperature.

Minimal production of prompt gravitational waves during reheating

Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent S-type axion dual to a two form B  μν  in 4D and a T-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For T-type axions our conclusions largely agree with earlier workers for the axion quality problem, but we also reconcile why T-type axions can couple to matter localized on 3-branes with Planck suppressed strength even when the axion decay constants are of order the KK scale. For S-type axions, we review the duality between form fields and massive scalars and show how duality impacts naturalness arguments about the UV sensitivity of the scalar potential. In particular UV contributions on the KR side suppress contributions on the scalar side by powers of m/M with m the axion mass and M the UV scale. We re-examine how the axion quality problem is formulated on the dual side and compare to recent treatments. We study how axion quality is affected by the ubiquity of p-form gauge potentials (for both p = 2 and p = 3) in string vacua and identify two criteria that can potentially lead to a problem. We also show why most fields do not satisfy these criteria, but when they do the existence of multiple fields also provides mechanisms for resolving it. We conclude that the quality problem is easily evaded.

Canada

C. Burgess

CERN

United Kingdom

F. Quevedo

UV and IR effects in axion quality control

The QCD axion can be formulated in a dual description as a massive 2-form field. In this picture, the QCD axion quality problem translates into the question if there are additional 3-forms coupled to the axion other than the QCD 3-form that emerges at low energy. If such forms exist, the quality problem can be resolved via the introduction of other massive 2-forms (and thus corresponding axions), one for each additional 3-form. This can motivate an “axiverse from a high quality QCD axion”. In this work, we discuss this issue in the general case where the QCD axion couples to arbitrarily many 3-forms. Given the multiple axion solution, we discuss the phenomenological implications of the enhanced quality of the QCD axion in the dual description. These include sub-eV axion-like particle search through the axion-photon coupling, the cosmological consistency of a large decay constant QCD axion, and a model for the observed cosmic birefringence.

Germany

Jacob Leedom

Implications of protecting the QCD axion in the dual description

We consider a supersymmetric mirror Twin Higgs model in a gravity-mediated supersymmetry-breaking scenario. We point out that the Polonyi field can be odd under the Z 2 symmetry exchanging the Standard Model with the mirror sector while gaugino masses are generated at tree-level. We discuss the dynamics of the Polonyi field during and after inflation and show that the Polonyi problem is absent. The Polonyi field couples to the two sectors with opposite signs, which may serve as origin of the Z 2-breaking of the Higgs potential in Twin Higgs models. We also estimate the Z 2-breaking in soft masses of supersymmetric particles.

Japan

Keisuke Harigaya

Z 2-odd Polonyi field in twin Higgs model

We propose an inflation model in which the inflationary era is driven by the strong dynamics of <math><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> gauge theory. The quark condensation in the confined phase of <math><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> gauge theory generates the inflaton potential comparable to the energy of the thermal bath at the time of phase transition. Afterwards, with a super-Planckian field value at the global minimum, the inflation commences at a false vacuum region lying between true vacuum regions and hence the name “topological inflation.” Featured by the huge separation between the scale of the false vacuum (<math><mi>V</mi><mo>(</mo><mn>0</mn><msup><mo>)</mo><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup><mo>∼</mo><msup><mn>10</mn><mn>15</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>) and the field value at the global minimum (<math><msub><mi>ϕ</mi><mi>min</mi></msub><mo>∼</mo><msub><mi>M</mi><mi>P</mi></msub></math>), the model can be consistent with cosmic microwave background (CMB) observables without suffering from the initial condition problems. Crucially, this is achieved only with some mild tuning of parameters in <math><mi>V</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></math>. In addition to <math><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mo>)</mo></math>, this model is based on an anomaly free <math><msub><mi>Z</mi><mrow><mn>6</mn><mi>R</mi></mrow></msub></math> discrete <math><mi>R</mi></math> symmetry. Remarkably, while all parameters are fixed by CMB observations, the model predicts a hierarchy of energy scales including the inflation scale, supersymmetry-breaking scale, R-symmetry breaking scale, Higgsino mass and the right-handed neutrino mass given in terms of the dynamical scale of <math><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mo>)</mo></math>.

China

Weikang Lin

Tsutomu T. Yanagida

Dynamically induced topological inflation

In this work, we discuss how the use of the symmetries well motivated in physics beyond the Standard model (BSM) can guarantee the high quality axions. We avoid to introduce symmetries only useful for addressing the axion quality problem. Rather, we rely on symmetries well motivated by other issues in BSM: supersymmetry, U(1)B−L and the discrete R-symmetry Z  NR . We show that the interplay among these guarantees the high quality of the axion even for the gravitino mass and axion decay constant as large as m 3/2 =   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (10)TeV and F  a  =   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1015)GeV respectively. The key point of this work relies on the observation that the MSSM contribution to the mixed anomalies Z  NR  − [SU(2) L ]2 and Z  NR  − [SU(3) c ]2 is not enough for gauging Z  NR  for N ≠ 6, which necessitates the introduction of new matter fields. We make the introduction to achieve zero mixed anomalies, which logically supports a desired large enough N for Z  NR . This mechanism effectively makes Z  NR  equal to U(1) R  and thus offers a logically complete solution to the axion quality problem.

Tsutomu Yanagida

High quality axion in supersymmetric models

We present a supersymmetric model where energy scales of a discrete <math><mi>R</mi></math>-symmetry breaking (<math><msub><mi>Z</mi><mrow><mn>6</mn><mi>R</mi></mrow></msub></math>) and cosmic inflation are commonly attributed to the confinement scale of a hidden <math><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> strong dynamics. Apart from these, the supersymmetry-breaking scale, the Higgsino mass, and the right-handed neutrino masses are all shown to stem from the <math><msub><mi>Z</mi><mrow><mn>6</mn><mi>R</mi></mrow></msub></math> breaking scale inferred from cosmic microwave background observables. We will show that the model is characterized by the supersymmetry-breaking soft mass <math><msub><mi>m</mi><mrow><mi>soft</mi></mrow></msub><mo>≃</mo><mn>100</mn><mi>–</mi><mn>1000</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> and the reheating temperature <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>rh</mi></mrow></msub><mo>≃</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Then we discuss how these predictions of the model can be tested with the help of the spectrum of the gravitational wave induced by the short-lived cosmic string present during the reheating era.

Discrete <math><mi>R</mi></math>-symmetry, various energy scales, and gravitational waves

In this paper, we discuss interesting scenarios resulting from the interplay between the gravitino and the lightest right-handed (s)neutrino. We consider two gravitino mass regimes vastly separated, that is, <math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>O</mi><mo>(</mo><mn>100</mn><mo>)</mo><mtext> eV</mtext></math> and <math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>≃</mo><mn>100</mn><mtext> GeV</mtext></math>. For the former case, a significant amount of the entropy production in the cosmological history to dilute the gravitino relic abundance is unavoidable for consistency with the number of satellite galaxies in the Milky way. We will show that the right-handed (s)neutrino can play the role of the heavy particle whose late time decay provides such an additional radiation. For the later case, the gravitino of <math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>≃</mo><mn>100</mn><mtext> GeV</mtext></math> may resolve the <math><msub><mrow><mi>S</mi></mrow><mrow><mn>8</mn></mrow></msub></math> tension as a decaying dark matter. We will show how the lightest right-handed neutrino and its superpartner can help the gravitino decaying dark matter be equipped with a long enough life time and mass degeneracy with a massive decay product to address the <math><msub><mrow><mi>S</mi></mrow><mrow><mn>8</mn></mrow></msub></math> tension.