It was proposed that five-dimensional (5D) inflation can blow up the size of a compact dimension from the 5D Planck length to the micron size, as required by the dark dimension proposal, relating the weakness of the actual gravitational force to the size of the observable universe. Moreover, it was shown that 5D inflation can generate the (approximate) flat power spectrum of primordial density fluctuations consistent with present observations. Here we compute the bispectrum of primordial scalar perturbations and show that unlike the power spectrum, it differs from the four-dimensional case at all angular distances, due to the fact that in contrast to global dilatations, invariance under special conformal transformations is not restored at late times. Moreover there is an additional enhancement in the squeezed limit.

Thailand

France

Ignatios Antoniadis

Auttakit Chatrabhuti

Jules Cunat

Hiroshi Isono

Bispectrum from five-dimensional inflation

The proposal of a rapid sign-switching cosmological constant in the late universe, mirroring a transition from anti-de Sitter (AdS) to de Sitter (dS) space, has significantly improved the fit to observational data and provides a compelling framework for ameliorating major cosmological tensions, such as the $\textit{H}$ and $\textit{S}$ tensions. An attractive theoretical realisation that accommodates the AdS → dS transition relies on the Casimir forces of fields inhabiting the bulk of a 5-dimensional (5-dim) set up. Among the fields characterising the dark sector, there is a real scalar field $\textit{ϕ}$ endowed with a potential holding two local minima with very small difference in vacuum energy and bigger curvature (mass) of the lower one. Shortly after the false vacuum tunnels to its true vacuum state, $\textit{ϕ}$ becomes more massive and its contribution to the Casimir energy becomes exponentially suppressed. The tunneling process then changes the difference between the total number of fermionic and bosonic degrees of freedom contributing to the quantum corrections of the vacuum energy, yielding the AdS → dS transition. We investigate the properties of this theoretical realisation to validate its main hypothesis and characterise free parameters of the model. We adopt the Coleman-de Luccia formalism for calculating the transition probability within the thin-wall approximation. We show that the Euclidean bounce configuration that drives the transition between $\textit{ϕ}$ vacua has associated at least a sixth order potential. We also show that distinctive features of the required vacuum decay to accommodate the AdS $\textit{→}$ dS transition are inconsistent with a 5-dim non-compact description of the instanton, for which the bounce is $\textit{O}$(5) symmetric, and instead call for a 5-dim instanton with a compact dimension, for which the bounce is $\textit{O}$(4) × U(1) symmetric.

United States

Luis Anchordoqui

Daniele Bielli

Thin-wall vacuum decay in the presence of a compact dimension meets the $\textit{H}$

In a recent paper, we computed the bispectrum of primordial density perturbations in CMB to second order in the slow-roll parameters of single field inflation, and found logarithmic infrared contributions that diverge in both large physical distances and squeezed limit where one momentum vanishes. In this work, we provide an independent test of the result by checking its conservation and the validity of the consistency relation between the squeezed limit of the bispectrum and the square of the power spectrum. Despite the violation of the main assumption for its general proofs which is the finiteness of the relevant observables in these limits, we find that the identity continues to hold in the vicinity of the squeezed limit and large time.

Bispectrum at NLO in single field inflation: conservation and squeezed limit

We study the problem of false vacuum decay in arbitrary dimensions, in the presence of gravity, and compute the transition probability within the thin-wall approximation, generalising the results of Coleman and de Luccia. In the particular case of one compact dimension, we present explicit formulae for the Euclidean Bounce configuration that drives the transition from a de Sitter to Minkowski or from a Minkowski to anti-de Sitter vacua.

Thin-wall vacuum decay in the presence of a compact dimension

We extend a recently proposed framework, dubbed inflation by supersymmetry breaking, to hybrid inflation by introducing a waterfall field that allows to decouple the supersymmetry breaking scale in the observable sector from the inflation scale, while keeping intact the inflation sector and its successful predictions: naturally small slow-roll parameters, small field initial conditions and absence of the pseudo-scalar companion of the inflaton, in terms of one free parameter which is the first order correction to the inflaton Kähler potential. During inflation, supersymmetry is spontaneously broken with the inflaton being the superpartner of the goldstino, together with a massive vector that gauges the R-symmetry. Inflation arises around the maximum of the scalar potential at the origin where R-symmetry is unbroken. Moreover, a nearby minimum with tuneable vacuum energy can be accommodated by introducing a second order correction to the Kähler potential. The inflaton sector can also play the role of the supersymmetry breaking ‘hidden’ sector when coupled to the (supersymmetric) Standard Model, predicting a superheavy superparticle spectrum near the inflation scale. Here we show that the introduction of a waterfall field provides a natural way to end inflation and allows for a scale separation between supersymmetry breaking and inflation. Moreover, the study of the global vacuum describing low energy Standard Model physics can be done in a perturbative way within a region of the parameter space of the model.

China

Kazakhstan

Yermek Aldabergenov

Hybrid inflation from supersymmetry breaking

We study in more detail the cubic constraints for  $${\mathcal N}=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   chiral superfields proposed in the earlier work Eur. Phys. J. C 81, 523 (2021), which describe low-energy goldstino-axion dynamics in global non-linearly realized supersymmetry. We generalize the constraint (i) by gauging the abelian symmetry that shifts the axion, and (ii) to supergravity. In the former case we show that after adding the abelian gauge multiplet, the construction can be formulated as a cubic nilpotent massive vector superfield. In the latter case we find explicit solution to the constraint including contributions from the supergravity multiplet. We also propose microscopic supergravity models (with linear supersymmetry), including a toy model for the string dilaton, which give rise to the cubic constraints at low energies.

Aspects of cubic nilpotent superfields

We study real fifth-order superfield constraint for  $${{\mathcal {N}}}=2$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </math>   vector (and tensor) multiplet and derive most general solution describing complete supersymmetry breaking, and preserving a real scalar, two goldstini, and an abelian gauge field as low-energy degrees of freedom on which both supersymmetries are realized non-linearly. The surviving scalar is identified as an axion of a broken global abelian symmetry, while its scalar partner (saxion) is eliminated in terms of the goldstini. We provide an example of a UV model giving rise to the quintic constraint, and discuss the connection of this constraint and its solution to other known superfield constraints in  $${{\mathcal {N}}}=2$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </math>   and  $${{\mathcal {N}}}=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   cases.

United Kingdom

Quintic constraints for  $${{\mathcal {N}}}=2$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </math>   multiplets and complete SUSY breaking

We study reheating after the end of inflation in models where the inflaton is the superpartner of goldstino and is charged under a gauged U(1) R-symmetry. We consider two classes of models – one is small field characterized by an almost flat Kähler space, and the other large field characterized by a hyperbolic Kähler space SU(1, 1)/U(1), while in both cases the inflaton superpotential is linear due to the R-symmetry. The inflationary observables of our models fit within 2 $$\sigma $$  <math> <mi>σ</mi> </math>   CMB values. Upon coupling the inflaton sector to the (supersymmetric) Standard Model, we compute the MSSM parameters, mass spectrum, and decay modes of the inflaton, with the resulting reheating temperature around  $$10^8$$  <math> <msup> <mn>10</mn> <mn>8</mn> </msup> </math>   GeV. We also find that both models can accommodate superheavy LSP dark matter, depending on the parameter choice.

Reheating after inflation by supersymmetry breaking

We find new solutions to real cubic constraints on  $$N=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   chiral superfields transforming under global abelian symmetries. These solutions describe the low-energy dynamics of a goldstino interacting with an axion (both belonging to the same chiral superfield) with non-linearly realized supersymmetry. We show the relation between our model and the approach of Komargodski and Seiberg for describing goldstino-axion dynamics which uses orthogonal nilpotent superfields.

Nilpotent superfields for broken abelian symmetries

We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.