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Gauge Fields and Physics of Inflation

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Gauge Fields and Physics of Inflation A New Paradigm for Particle Cosmology Azadeh Malek-Nejad November 2020 Virtual HET @ Brookhaven National Lab Background: Discover magazine PART ONE Motivation & Big Picture PART TWO All of the Exciting Details! Cosmic History Time CMB photon Energy Cosmic History Time CMB is nearly homogenous & isotropic! CMB photon T CMB =2.7 K with small fluctuation ∆푇 = 10−5! 푇CMB Energy Cosmic Inflation Time A period of exponential expansion of space shortly Inflation after the Big Bang 푎푎푓 CMB 푓 photon 푎푖 푎푓 = 푒60 ≈ 1026! 푎푖 Energy Cosmic Inflation Time A period of exponential expansion of space shortly Inflation after the Big Bang 푎푓 CMB photon 푎푖 푎푓 = 푒60 ≈ 1026! 푎푖 Bacterium 퐷 ≈ 10 휇푚 Way Milky Energy Cosmic Inflation Time What caused inflation? A scalar field “slow-rolling” Inflation toward its true vacuum CMB provides a simple model photon for inflation. Energy Quantum Vacuum ℏ ≠ ퟎ Due to Uncertainty Principle ℏ ∆푥 ∆푝 ≥ ൗ2 the quantum vacuum is NOT nothing! Simulation credit: Derek Leinweber Quantum Vacuum ℏ ≠ ퟎ Due to Uncertainty Principle ℏ ∆푥 ∆푝 ≥ ൗ2 the quantum vacuum is NOT nothing! But, a vast ocean made of Virtual particles Quantum Vacuum Particle Production Due to Uncertainty Principle Background field can upgrade them into actual particles! ∆푥 ∆푝 ≥ ℏൗ 2 Examples of such BG fields: the quantum vacuum is 1) Electric (Schwinger effect) NOT nothing! 2) Gravitational (Gravitational production) But, a vast ocean made of Virtual particles Actual particles BG field Cosmic Perturbations - density Exponential expansion turns CMB Matter initial quantum vacuum into Primordial 푎 푎푓 푖 CMB photon actual cosmic perturbations! We all came ultimately from quantum fluctuations! Energy Cosmic Perturbations – Gravitational Waves Inflation also predicts CMB B-mode primordial GWs: polarization CMB photon Primordial GW relic GWs Energy Cosmic Perturbations – Gravitational Waves o Inflation also predicts CMB B-mode primordial GWs: polarization 푣푎푐 ℎ푖푗=0 ℎ±= ℎ± o Unpolarizaed CMB photon 푣푎푐 2 푣푎푐 2 <| ℎ+ | >= <| ℎ− | > Primordial o Nearly Gaussian GW relic GWs Energy Cosmic Perturbations – Gravitational Waves o Inflation also predicts primordial GWs: 푣푎푐 ℎ푖푗=0 ℎ±= ℎ± o Unpolarizaed CMB photon 푣푎푐 2 푣푎푐 2 <| ℎ+ | >= <| ℎ− | > Primordial o Nearly Gaussian GW relic o CMB polarization GWs CMB CMB CMB Primordial Polarization LiteBIRD As Yet: o Observations are in perfect agreement with Inflation. o The Particle Physics of Inflation is still unknown. o The Standard models of inflation are based on Scalars. What about Gauge Fields? Why Gauge Fields during Inflation?! • Why not? I. Inflation happened at highest energy scales observable! II. Gauge fields are ubiquitous in physics & Energy building blocks of standard model (SM) and beyond. • What do they do in inflation? Can Gauge Fields Contribute to Physics of Inflation & leave an observable signature? 14 퐸퐼푛푓 ~< 10 퐺푒푉 Comparing to LHC 푬 Mission Impossible?! 푰풏풇 < ퟏퟎퟏퟏ ‼‼ 푬푳푯푪 ~ Challenges: Adding new terms 1) Conformal symmetry of Yang-Mills to the gauge theory gauge field decays like 퐴휇~ 1/푎 휅 (퐹퐹෨)2 384 2) Respecting gauge symmetry or 휆 Axion 퐹퐹෨ 휑 Not to break gauge symmetry explicitly 8푓 Jabbari, Jabbari, 2011 - 3) Spatial isotropy & homogeneity 풂 Sheikh SU(2) vacuum 푨흁 = 푨흁 푻풂 U(1) vacuum 푨흁 & 푎푏푐 [푻푎, 푻푏] = 휀 푻푐 A.M. 푧 푧 Spatially isotropic 3 푨 = 푸 풕 휹ퟑ 풂 풂 퐴푧 풊 풊 푨풊 = 푸 풕 휹풊 1 푦 퐴푥 2 푦 퐴푦 푥 푥 so(3) & su(2) are isomorphic Why Gauge Fields during Inflation?! Non-Abelian Gauge fields can contribute to inflation & respect spatial isotropy! A new class of inflation models with SU(2) gauge fields & axions, SU(2)-axion models! It opens a New Window to Particle Cosmology: A.M. & Sheikh-Jabbari, 2011 Novel Observable Signatures e.g. Chiral, non-Gaussian GWs! SU(2)-axion Inflation: a Complete Setup SM of Particle Physics, the most Fundamental discrete Symmetries and their rigorous theory of physics cannot violation played a key role in understanding explain Cosmology! SM, e.g. C & P violation in weak interactions, CP violation to explain matter asymmetry. Big Questions of modern Cosmology & Particle Physics: Yet, it is mostly assumed that physics of inflation is P and CP symmetric. I) ) Particle physics of Inflation, II) Origin of matter asymmetry, SU(2)-axion inflation III) Particle nature of DM, Spontaneously breaks P and CP and relates all of these seemingly IV) Primordial GWs unrelated Phenomena in early and late (only missing prediction of inflation) cosmology! SU(2) Gauge fields and Inflation: Two examples • Gauge-flation A. M. & Sheikh-Jabbari, 2011 푅 1 휅 푆 = න푑4푥 −푔 − − 퐹2 + (퐹퐹෨)2 퐺푓 2 4 384 • Chromo-natural P. Adshead, M. Wyman, 2012 푅 1 1 휑 휆 푆 = න푑4푥 −푔 − − 퐹2 − (휕 휑)2 − 휇4 1 + cos( ) − 휑퐹퐹෨ 퐶푛 2 4 2 휇 푓 8푓 • Inspired by them, several different models with SU(2) fields have been proposed and studied. A New Window to Particle Cosmology A. M. and M. M. Sheikh-Jabbari, 2011 • SU(2)-axion models acquire a vacuum P. Adshead, M. Wyman, 2012 during inflation. This vacuum violates Parity! P & A. M. 2014 & 2016 • Particles with spin, e.g. Fermions & Vacuum structure of SU(2)-axion inflation Axion field Spin-2 fields are sensitive to this non-trivial Vacuum during inflation! • Pre-Hot Big Bang Particle Production! SU(2) field ( during inflation) A.M. 2019 Particle Production Virtual particles • Vacuum is a vast ocean of virtual particles & • Background field upgrades it to actual particles! BG fields Background Gauge field (Schwinger effect) • In flat space, it has never been observed, E > 1018푉/푚. Actual particles • Schwinger particle production is important in Physics of Inflation: Particle Production during Inflation! time A New Window to Particle Cosmology A. M. et al, 2011 P. Adshead, et al, 2012 Cosmic Inflation 2019 2018 Lozanov This vacuum violates Parity! P & A. M. 2014 & 2016 A.M., , A. M. , E. Komatsu E.M. , A. A.M., 2019 A.M., A. M. et. al, 2011 & 2013 Mirzagholi Dimastrogiovanni et. al 2013 Lozanov, A. M., Komatsu 2018 Particle Production P. Adshead et. al,2013 (during Inflation) A.M., 2019 A. M, 2014 & 2016 A. M. et. al, 2013 R. Caldwell, C. Devulder, 2017 P. Adshead et. al 2013 ℎ ≠ ℎ P. Adshead et. al 2017 Observables Dimastrogiovanni et. al 2013 + − S. Alexander et. al 2018 A New Window to Particle Cosmology A. M. et al, 2011 • New tensorial field in perturbed SU(2): P. Adshead, et al, 2012 푎 푎 훿A푖 ∋ 퐵푖푗훿푖 2018 2 2 • It is Chiral <|퐵+| >≠ <|퐵−| > P & A. M. 2014 & 2016 • linearly coupled to Gravitational Waves (GWs) Komatsu E.M. , A. A. M. et. al, 2011 & 2013 Dimastrogiovanni et. al 2013 ℎ푖푗= -16휋G 훿훱푖푗 P. Adshead et. al,2013 푠 ℎ ≠ ℎ 푣푎푐 푠 ℎ± is Chiral &ℎ+ ≠ ℎ− ℎ±= ℎ± + ℎ± A. M. et. al, 2013 & non-Gaussian P. Adshead et. al 2013 Vacuum Sourced Dimastrogiovanni et. al 2013 • Novel Observable Signatures on CMB! ℎ+ ≠ ℎ− Future CMB missions, e.g. LiteBIRD & CMB-S4, will nail it! A New Window to Particle Cosmology A. M. et al, 2011 • New Spin-2 field in perturbed SU(2): P. Adshead, et al, 2012 푎 푎 훿A푖 ∋ 퐵푖푗훿푖 2018 • It is Chiral 퐵푅 ≠ 퐵퐿 P & A. M. 2014 & 2016 • linearly coupled to Gravitational Waves Komatsu E.M. , A. A. M. et. al, 2011 & 2013 Dimastrogiovanni et. al 2013 ℎ푖푗= -16휋G 훿훱푖푗 P. Adshead et. al,2013 푣푎푐 푠 ℎ±= ℎ± + ℎ± A. M. et. al, 2013 P. Adshead et. al 2013 Dimastrogiovanni et. al 2013 • in inflation so it is a natural setting for CP ℎ+ ≠ ℎ− A. M, 2014 & 2016 leptogenesis to explain the matter asymmetry! A New Window to Particle Cosmology • Scalar doublet, and Dark Fermions charged under the Primordial SU(2) 2019 will be created by it! Lozanov P & A. M. 2014 & 2016 A.M., , 2019 • A.M., They will backreact to it as well. Mirzagholi Lozanov, A. M., Komatsu 2018 • A new non-thermal mechanism for generating Dark Fermions during Inflation! A.M., 2019 • This Dark fermions can be part of Dark Matter today. Gauge Fields in Inflation Gauge Fields CMB Primordial photon GWs Spontaneous CP Chiral & non-Gaussian Inflationary Primordial Dark & Leptogenesis GW Energy PART TWO: (the exciting details) o SU(2)-Axion Model Building o Particle Production in Inflation SU(2)-Axion Model Building How su(2) algebra restores the spatial isotropy? Let us work in temporal gauge, 퐴0 = 0. 푧 U(1) vacuum 퐴휇 3 A푖 = 푄 푡 훿푖 푦 푥 푎 SU(2) VEV, 퐴휇 = 퐴휇 푇푎 Isomorphy of so(3) & su(2) algebras 푎 푎 푧 A푖 = 푄 푡 훿푖 푧 푧 3 3 퐴푧 퐴푧 1 푦 푦 1 푦 퐴푥 2 퐴푥 2 퐴푦 퐴푦 A.M. and M. M. Sheikh-Jabbari, 2011 푥 푥 푥 SU(2)-Axion Model Building • Gauge-flation A. M. and M. M. Sheikh-Jabbari, 2011 푅 1 휅 푆 = න푑4푥 −푔 − − 퐹2 + (퐹퐹෨)2 퐺푓 2 4 384 • Chromo-natural P. Adshead, M. Wyman, 2012 푅 1 1 휑 휆 푆 = න푑4푥 −푔 − − 퐹2 − (휕 휑)2 − 휇4 1 + cos( ) − 휑퐹퐹෨ 퐶푛 2 4 2 휇 푓 8푓 • Inspired by them, several different models with SU(2) fields have been proposed and studied. An incomplete list of Different Realizations of the Setup: 1. A. M. and M. M. Sheikh-Jabbari, Phys. Rev. D 84:043515, 2011 [arXiv:1102.1513] 2. P. Adshead, M. Wyman, Phys. Rev. Lett.(2012) [arXiv:1202.2366] 0 0 3. A. M. JHEP 07 (2016) 104 [arXiv:1604.03327] 0 0 4. C. M. Nieto and Y. Rodriguez Mod. Phys. Lett. A31 (2016) [arXiv:1602.07197] 1 0 5. E. Dimastrogiovanni, M.
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