<p>We show that the simplest generalization of the chaotic inflation model <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></math> with nonminimal coupling to gravity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mi>R</mi></mrow></math> provides a good match to the results of the latest data release of the Atacama Cosmology Telescope and South Pole Telescope, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>r</mi><mo>≈</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>.</p>

United States

Renata Kallosh

Andrei Linde

Netherlands

Diederik Roest

Atacama Cosmology Telescope, South Pole Telescope, and Chaotic Inflation

We discuss known maximal D-dimensional supergravities of two types: type I with G/H coset spaces and type II derived by compactification from higher dimensions without dualization, these have less manifest symmetries. In 4D and 6D in type I models we perform explicit gauge-fixing of local H symmetries in unitary gauges: symmetric, Iwasawa and partial Iwasawa. In 4D supergravity I in symmetric gauge global H-invariance and nonlinearly realized G-symmetry are valid on shell, classically. The global H-symmetry and G-symmetry in Iwasawa-type gauges in type I and in type II supergravities are not manifest, if at all present. This fact raises the issue of the gauge equivalence of the S-matrix of various gauge-fixed D-dimensional supergravities and its relation to the ones computable using superamplitude methods.

France

Henning Samtleben

Belgium

Antoine Proeyen

Gauge-fixing local H symmetry in supergravities

We introduce Ward identities for superamplitudes in D-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$ -extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an n-partice superamplitude take a simple universal form for half BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of the n superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by (D − 2)L + 2 −   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  or (D − 2)L + 2 −   <math> <mn>2</mn> <mi>N</mi> </math>  $$ 2\mathcal{N} $$ , respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.

Ward identities for superamplitudes

We study d = 4,   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  ≥ 5 supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local   <math> <mi>H</mi> </math>  $$ \mathcal{H} $$ -symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry.

Japan

Yusuke Yamada

Deformation of d = 4,   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  ≥ 5 supergravities breaks nonlinear local supersymmetry

It was argued in [1] that the Volkov-Akulov (VA) model as well as similar models in supergravity and the related KKLT model in string theory, suffer from tachyonic instabilities due to goldstino condensation. The authors of [1] constructed a specific model with two unconstrained interacting chiral superfields with linearly realized supersymmetry which has an unstable vacuum. They claimed that this model becomes equivalent to the VA model in the UV limit. We show that the UV limit of their model is discontinuous, and the vacuum instability of the model proposed in [1] is not relevant to the VA model, to related models in supergravity, and to the KKLT construction.

Timm Wrase

Goldstino condensation?

We construct <math><mi>α</mi></math>-attractor versions of hybrid inflation models. In these models, the potential of the inflaton field <math><mi>φ</mi></math> is uplifted by the potential of the second field <math><mi>χ</mi></math>. This uplifting ends due to a tachyonic instability with respect to the field <math><mi>χ</mi></math>, which appears when <math><mi>φ</mi></math> becomes smaller than some critical value <math><msub><mi>φ</mi><mi>c</mi></msub></math>. In the large <math><mi>N</mi></math> limit, these models have the standard universal <math><mi>α</mi></math>-attractor predictions. In particular, <math><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>1</mn><mo>−</mo><mfrac><mn>2</mn><mi>N</mi></mfrac></math> for the exponential attractors. However, in some special cases, the large <math><mi>N</mi></math> limit is reached only beyond the horizon, for <math><mi>N</mi><mo>≳</mo><mn>60</mn></math>. This may change predictions for the cosmological observations. For any fixed <math><mi>N</mi></math>, in the limit of large uplift <math><msub><mi>V</mi><mrow><mi>up</mi></mrow></msub></math>, or in the limit of large <math><msub><mi>φ</mi><mi>c</mi></msub></math>, we find another attractor prediction, <math><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>1</mn></math>. By changing the parameters, <math><msub><mi>V</mi><mrow><mi>up</mi></mrow></msub></math> and <math><msub><mi>φ</mi><mi>c</mi></msub></math>, one can continuously interpolate between the two attractor predictions <math><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>1</mn><mo>−</mo><mfrac><mn>2</mn><mi>N</mi></mfrac></math> and <math><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>1</mn></math>. This provides significant flexibility, which can be very welcome in view of the rapidly growing amount and precision of the cosmological data. Our main result is not specific to the hybrid inflation models. Rather, it is generic to any inflationary models, where the inflaton potential, for some reason, is uplifted, and inflation ends prematurely.

Hybrid cosmological attractors

We perform canonical quantization of gravity in the background of a Schwarzschild black hole in the generalized Regge-Wheeler gauge proposed in Kallosh and Rahman [Quantization of gravity in the black hole background, Phys. Rev. D 104, 086008 (2021)]. We find that the Hamiltonian at the quadratic level is unitary and ghost-free. Two canonical degrees of freedom are associated with Zerilli-Moncrief and Cunningham-Price-Moncrief functions of the metric perturbations. The <math><mo>ℓ</mo><mo>&lt;</mo><mn>2</mn></math> part of the Hamiltonian vanishes. This quantization with the unitary Hamiltonian for gravity is valid also in Minkowski space in spherical coordinates.

Quantization of gravity in spherical harmonic basis

We perform a covariant (Lagrangian) quantization of perturbative gravity in the background of a Schwarzschild black hole. The key tool is a decomposition of the field into spherical harmonics. We fix Regge-Wheeler gauge for modes with angular momentum quantum number <math><mi>l</mi><mo>≥</mo><mn>2</mn></math>, while for low-multipole modes with <math><mi>l</mi><mo>=</mo><mn>0</mn></math> or 1—for which Regge-Wheeler gauge is inapplicable—we propose a set of gauge-fixing conditions which are 2D background covariant and perturbatively well defined. We find that the corresponding Faddeev-Popov ghosts are nonpropagating for the <math><mi>l</mi><mo>≥</mo><mn>2</mn></math> modes, but are in general nontrivial for the low-multipole modes with <math><mi>l</mi><mo>=</mo><mn>0</mn></math>, 1. However, in Schwarzschild coordinates, all time derivatives acting on the ghosts drop from the action and the low-multipole ghosts have instantaneous propagators. Up to possible subtleties related to quantizing gravity in a space with a horizon, Faddeev’s theorem suggests the possibility of an underlying canonical (Hamiltonian) quantization with a manifestly ghost-free Hilbert space.

Adel A. Rahman

Quantization of gravity in the black hole background

We study M-theory compactified on twisted 7-tori with G 2-holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic Kähler potential. We propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (4, 7) code. The corresponding 7-moduli models have Minkowski vacua with one flat direction. We also propose superpotentials based on octonions/error correcting codes for Minkowski vacua models with two flat directions. We update phenomenological α-attractor models of inflation with 3α = 7, 6, 5, 4, 3, 1, based on inflation along these flat directions. These inflationary models reproduce the benchmark targets for detecting B-modes, predicting 7 different values of   <math> <mi>r</mi> <mo>=</mo> <mn>12</mn> <mi>α</mi> <mo>/</mo> <msubsup> <mi>N</mi> <mi>e</mi> <mn>2</mn> </msubsup> </math>  $$ r=12\alpha /{N}_e^2 $$  in the range 10 −2 ≳ r ≳ 10 −3, to be explored by future cosmological observations.

Murat Gunaydin

M-theory cosmology, octonions, error correcting codes

Kachru-Kallosh-Linde-Trivedi (KKLT) scenario has succeeded in stabilizing the volume modulus and constructing metastable de Sitter (dS) vacua in type IIB string theory. We revisit to investigate the possibility of the oscillon (or I-ball) formation in the KKLT scenario when the volume modulus is initially displaced from the dS minimum. Special attention is paid to physically realistic initial conditions of the volume modulus, which was not taken in the literature. Using lattice simulations, we find that oscillons do not form unless the volume modulus is initially placed at very near the local maximum, which requires severe fine-tuning.