Dark Radiation predictions from general Large Volume Scenarios

Abstract

Recent observations constrain the amount of Dark Radiation (∆N eff ) and may even hint towards a non-zero value of ∆N eff . It is by now well-known that this puts stringent constraints on the sequestered Large Volume Scenario (LVS), i.e. on LVS realisations with the Standard Model at a singularity. We go beyond this setting by considering LVS models where SM fields are realised on 7-branes in the geometric regime. As we argue, this naturally goes together with high-scale supersymmetry. The abundance of Dark Radiation is determined by the competition between the decay of the lightest modulus to axions, to the SM Higgs and to gauge fields, and leads to strict constraints on these models. Nevertheless, these constructions can in principle meet current DR bounds due to decays into gauge bosons alone. Further, a rather robust prediction for a substantial amount of Dark Radiation can be made. This applies both to cases where the SM 4-cycles are stabilised by D-terms and are small 'by accident', i.e. tuning, as well as to fibred models with the small cycles stabilised by loops. In these constructions the DR axion and the QCD axion are the same field and we require a tuning of the initial misalignment to avoid Dark Matter overproduction. Furthermore, we analyse a closely related setting where the SM lives at a singularity but couples to the volume modulus through flavour branes. We conclude that some of the most natural LVS settings with natural values of model parameters lead to Dark Radiation predictions just below the present observational limits. Barring a discovery, rather modest improvements of present Dark Radiation bounds can rule out many of these most simple and generic variants of the LVS.

Global embedding of fibre inflation models

“…This is crucial to have full control over the inflationary dynamics since it determines the properties of all directions orthogonal to the inflaton and fixes all the mass and energy scales in the model. On top of moduli stabilisation, other important issues to trust inflationary models building are the study of the post-inflationary cosmological history starting with reheating [9][10][11][12][13] and the interplay between inflation and other phenomenological implications of the same model like the supersymmetry breaking scale [14][15][16][17][18], the nature of dark matter [19][20][21][22][23] and dark radiation [24][25][26][27] or the origin of the matter-antimatter asymmetry [28,29].…”

General analysis of dark radiation in sequestered string models

“…2 In this way, the decay rate of the lightest modulus to visible sector gauge bosons becomes comparable to the decay to bulk axions, and so the prediction for ∆N eff can become smaller. In fact, the simplest model with a shift-symmetric Higgs sector yields ∆N eff ≃ 0.5 [28]. However this case necessarily requires high-scale SUSY since without sequestering M soft ∼ m 3/2 (up to loop factors), and so from (1.2) we see that the cosmological bound m mod ∼ m 3/2 √ ǫ 30 TeV implies…”

“…[27] showed how sequestered LVS models where the Calabi-Yau (CY) volume is controlled by more than one divisor are ruled out since they predict huge values of extra dark radiation of order ∆N eff ∼ 10 4 . On the other hand, [28] focused on non-sequestered LVS models where the visible sector is realised via D7-branes wrapping the large cycle controlling the CY volume. 2 In this way, the decay rate of the lightest modulus to visible sector gauge bosons becomes comparable to the decay to bulk axions, and so the prediction for ∆N eff can become smaller.…”

“…2 Another option involves flavour D7-branes wrapped around the volume divisor and intersecting the visible sector D3-branes localised at a singularity [28].…”

Reheating and dark radiation after fibre inflation

“…If the visible sector lives on D3-branes at singularities, the gauge kinetic function is set at tree-level by the dilaton, and so both the volume mode χ and the inflaton φ couple to visible sector gauge bosons only at loop level. All the other inflaton couplings to visible sector fields are further suppressed since [17][18][19][20][21]: (i) the couplings to quarks and leptons are chirality suppressed; (ii) depending on the level of sequestering of the visible sector from the sources of supersymmetry breaking, the decay of the inflaton to supersymmetric particles is either kinematically forbidden or mass suppressed; (iii) there is no tree-level inflaton coupling to Higgses induced by a Giudice-Masiero term in the Kähler potential since, as can be seen from (2.26), the volume mode V is given at leading order just by the heavy field χ. 3 Hence in the case of D3-branes, the main inflaton decay channel is into gauge bosons but the branching ratio into visible sector particles is negligible with respect to the one into hidden sector degrees of freedom since [69]:…”