We demonstrate that a broad class of modular inflation models predicts the emergence of new physics within an energy range of approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>15</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>17</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. This prediction arises by comparing the moduli-dependent species scale with observational constraints on inflation. Specifically, we illustrate this within the context of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">Z</mi><mo stretchy="false">)</mo></math>-modular inflation models by reexpressing inflationary observables in terms of the species scale. We further discuss the implications of this approach for generic Calabi-Yau threefolds.

South Korea

Shuntaro Aoki

Japan

Hajime Otsuka

Inflationary constraints on the moduli-dependent species scale in modular invariant theories

We investigate the role of the Higgs field as a fundamental scalar in the Standard Model within the framework of modular inflation models, where a modulus field acts as the inflaton and its interactions are governed by an underlying modular symmetry. In general, the Higgs field can participate in the dynamics of modular inflation, leading to a two-field inflationary system—termed Higgs-Modular inflation—which exhibits nontrivial dynamics and interesting phenomenological implications. We analyze Higgs-Modular inflation both analytically and numerically, highlighting its attractor behavior and the resulting observational constraints. In particular, we find that Higgs-Modular inflation is favored by the latest data release from the Atacama Cosmology Telescope in certain regions of parameter space. This is in contrast to both pure Higgs inflation and pure modular inflation with a Starobinsky-type potential, which tend to predict a relatively low spectral index. Additionally, we discuss the cutoff scale of this inflationary model and the reheating processes induced by the decays of the modulus and the Higgs field.

Ryota Yanagita

Higgs-modular inflation

Cosmological collider signals of primordial non-Gaussianity arise at tree level when an extra scalar has Hubble mass during inflation. We critically review the formalism finding that a large class of inflationary theories, based on Planck-scale physics, predict a scalar bi-spectrum around the gravitational floor level. This mild signal arises for example in $\textit{R}$ gravity, in the regime where its gravitational scalar has Hubble-scale mass. Signals much above the gravitational floor arise in theories where scalars undergo multiple turns during inflation, thanks to sub-Planckian physics.

Poland

Anish Ghoshal

Italy

Alessandro Strumia

Cosmological collider non-Gaussianity from multiple scalars and $\textit{R}$

Using the recently developed cosmological bootstrap method, we compute the exact analytical solution for the seed integral appearing in cosmological correlators with double massive scalar exchanges. The result is explicit, valid in any kinematic configuration, and free from spurious divergences. It is applicable to any number of fields’ species with any masses. With an appropriate choice of variables, the results contain only single-layer summations. We also propose simple approximate formulas valid in different limits, enabling direct and instantaneous evaluation. Supported by exact numerical results using CosmoFlow, we explore the phenomenology of double massive exchange diagrams. Contrary to single-exchange diagrams with ubiquitous Lorentz-covariant interactions, the size of the cubic coupling constant can be large while respecting perturbativity bounds. Because of this property, the primordial bispectrum from double-exchange diagrams can be as large as, coincidentally, current observational constraints. In addition to being sizable on equilateral configurations, we show that the primordial bispectrum exhibits a large cosmological collider signal in the squeezed limit, making the double massive exchanges interesting channels for the detection of massive primordial fields. We propose to decisively disentangle double-exchange channels from single-exchange ones with cosmological observations by exploiting the phase information of the cosmological collider signal, the inflationary flavor oscillations from multiple fields’ species exchanges and the double soft limit in the primordial trispectrum.

France

Lucas Pinol

Fumiya Sano

Masahide Yamaguchi

Yuhang Zhu

Cosmological correlators with double massive exchanges: bootstrap equation and phenomenology

Massive fields can imprint unique oscillatory features on primordial correlation functions or inflationary correlators, which is dubbed the cosmological collider signal. In this work, we analytically investigate the effects of a time-dependent mass of a scalar field on inflationary correlators, extending previous numerical studies and implementing techniques developed in the cosmological bootstrap program. The time-dependent mass is in general induced by couplings to the slow-roll inflaton background, with particularly significant effects in the case of non-derivative couplings. By linearly approximating the time dependence, the mode function of the massive scalar is computed analytically, on which we derive analytic formulae for two-, three-, and four-point correlators with the tree-level exchange of the massive scalar. The obtained formulae are utilized to discuss the phenomenological impacts on the power spectrum and bispectrum, and it is found that the scaling behavior of the bispectrum in the squeezed configuration, i.e., the cosmological collider signal, is modified from a time-dependent Boltzmann suppression. By investigating the scaling behavior in detail, we are in principle able to determine the non-derivative couplings between the inflaton and the massive particle.

Toshifumi Noumi

Analytic formulae for inflationary correlators with dynamical mass

We consider the embedding of Higgs inflation with a nonminimal coupling into the Weyl gravity. In this model, the effective current-current interactions from the heavy Weyl gauge field cancel the noncanonical Higgs kinetic term in Einstein frame, so the unitarity problem of the original Higgs inflation becomes less severe. For a simple case where the couplings of the heavy Weyl gauge field appears from the nonminimal couplings to the Ricci curvature scalar in Weyl gravity, we find that the resultant model for Higgs inflation is the same as in the Palatini formulation for Higgs inflation. The crucial difference of our model from the Palatini formulation for Higgs inflation is that there is a light Weyl gauge field coupled to the Higgs fields. We also generalize the unitarization of Higgs inflation with general covariant kinetic terms for the dilaton and the Higgs fields and realize a successful Higgs inflation, interpolating between the Palatini formulation for Higgs inflation and a Higgs-like inflation. We also discuss the Higgs mechanism for the light Weyl gauge field with an extra singlet scalar and show some interesting signatures for Higgs physics, such as the overall suppression of Higgs couplings and the direct couplings of the light Weyl gauge field to the Higgs boson.

Hyun Min Lee

Weyl gravity extension of Higgs inflation

Inflationary scenarios motivated by high-energy physics generically contain a plethora of degrees of freedom beyond the primordial curvature perturbation. The latter interacts in a simple way with what we name “inflationary flavor eigenstates,” which differ, in general, from freely propagating “mass eigenstates.” We show that the mixing between these misaligned states results in new striking behaviors in the squeezed limit of the curvature perturbation three-point function, depending not only on the mass spectrum but also on the “mixing angles” of the theory. These results bring about a new perspective on the cosmological collider program: contrary to a widespread belief, the primordial signal needs not be dominated by the lightest extra degree of freedom. Instead, we show that it may display either modulated oscillations, a broken power law, or a transition from oscillations to a power law, thus offering a detailed cosmic spectroscopy of the particle content of inflation.

Spain

Sébastien Renaux-Petel

Inflationary flavor oscillations and the cosmic spectroscopy

We study the post-inflationary dynamics for reheating and freeze-in dark matter in the Higgs-R 2 inflation model. Taking the perturbative approach for reheating, we determine the evolution of the temperature for radiation bath produced during reheating and determine the maximum and reheating temperatures of the Universe. Adopting a singlet scalar dark matter with a conformal non-minimal coupling and a vanishing Higgs-portal coupling, we discuss the freeze-in production of dark matter both from the non-thermal scattering during reheating and the thermal scattering after reheating. We find that thermal scattering is dominant for dark matter production in our model due to the high reheating temperature. The reheating temperature in our model is determined dominantly by the Higgs condensate to be up to about 1014 GeV and dark matter with masses up to about 109 GeV can be produced with a correct relic density.

Hyun Lee

Adriana Menkara

Kimiko Yamashita

Reheating and dark matter freeze-in in the Higgs-R 2 inflation model

We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting derivative terms to obtain algebraic constraints on superfields. Thanks to the supersymmetry breaking contribution by the kinetic energy, the validity of constrained superfields can be extended to cosmological regimes and phenomena such as reheating after inflation, kinetic-energy domination, and the kinetic and standard misalignment of axion.

Takahiro Terada

Constrained superfields in dynamical background

We propose a new construction of the supergravity inflation as an UV completion of the Higgs-R 2 inflation. In the dual description of R 2-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.