Holographic Models with a Small Cosmological Constant at

Holographic Models with a Small Cosmological Constant at Finite T Based on Work in progress with Jay Hubisz, Don Bunk [ar. Xiv: 1505. xxxxx] Bithika Jain Syracuse University PHENO, May 4 th , 2015 Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 1

Ad. S/CFT phenomenological correspondence Randall Sundrum I Setup UV brane IR brane UV cutoff Explicit breaking y 0 y 1 IR CFT scale y Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T Spontaneous breaking PHENO’ 15 2

Ad. S/CFT phenomenological correspondence Some RS models plagued by eternal inflation 1 1 Creminelli Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T et. al (2001) PHENO’ 15 3

Models with “soft wall” breaking • Soft-wall Model Bulk scalar potential with “soft” dependence on ϕ ⇒ Spontaneous breaking of scale 2 Bellazzini et. al (2013 ) invariance (SBSI) 2 UV Soft wall geometric model of SBSI IR Bulk scalar profile Soft wall generic when IR brane tension >0 IR brane plays subdominant role: just cuts off growth of scalar field and curvature Bithika Jain (Syracuse U) Cond , f ≠Ad. S ~ Ad. S y=y 0 y=yc Holographic models with small cosmological constant at Finite T y=y 1 PHENO’ 15 4

Zero temperature Weak scalar field dependence Using holography to compute the effective dilaton (f) potential Vdilaton CC small Light dilaton Soft wall realisation of small condensate contribution to CC in models with non-linearly realised SBSI Different from GW mechanism Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 5

Finite temperature Geometry includes a black hole horizon at a finite point, yh in extra dimension, y. Black Brane Hawking radiation from this BH allows BH to reach in equilibrium with thermal bath. UV Partition function associated with these Classical solutions Free energy of system y 0 yh y Free energy, V = VUV + Vhorizon = U – T S IR brane has been replaced with a BH horizon at yh Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 6

Finite Temperature backre action UV No backreaction y 0 yh y With back-reaction included Phase transition would occur at higher temperatures Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 7

Phase transitions Black hole solution Warped solution dominated by the scalar field f Dominates the bubble action At T=Tc , first order phase transition occurs At T<Tc system is in warped scalar field dependent phase Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 8

Bubble nucleation System at T = Tc In 4 D , True vacuum bubble forms In 5 D, spherical brane patches form on the horizon Bithika Jain (Syracuse U) Expands until false vacuum bubble disappears. They expand coalesce to form a complete 3 -brane Holographic models with small cosmological constant at Finite T PHENO’ 15 9

Bubble nucleation • 3 Randall, Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T Servant (2007) PHENO’ 15 10

Summary • We have explored “soft-wall” realization of the Randall Sundrum geometry • SBSI manifests as continuous geometry (soft wall SBSI ) with IR brane playing lesser role of a cutoff • As the universe cools, a first order phase transition between two phases, Ad. S-S like (high T) to warped geometry (low T) occurs • Back reaction is a crucial element in assisting phase transition at high T • Punchline: no eternal inflation ⇒ cosmology is safe (bubble nucleation rates faster than RS ) Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 11

TH Bithika Jain (Syracuse U) NK YOU! Holographic models with small cosmological constant at Finite T PHENO’ 15 12

Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 13

Cosmological Constant Problem Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 14

Cosmological constant problem • Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 15

Different approaches to CC Problem • Deep symmetries – SUSY in flat space claims to solve the CC problem halfway (on a log scale) – In curved space time- Supergravity has to be considered – fine tuning can fantastically make the Kahler derivative vanish and give small CC(? ) • Miscellaneous Adjustment Mechanisms – Conformal invariance canceling gravity effects to give small CC – SEH+ scalar , which evolves to make CC vanish …. . • Anthropic principle – ``observers will only observe conditions which allow for observers'' Any solution to the CC problem is likely to have a wider impact on other areas of physics/astronomy Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 16

RS model – CC problem UV brane Tuned brane tension For zero CC Te. V brane y 0 5 D Bulk IR CFT scale y 1 Spontaneous breaking Tuned brane tension for Zero radion potential y Goldberger Wise Mechanism: Prevents branes from colliding or flying away V 1 and V 0 depend on scalar field ϕ Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 17

Scaling and Dilaton Basics • Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 18

Spontaneous breaking • Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 19

Dilaton Quartic • Dilaton quartic → not allowed in standard Goldstone Boson Plays a crucial role in SBSI Obstruction to SBSI (Fubini’ 76), 3 possibilities a>0→f=0 (no breaking) Bithika Jain (Syracuse U) a < 0 → f =� (runaway) a=0 → f= anything (flat direction) Holographic models with small cosmological constant at Finite T PHENO’ 15 20

Near-marginal deformation Add Explicit breaking term with an almost marginal operator • Near marginal Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 21

Dilaton mass Explicit breaking Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 22

Various dynamical possibilities Non- SUSY walking Tuned Non- SUSY walking + RS GW Bithika Jain (Syracuse U) N=4 SUSY Non- SUSY with light dilaton Holographic models with small cosmological constant at Finite T PHENO’ 15 23

Various dynamical possibilities Non- SUSY walking Tuned Non- SUSY walking + RS GW Bithika Jain (Syracuse U) N=4 SUSY Non- SUSY with light dilaton Holographic models with small cosmological constant at Finite T PHENO’ 15 24

* CPR proposal • Dynamical (theory space) requirement Explicit breaking at condensate scale Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 25

Basic Principle Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 26

Ad. S/CFT phenomenological correspondence Adding explicit breaking perturbation in Ad. S/CFT 4 D effective Lagrangian Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 27

Generalized Randall-Sundrum 5 D scalar minimally coupled to gravity Bellazzini, Csaki, Hubisz, Terning, Serra, ’ 13 Coradeschi, Lodone, Pappadopulo, Rattazzi, Vitale, ’ 13 New notation !! Ad. S/CFT: EOM captures running even when far from Ad. S Deviations from Ad. S encoded in G(y) Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 28

Scalar Einstein Equations of motion: Eliminate G(y) in the scalar field EOM to get the Master Evolution equation : Backreaction term Captures running (and condensation) of sourced operators in ~CFT Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 29

Dilaton effective potential Bulk action → total derivative (Bellazini et. al. 1305. 3919) Entire effective potential= boundary term with brane localized potentials and jump conditions UV brane IR brane What is the behaviour of the dilaton effective potential for various bulk scalar potentials? (various deformations of CFT) Task = work out UV and IR asymptotics How is spontaneously broken scale invariance manifested? Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 30

General Bulk Potentials (UV) Small Bulk mass Term Approximate (small backreaction) solution: Slow running Almost Ad. S UV contribution to dilaton effective potential Bare CC Bithika Jain (Syracuse U) marginal “almost quartic” Holographic models with small cosmological constant at Finite T PHENO’ 15 31

General Bulk Potentials (IR) Φ in the deep IR: Solutions independent of V(ϕ) Now, In deep IR Expand scalar EOM in small δv Integrable in asymptotic limit! Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 32

Dilaton Potential Bare CC set to zero At min CC is suppressed by ϵ! / Neff Soft wall realisation of small condensate contribution to CC in models with non-linearly realised SBSI Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 33

Finite temperature Black hole in Ad. S Same action-euclidean signature, compactified time, t⊂ {0, � =1/T} EOMs Master Evolution Equation Horizon BCs : Holographic Dilaton Potential: Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 34

Black brane thermodynamics • At finite T, we have 2 different bulk spaces: warped and Ad. S-S describing states of thermodynamics equillibrium • Canonical ensemble of Ad. S space = Ad. S- Schwarzschild (Ad. S- S) (Hawing, Page’ 83) Th Black hole horizon hawking radiation Hot bulk • Universe filled with Thermal CFT state with Th • Energy & Entropy of heat bath described by corresponding Black hole Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 35

Transition rate Bithika Jain (Syracuse U) Holographic models with small cosmological constant at Finite T PHENO’ 15 36