BLEJSKE DELAVNICE IZ FIZIKE LETNIK 24, . ST. 1 BLED WORKSHOPS IN PHYSICS VOL. 24, NO. 1 ISSN 1580-4992 Proceedings to the 26th Workshop What Comes Beyond the Standard Models Bled, July 10–19, 2023 Edited by Norma Susana Manko.c Bor.stnik Holger Bech Nielsen Maxim Yu. Khlopov Astri Kleppe UNIVERZA V LJUBLJANI Fakulteta za matematiko in fziko LJUBLJANA, DECEMBER 2023 The 26th Workshop What Comes Beyond the Standard Models, 10.– 19. July 2023, Bled Was organized by Society of Mathematicians, Physicists and Astronomers of Slovenia And sponsored by Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana Society of Mathematicians, Physicists and Astronomers of Slovenia Beyond Semiconductor (Matja . z Breskvar) VIA (Virtual Institute of Astroparticle Physics), Paris MDPI journal “Symmetry”, Basel MDPI journal “Physics”, Basel MDPI journal “Universe””, Basel Scientifc Committee John Ellis, King’s College London / CERN Roman Jackiw, MIT Masao Ninomiya, Yukawa Institute for Theoretical Physics, Kyoto University Organizing Committee Norma Susana Manko.c Bor.stnik Holger Bech Nielsen Maxim Yu. Khlopov The Members of the Organizing Committee of the International Workshop “What Comes Beyond the Standard Models”, Bled, Slovenia, state that the articles published in the Proceedings to the 26th Workshop “What Comes Beyond the Standard Models”, Bled, Slovenia are refereed at the Workshop in intense in-depth discussions. Workshops organized at Bled . What Comes Beyond the StandardModels (June 29–July 9, 1998), Vol. 0 (1999) No. 1 (July 22–31, 1999) (July 17–31, 2000) (July 16–28, 2001), Vol. 2 (2001) No. 2 (July 14–25, 2002), Vol. 3 (2002) No. 4 (July 18–28, 2003) Vol. 4 (2003) Nos. 2-3 (July 19–31, 2004), Vol. 5 (2004) No. 2 (July 19–29, 2005) , Vol. 6 (2005) No. 2 (September 16–26, 2006), Vol. 7 (2006) No. 2 (July 17–27, 2007), Vol. 8 (2007) No. 2 (July 15–25, 2008), Vol. 9 (2008) No. 2 (July 14–24, 2009), Vol. 10 (2009) No. 2 (July 12–22, 2010), Vol. 11 (2010) No. 2 (July 11–21, 2011), Vol. 12 (2011) No. 2 (July 9–19, 2012), Vol. 13 (2012) No. 2 (July 14–21, 2013), Vol. 14 (2013) No. 2 (July 20–28, 2014), Vol. 15 (2014) No. 2 (July 11–19, 2015), Vol. 16 (2015) No. 2 (July 11–19, 2016), Vol. 17 (2016) No. 2 (July 9–17, 2017), Vol. 18 (2017) No. 2 (June 23–July 1, 2018), Vol. 19 (2018) No. 2 (July 6–14, 2019), Vol. 20 (2019) No. 2 (July 4–12, 2020), Vol. 21 (2020) No. 1 (July 4–12, 2020), Vol. 21 (2020) No. 2 (July 1–12, 2021), Vol. 22 (2021) No. 1 (July 4–12, 2022), Vol. 23 (2022) No. 1 . Hadrons as Solitons (July 6–17, 1999) . Few-Quark Problems (July 8–15, 2000), Vol. 1 (2000) No. 1 . Selected Few-BodyProblemsin Hadronic and Atomic Physics (July 7–14, 2001), Vol. 2 (2001) No. 1 . Quarks and Hadrons (July 6–13, 2002), Vol. 3 (2002) No. 3 . Effective Quark-Quark Interaction (July 7–14, 2003), Vol. 4 (2003) No. 1 . Quark Dynamics (July 12–19, 2004), Vol. 5 (2004) No. 1 . Exciting Hadrons (July 11–18, 2005), Vol. 6 (2005) No. 1 . Progress in Quark Models (July 10–17, 2006), Vol. 7 (2006) No. 1 . Hadron Structure and Lattice QCD (July 9–16, 2007), Vol. 8 (2007) No. 1 . Few-Quark States and the Continuum (September 15–22, 2008), Vol. 9 (2008) No. 1 . Problems in Multi-Quark States (June 29–July 6, 2009), Vol. 10 (2009) No. 1 . Dressing Hadrons (July 4–11, 2010), Vol. 11 (2010) No. 1 . Understanding hadronic spectra (July 3–10, 2011), Vol. 12 (2011) No. 1 . Hadronic Resonances (July 1–8, 2012), Vol. 13 (2012) No. 1 . Looking into Hadrons (July 7–14, 2013), Vol. 14 (2013) No. 1 . Quark Masses and Hadron Spectra (July 6–13, 2014), Vol. 15 (2014) No. 1 . Exploring Hadron Resonances (July 5–11, 2015), Vol. 16 (2015) No. 1 . Quarks, Hadrons, Matter (July 3–10, 2016), Vol. 17 (2016) No. 1 . Advances in Hadronic Resonances (July 2–9, 2017), Vol. 18 (2017) No. 1 . Double-charm Baryons and Dimesons (June 17–23, 2018), Vol. 19 (2018) No. 1 . Electroweak Processes of Hadrons (July 15–19, 2019), Vol. 20 (2019) No. 1 . . Statistical Mechanics of Complex Systems (August 27–September 2, 2000) . Studies of Elementary Steps of Radical Reactions in Atmospheric Chemistry (August 25–28, 2001) Preface in English and Slovenian Language N. S. Manko.c Bor.stnik Department of Physics, University of Ljubljana This year was 26th time that our series of workshops on ”What Comes Beyond the Standard Models?” took place. The series started in 1998 with the idea of organising a workshop in which participants would spend most of the time in discussions, confronting different approaches and ideas. The picturesque town of Bled by the lake of the same name, surrounded by beautiful mountains and offering pleasant walks, was chosen to stimulate the discussions. The idea was successful and has developed into an annual workshop, which is taking place every year since 1998. Very open-minded and fruitful discussions have become the trademark of our workshops, producing several published works. It took place in the house of Plemelj, which belongs to the Society of Mathematicians, Physicists and Astronomers of Slovenia. The workshops at Bled changed after the Covid pandemic: For two years, the workshop became almost virtual and correspondingly less open-minded. The discussions, which before asked the speaker to explain and prove each step, can not be done so easily virtually. However, many questions still interrupt the presentations, so that the speakers must often continue their talks several times in the following days. Also, this year, most of the talks were presented virtually. Most of the contributions present theoretical concepts of solving the open problems of elementary fermion and boson felds and of cosmology. Recent experiments in astrophysical stochastic gravitational wave background receive comments and suggestions for possible interpretation in contributions. But there are also the contributions of experimental groups This year the excellent experimental group report the measurements of 22 independent annual cycles with various confgurations, which ensures us that they do measure the dark matter. The origin of the dark matter seems to be the most discussed open problem in the literature in the last few years. Also, most of the authors of the contributions report , beside about other ideas, also on their ideas about the origin of dark matter. The speakers also defended several concepts on how to solve the open problems in cosmology, all of which are unavoidably connected with the understanding of the elementary fermion and boson felds and the laws of nature. The participants suggest: The laws of nature are simple and elegant, which requires treating all the fermion and boson felds in an unique way, with their internal spaces and their properties in the ordinary space included. This concept requires that the space-time is not the observed one but much larger, with a unique in­teraction in all dimensions and the maximal symmetry in both spaces. It is the break of the starting symmetry, caused by phase transitions, which is responsible in (3 + 1)-dimensions for the observed properties of quarks and leptons, of their boson gauge felds, the scalar felds, for explaining the masses of all the fermions with the masses of the fermions forming the dark matter included, explaining the appearance of the matter/antimatter asymmetry as well as all the observations and measurements. Extending the point particles to strings might take care of the renormalisability of this theory. All kinds of grand unifying theories are less requiring concepts of the one pre­sented under the frst point, but can be included in the above concept and can help to suggest a way of breaking symmetries and to propose measurements and observations. Among the assumptions that try to explain the cosmological measurements, it is the recently proposed thesis that the smallness of dark energy, known as the cosmological hierarchy, can be explained by assuming that one of the dimensions in d> (3 + 1) is of the micron size. Also, these year contributions present the mathematical concepts, which might help to justify the choice of “simple and elegant” laws of nature in maximally symmetric (internal and external) spaces (offering the explanations for all the assumptions of the standard model). Such a mathematical point of view can help to fnd ways of breaking symmetries, “chosen by nature”. There is also the warning about how carefully relativistic quantum mechanics has to be taken into account in the dispersion relations of the wave packets, when measuring the arrival time of high energy cosmic rays. The authors discuss the possibility that the primordial black holes are responsible for the stochastic gravitational wave background. Several other things are dis­cussed, such as the baryon number non-conservation (at least not in the ordinary matter sector), the mass spectrum of black holes and the properties of domain walls. The authors pay particular attention to dark matter streaming around our Earth, which might be responsible for many observed but unexplained observations. Many a presented and developed idea in this proceeding might not be in agree­ment with the others presented in thhe same proceedings. But yet different ideas, if developed in a consistent way, might help to understand the problems in con­nection with the measurements and observations, which only can confrm what is the status of the laws in our universe. The idea, presented in the last New Scientist about the possibility that the dark matter is created in the second Big Bang can hardly be true if the laws of nature are simple and elegant in the space which has more than (3 + 1)=dimensions. However, some authors had similar ideas before. Looking at the collection of open questions that we set ourselves before starting these Bled workshops and continuously supplementing in each workshop, it shows up that we are all the time mostly looking for an answer to the essential question: How to explain all the assumptions of the standard model, which would offer not only the understanding of all the assumed properties for quarks and leptons and all the observed boson felds with the Higgs scalars included, but also for the observed phenomena in cosmology; like it is the understanding of the expansion rate of the universe, of the appearance of the dark matter, of black holes with their (second quantised) quantum nature included, of the necessity of the existence of dark energy and many others. When trying to understand the quantum nature of fermion and boson felds, we are looking for a theory which is anomaly free and possibly renormalisable so that we would be able to predict the properties of second quantised felds when proposing measurements, as well as when trying to understand the behaviour of fermion and boson felds within black holes in ordinary matter and dark matter. Many talks are ”unusual” in that they seek to fnd a new, more trustworthy way of understanding and describing the observed phenomena. This year was very special: The organisers are asking the University of Ljubljana for the help in arranging the DOI number. Although the Society of Mathematicians, Physicists and Astronomers of Slovenia remain our organiser, for what we are very grateful, yet the Faculty of Mathematics and Physics starts to be our publisher together with the University of Ljubljana. The technical procedure is now different, and the possibility that the participants send the contributions “the last moment” is less available. Several participants have not succeeded in sending their contributions in time. We publish only abstracts of those who sent in time at least abstracts. Their contribu­tions will be published next year if they want. The same will also happen with contributions, which have not succeeded to send even abstracts in time. From July to November is a short time, in particular, since this period includes vacations. The organisers are grateful to all the participants for the lively presentations and discussions and an excellent working atmosphere, although most participants appeared virtually, led by Maxim Khlopov. The reader can fnd all the talks and soon also the whole Proceedings on the offcial website of the Workshop: http://bsm.fmf.uni-lj.si/bled2023bsm/presentations.html, and on the Cosmovia Forum https://bit.ly/bled2023bsm .. Norma Manko.c Bor.stnik, Holger Bech Nielsen, Maxim Khlopov, Astri Kleppe Ljubljana, December 2023 1 Predgovor (Preface in Slovenian Language) Letos je serija delavnic z naslovom ,,Kako prese. ci oba standardna modela, koz­molo.sibkega” (”What Comes Beyond the Standard Models?”) skega in elektro.stekla ze.sestindvajseti..zelji, da bi udele. c. Prva delavnica je stekla leta 1998 v .zenci v iz.cno soo.cne ideje in teorije. Slikovito mestece crpnih diskusijah kriti.cali razli.Bled, ob jezeru z enakim imenom, obkro.cki, nad katerimi zeno s prijaznimi hrib.kipijo slikovite gore, ki ponujajo prijetne sprehode in pohode, ponujajo prilo. znosti za diskusije. Ideja je bila uspesna, razvila se je v vsakoletno delavnico, ki te.ce..sestindvajseti. ze.c. Zelo odprte, prijateljske in u. cinkovite diskusije so postale ”blagovna znamka” na. sih delavnic, ideje, ki so se v diskusijah rodile, pa so pogosto botrovale ob-javljenim .si na Bledu tik ob jezeru. clankom. Delavnice domujejo v Plemljevi hi.Hi.stvu matematikov, fzikom in astronomov zapustil svetovno priznani so je Dru.slovenski matematik Jozef Plemelj. Delavnice na Bledu so se po pandemiji covida spremenile: . Ze dve leti je bila delavnica skoraj virtualna in temu primerno manj odprta in tudi manj prijateljska. Razprave, ki govorca prijazno prosijo, da naj vsak korak razlo. zi in predstavi dokaze, v virtualni diskusiji ni mogo.cinkovite. Vendar pa . ce narediti tako u.se vedno poslu.sanj, tako da morajo govorci ve. salci postavljajo veliko vpra.ckrat nadaljevati svoje predavanje v naslednjih dneh. Tudi v leto. snji delavnici je tekla ve. cina predavanj preko spleta. Ve.cnih; predstavljajo teoreti. cina prispevkov je tudi letos teoreti.cne koncepte re. sevanja odprtih problemiov elementarnih fermionskih in bozonskih polj ter kozmologije. Nedavna merjenja astrofzikalnih stohasti. cnih gravitacijskih valov odmevajo tudi v leto. snjih prispevkih. Ponujajo predloge za interpretacijo. V zborniku je tudi odli.ca o merit- cni prispevek eksperimentalne skupine, ki poro.vah dvaindvajsetletnih letnih modulacijah, ki jih experimentalno posodablja in nas prepri. ca, da je to, kar merijo, lahko samo posledica interakcije temne snovi z merilnimi aparaturami. Zdi se, da v zadnjih letih najve.sa ugotoviti, iz e c prispevkov v literaturi posku.¸sa je temna snov. Tudi ve . cina avtorjev prispevkov v zborniku predstavi, med drugimi zamislimi, svoje zamisli o izvoru temne snovi. Prispevki, ki pojasnjujejo kozmolo. ske meritve, ne morejo mimo dejstva, da so odprta vpra. sanja v kozmologiji neizogibno povezana z razumevanjem elemen­tarnih fermionskih in bozonskih polj ter zakonov narave. Udele. zenci predlagajo: Naravni zakoni so preprosti in elegantni, kar pa zahteva obravnavanje vseh fermionskih in bozonskih polj na enoten na.cno z njihovimi notranjimi cin; vklju.prostostnimi stopnjami in njihovimi lastnostmi v prostoru -. casu. Ta koncept pa zahteva, da je prostor-.cji od (3 + 1), ki ga opazimo in da je interakcija med c ve.fermioni in bozoni v vseh prostorih z maksimalno simetrijo enaka in velja za notranje prostore in za ve.zni prostor-.cijo c razse.cas. Zlomitev simetrije, ki jo povzr.fazni prehodi, pa privede fermione in bozone v (3 + 1)-razse.casu znem prostoru-.do kvarkov in leptonov, njihovih bozonskih umeritvenih polj, do skalarnih polj, ki so vzrok masam kvarkov in leptonov in . sibkih bozonov, tudi masi skupkov temne snovi iz nove dru. zine kvarkov in leptonov; pojasnijo pojav nesimetrije med barionsko snovjo in antisnovjo in ponudijo razlago tudi za kozmolo.opazovanja ska.in meritve. Raz.ckastih fermionskih in bozonskih polj, tudi skalarnih, v siritev to.strune bi lahko poskrbela za renormalizabilnost te teorije. Vse vrste teorij velikega poenotenja so manj zahtevne od omenjenega koncepta, se pa dajo vgraditi v omenjeni koncept. Pomagajo pri iskanju na. cina zlomitve simetrije, ki ga je uporabila narava in predlagajo nove meritve in opazovanja. Med predpostavkami, ki posku.ziti kozmolo. sajo razlo.ske meritve, se zdi nedavno predlagana teza, da je majhnost temne energije, znana kot kozmolo. ska hierarhija, mogo.ziti s predpostavko, da je ena od dimenzij v d> (3 + 1) mikronske ce razlo.velikosti. Tudi tokratni prispevki predstavljajo matemati. cne koncepte, ki lahko pomagajo utemeljiti izbiro “preprostih in elegantnih“ zakonov narave v maksimalno simetri. cnih (notranjih in zunanjih) prostorih (ki ponujajo razlage za vse predpostavke standard-nega modela). Tak.cn teza lahko pomaga najti nove na. sna matemati.cine zlomitve simetrij, ki so bli.zje temu, kar “izbere narava“. Avtor enega prispevka opozarja na nujnost upo.cne kvantne stevanja relativisti.mehanike zaradi disperzije valovnih paketov na kozmolo. skih skalah pri merjenju .zmi.zarkov. casa prihoda visokoenergijskih kozmi.cnih .Avtorji prispevkov razpravljajo o mo.cajo ozadje stohasti. znosti, da povzro.c nega gravitacijskega valovanja prvotne (primordialne) . crne luknje. Pojasnjujejo neohran­janje barionskega .crnih lukenj in stevila (v sektorju navadne snovi), masni spekter .lastnosti domenskih sten. Avtorji obves..cejo okoli na. cajo bralca, da tokovi temni snovi, ki te.sega planeta Zemlje, lahko odgovorni za mnoga doslej nepojasnjena opa. zenja. Marsikatera predstavljena in razvita ideja v tem zborniku morda ni skladna z drugimi tezami. A vendarle nove, druga. cn in dobro utemeljene ideje lahko poma­gajo bolje razumeti te. zave z razumevanjem meritev in opazovanji. Ideja, predstavljena v zadnjem New Science, o mo. znosti, da nastane temna snov ob drugem velikem poku, skoraj ne more biti resni.ce so naravni zakoni preprosti cna, .in elegantni v prostoru, ki ima ve. c kot (3 + 1)-dimenzijo. Dodajmo, da so nekateri avtorji teh prispevkov tudi . ze imeli podobne zamisli, za katere pa se zdi, da niso v skladu vsaj z nekaterimi od meritev. Pogled na zbirko odprtih vpra.cetek Blejskih sanj, ki smo si jih zastavili pred za.delavnic in jih ob vsaki delavnici dopolnjevali. sporoca, da vsa ta leta i.s.. cemo odgovor na vpra.ziti vse predpostavke standardnega modela, da bi sanje: Kako razlo.ponudilo ne le razumevanje vseh predpostavljenih lastnosti za kvarke in leptone in vsa bozonska polja, vklju. cno s Higgsovimi skalarji in gravitacijo, ampak bi tudi pojasnilo pojave, ki jih opazimo v vesolju. Ko poskusamo razumeti kvantno naravo fermionskih in bozonskih polj, i.s.. cemo teorijo brez anomalij, ki jo je mogo. ce renormalizirati, to je oceniti peispevke v vseh redih, tudi znotraj .crnih luknenj. Marsikateri prispevek je “nenavaden”, ker posku. sa nov, bolj verodostojen in bolj celosten na.cin razumevanja in opisovanja opa. zenih pojavov. Leto. snjenje leto je posebno: organizatorji Univerzo v Ljubljani prosijo za pomoc.pri ureditvi DOI. . Cetudi ostaja Dru.stvo matematikov, fzikov in astronomov Slovenije ostaja organizator Blejskih delavnic in smo mu zato hvale.s zalo. zni bo na.znik postala Fakulteta za matematiko in fziko skupaj z Univerzo v Ljubljani . Tehni. cni postopek je zdaj bolj zapleten, posledi.znost, da po.zenci prispevke “zadnji cno pa je mo.sljejo udele.trenutek“ manj.sa. Kar nekaj udele.casno poslati prispevka. Nekateri pa so zencen ni uspelo pravo.uspeli poslati povzetke, ki jih objavljamo. Njihove prispevke ostalih, bomo objavili v nasednjem zborniku, .zeleli, Od julija do novembra .ce, ce bodo .cas hitro ste.poisebej, ker je v tem obdobju tudi .cas.cpo.citnic. Organizatorji se iskreno zahvaljujejo vsem sodelujo.cinkovite cim na delavnici za u.predstavitve del, za .sje, kljub temu, da je zivahne razprave in dobro delovno vzdu.ve.zencev sodelovala preko spleta, ki ga je vodil Maxim Yu. Khlopov. cina udele.Bralec najde vse pogovore in kmalu tudi celoten Zbornik na uradni spletni strani delavnice: http://bsm.fmf.uni-lj.si/bled2023bsm/presentations.html, in na fo­rumu Cosmovia https://bit.ly/bled2023bsm .. Contents 1 The Swampland Program, Extra Dimensions, and Supersymmetry LuisA. Anchordoqui, Ignatios Antoniadis, and DieterL ust¨............... 1 2 Status of the DAMA project R. Bernabei,P. Belli,A. Bussolotti,V. Caracciolo,R. Cerulli,A. Leoncini,V. Merlo,F. Montecchia,F. Cappella,A. d’Angelo,A. Incicchitti,A. Mattei, C.J. Dai, X.H. Ma, X.D. Sheng, Z.P.Ye ...................................... 15 3 Balancing baryon and asymmetric dark matter excess V.A. Beylin,M.Yu. Khlopov,D.O. Sopin ............................... 26 4 Some Information-related aspects in fundamental particle modeling Elia Dmitrieff ....................................................... 36 5 Dispersion of Nonrelativistic and Ultrarelativistic Wave Packets on Cosmic Scales U. D. Jentschura and J. Nicasio ........................................ 50 6 Properties of fractons MaximYu. Khlopov, O.M. Lecian ...................................... 57 7 Recent advances of Beyond the Standard model cosmology MaximYu. Khlopov .................................................. 77 8 Multidimensional f(R)-gravity as the source of primordial black holes M.A. Krasnov,V.V. Nikulin ............................................ 87 9 How far has so far the Spin-Charge-Family theory succeeded to of­fer the explanation for the observed phenomena in elementary particle physics and cosmology N.S. Manko.stnik 97 c Bor................................................. 10 Clifford algebra, internal spaces of fermions and bosons, extened to strings N.S. Manko.c Bor.stnik, H.B. Nielsen .................................... 148 11 A Transformation Groupoid and Its Representation — A Theory of Dimensionality Euich Miztani ....................................................... 173 12 Our Dark Matter Stopping in Earth H.B. Nielsen and Colin D. Froggatt ..................................... 192 13 Deriving Locality, Gravity as Spontaneous Breaking of Diffeomor­phism Symmetry H.B. Nielsen ........................................................ 215 14 The gauge coupling unifcation in Grand Unifed Theories based on the group E8 K.V. Stepanyantz .................................................... 245 15 Clean energy from the dark Universe? K.Zioutasa,V. Anastassopoulosa,A.Argirioua,G. Cantatoreb,S. Cetinc,A. Gardikiotisa, H. Haralambouse, M. Karuzaf, A. Kryemadhig, M. Maroudasa, A. Mastronikolis,C. Oikonomoue,K. Ozbozdumani,Y.K. Semertzidisj,M. Tsagria, I.Tsagris .................................................... 267 16 Abstracts of talks presented at the Workshop and in the Cosmovia forum .................................................................... 277 17 Virtual Institute of Astroparticle physics as the online support for studies of BSM physics and cosmology MaximYu. Khlopov .................................................. 279 18 The Equation, a story A. Kleppe........................................................... 294 What Comes Beyond ... (p. 1) IN PHYSICS Bled, Slovenia, July 10–19, 2023 VOL. 24, NO. 1 1 The Swampland Program, Extra Dimensions, and Supersymmetry Luis A. Anchordoquia,b,c, Ignatios Antoniadisd,e, and Dieter L ¨ustf,g a Department of Physics and Astronomy, Lehman College, City University of New York, NY 10468, USA b Department of Physics, Graduate Center, City University of New York, NY 10016, USA c Department of Astrophysics, American Museum of Natural History, NY 10024, USA d Laboratoire de Physique Theorique et Hautes ´Energies -LPTHE, Sorbonne Universite,´ ´ CNRS, 4 Place Jussieu, 75005 Paris, France e Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, NY 10003, USA fMax–Planck–Institut f ¨ur Physik, Werner–Heisenberg–Institut, 80805 M ¨unchen, Germany gArnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universit¨at M ¨unchen, 80333 M ¨unchen, Germany Abstract. By combining swampland conjectures with observational data, it was recently suggested that the cosmological hierarchy problem (i.e. the smallness of the dark energy in Planck units) could be understood as an asymptotic limit in feld space, corresponding to a decompactifcation of one extra (dark) dimension of a size in the micron range. In these Proceedings we examine the fundamental setting of this framework and discuss general aspects of the effective low energy theory inherited from properties of the overarching string theory. We then explore some novel phenomenology encompassing the dark dimension by looking at potential dark matter candidates, decoding neutrino masses, and digging into new cosmological phenomena. Povzetek: Med domnevami, ki posku.ziti kozmolo. sajo razlo.ske meritve, se zdi sprejemljiva nedavno postavljena teza, da lahko majhnost temne energije (v Planckovih enotah), poznano pod imenom kozmolo.cni problem, pojasni domneva, da ima ena od razse. ski hierarhi.znosti vd > (3 + 1) velikost mikrona. V prispevku avtorjaji razis.. cjo veljavnost te predpostavke o temni dimenziji in razglabljajo o splo. snih lastnostih nizkoenergijske limite teorije strun. Ugotovijo, da lahko predpostavka o temni dimenziji prispeva k pojavu temne snovi v vesolju, napovedo masni spekter nevtrinov ter nove kozmolo.ske pojave. 1.1 Introduction The challenge for a fundamental theory of nature is to describe both particle physics and cosmology. Accelerator experiments and cosmological observations provide complementary information to constrain the same theory. We have long known that only about 4% of the content of the universe is ordinary baryonic matter; the remainder is dark matter (~ 22%) and dark energy (~ 74%). The .CDM model, in which the expansion of the universe today is dominated by the cosmological constant . and cold dark matter (CDM), is the simplest model that provides a reasonably good account of all astronomical and cosmological observations [1]. The cosmological evolution is described by Einstein’s equation, 1 8pG Rµ. - gµ.R + gµ.. = Tµ. , (1.1) 4 2c where Rµ. and R are respectively the Ricci tensor and scalar, gµ. is the metric tensor, Tµ. is the energy momentum tensor, and G = 1/(8pM2 ) is Newton’s p gravitational constant. The cosmological constant encapsulates two length scales: the size of the observable Universe [.]= L-2 and of the dark energy [./G × c3/h¯]= L-4. The observed value of the cosmological constant .obs ' 0.74 × 3H20/c2 ' 1.4 × (1026 m)-2 gives a characteristic length of dark energy ' 85 µm, where we have adopted the recent measurement of the Hubble constant H0 ' 73 km/s/Mpc by the HST + SH0ES team [2]. v At currently achievable collider center-of-mass energies s ~ 14 TeV or, equiv­alently, at distance scales < 10-21 m, the Standard Model (SM) of strong and electroweak interactions, amended with appropriate neutrino masses, provides a successful and predictive theoretical description of all available data [1]. The experimental success of the SM can be considered as the triumph of the gauge sym­metry principle to describe particle interactions. Its gauge structure is described by the symmetry group SU(3)C . SU(2)L . U(1)Y, with electroweak symmetry breaking at an energy scale of Mew ~ TeV. On the grounds of this, the masses of the weak force carriers (W± and Z0) are about 16 orders of magnitude smaller than Mp and so the weak force is 1024 times stronger than gravity. A way to connect these hierarchies between particle physics and cosmology is via the size of extra dimensions which are necessary ingredients for consistency of string theory [3]. Indeed, if their size is large compared to the fundamental (string) length, the strength of gravitational interactions becomes strong at distances larger than the actual four-dimensional (4D) Planck length [4, 5]. As a result, the string scale is detached from the Planck mass consistently with all experimental bounds if the observable universe is localized in the large compact space [5]. In these Proceedings we summarize the state-of-the-art in this subject area, and discuss future research directions. 1.2 Foundations of the Dark Dimension The Swampland program seeks to understand which are the “good” low-energy EFTs that can couple to gravity consistently (e.g. the landscape of superstring theory vacua) and distinguish them from the “bad” ones that cannot [6]. In theory space, the frontier discerning the good theories from those downgraded to the swampland is drawn by a family of conjectures classifying the properties that an EFT should call for/avoid to enable a consistent completion into quantum gravity. These conjectures provide a bridge from quantum gravity to astrophysics, cosmology, and particle physics [7–9]. For example, the distance conjecture (DC) forecasts the appearance of infnite towers of states that become exponentially light and trigger the collapse of the EFT at infnite distance limits in moduli space [10]. Connected to the DC is the anti-de Sitter (AdS) distance conjecture, which correlates the dark energy density to the mass scale m characterizing the infnite tower of states, m ~|.|a, as the negative AdS vacuum energy . . 0, with a a positive constant of O(1) [11]. Besides, under the hypothesis that this scaling behavior holds in dS (or quasi dS) space, an unbounded number of massless modes also pop up in the limit . . 0. As demonstrated in [12], applying the AdS-DC to dS space could help elucidate the radiative stability of the cosmological hierarchy ./M4 ~ 10-120, because it p connects the size of the compact space R. to the dark energy scale .-1/4 via R. ~ ..-1/4, where the proportionality factor is estimated to be within the range 10-1 < . < 10-4. Actually, the previous relation between R. and . derives from constraints by theory and experiment. On the one hand, since the associated Kaluza-Klein (KK) tower contains massive spin-2 bosons, the Higuchi bound [13] provides an absolute upper limit to a, whereas explicit string calculations of the vacuum energy (see e.g. [14–17]) yield a lower bound on a. All in all, the theoretical constraints lead to 1/4 = a = 1/2. On the other hand, experimental arguments (e.g. constraints on deviations from Newton’s gravitational inverse-square law [18] and neutron star heating [19]) lead to the conclusion encapsulated in R. ~ ..-1/4; namely, that there is one extra dimension of radius R. in the micron range, and that the lower bound for a = 1/4 is basically saturated [12]. A theoretical amendment on the connection between the cosmological and KK mass scales confrms a = 1/4 [20]. Assembling all this together, we can conclude that the KK tower of the new (dark) dimension opens up at the mass scale mKK ~ 1/R.. Within this set-up, the 5-dimensional Planck scale (or species scale where gravity 1/3 2/3 becomes strong [21–24]) is given by M* ~ mp . KK M It is of course interesting to explore whether there is a relation between the su­persymmetry (SUSY) breaking scale and the measured value of the dark energy density .. Such a relation can be derived by combining two quantum gravity consistency swampland constraints, which tie . and the gravitino mass M3/2, to the mass scale of a light KK tower and, therefore, to the UV cut-off of the EFT [25–27]. One can then use the constraint on M3/2 to infer the implications of the dark dimension scenario for the scale of supersymmetry breaking. In general, one can distinguish two situations. In the frst case, the gravitino mass and the cosmological constant are related to the same tower of states. This is arguably the simplest scenario, in which the natural scale for SUSY signatures is of order .1/8 ~ TeV, and therefore is within reach of LHC and of the next generation of hadron colliders [28]. In the second case, M3/2 and . are related to different towers. This scenario requires a decoupling of the gravitino mass from the cosmological constant and is thus more diffcult to realize in concrete models. Possible string theory and effective supergravity realizations of the dark dimension scenario with broken supersymmetry are discussed in [28]. 1.3 Dark Matter Candidates After the big bang, the cosmological energy density scales with time t as . ~ 1/(Gt2) and the density needed for a region of mass MBH to collapse within its Schwarzschild radius is . ~ c 6/(G3M2 BH), that being so primordial black holes (PBHs) would initially have around the cosmological horizon mass [29]  3 ct t MBH ~~ 1015 g . (1.2) G 10-23 s This means that a black hole would have the Planck mass (Mp ~ 10-5 g) if they formed at the Planck time (10-43 s), 1M if they formed at the QCD epoch (10-5 s), and 105M if they formed at t ~ 1 s, comparable to the mass of the holes thought to reside in galactic nuclei. This back-of-the-envelope calculation suggests that PBHs could span an enormous mass range. Despite the fact that the mass spectrum of these PBHs is not set in stone, on cosmological scales they would behave like a typical CDM particle. However, an all-dark-matter interpretation in terms of PBHs is severely constrained by observations [29–31]. The extragalactic .-ray background [32] and on the CMB spectrum [33] constrain PBH evaporation of black holes with masses . 1017 g, whereas the non-observation of microlensing events from the MACHO [34], EROS [35], Kepler [36], Icarus [37], OGLE [38] and Subaru-HSC [39] collaborations constrain black holes with masses & 1021 g. Of course it is of interest to see whether new effects associated to the dark dimension could relax these bounds. It has long been known that microscopic black holes – with Schwarzschild radii smaller than the size of the dark dimension – are quite different: they are bigger, colder, and longer-lived than a usual four-dimensional (4D) black hole of the same mass [40]. Indeed, black holes radiate all particle species lighter than or comparable to their temperature, which in four dimensions is related to the mass of the black hole by -1 M2 p MBH TBH = ~ MeV , (1.3) 8pMBH 1016 g whereas for fve dimensional black holes the temperature mass relation is found to be [41] r  .1/8 -1/2 31Mp MBH TBH = ~ MeV , (1.4) 64 p .1/2 M1/2 1010 g BH where we have taken . ~ 10-3 as suggested by astrophysical observations [42, 43]. It is evident that 5D black holes are colder than 4D black holes of the same mass. The Hawking radiation causes a 4D black hole to lose mass at the following rate [44] M2 X dMBH p fGs =- ci(TBH) ˜ dt 30720pM2 evap BH i -2 X ~ -7.5 × 10-8 MBH ci(TBH) ˜g/s , fGs (1.5) 1016 g i dMBH dt =- .1/4 M2 X Pl fGs ci(TBH) ˜ 640 p . MBH evap i X ~ -2.5 × 10-13 1 fGs g/s , (1.6) ci(TBH) ˜ MBH i where ci(TBH) counts the number of internal degrees of freedom of particle species i of mass mi satisfying mi  TBH, f˜ = 1 (f˜ = 7/8) for bosons (fermions), and where Gs=1/2 ˜ 2/3 and Gs=1 ˜ 1/4 are the (spin-weighted) dimensionless grey-body factors normalized to the black hole surface area [45]. In the spirit of [46], graviton emission can be neglected because the KK modes are excitations in the full transverse space, and so their overlap with the small (higher-dimensional) black holes is suppressed by the geometric factor (rs/R.)2 relative to the brane felds, where rs is the Schwarzschild radius [47]. Thus, the geometric suppres­sion precisely compensates for the enormous number of modes, and the total contribution of all KK modes is only the same order as that from a single brane feld. Now, integrating (1.5) and (1.6) it is easily seen that 5D black holes live longer than 4D black holes of the same mass. Armed with this result a straightforward calculation shows that for a species scale of O(109 GeV), an all-dark-matter in­terpretation in terms of 5D black holes must be feasible for masses in the range 1014