Conformal Freeze-in Sungwoo Hong Cornell work in progress with - PowerPoint PPT Presentation

Conformal Freeze-in Sungwoo Hong Cornell work in progress with Maxim Perelstein and Gowri Kurup Utah Workshop: Leaving no stone unturned!

I. Motivation / Question * Universe consistent with QM + SR * Universe described by QFT

I. Motivation / Question * Universe consistent with QM + SR * Universe described by QFT * Conventionally, cosmology via "particle" QFT

I. Motivation / Question * Universe consistent with QM + SR * Universe described by QFT * Conventionally, cosmology via "particle" QFT > mostly "particles" e.g. DM as massive particle DR as massless particle

I. Motivation / Question * Universe consistent with QM + SR * Universe described by QFT * Conventionally, cosmology via "particle" QFT > mostly "particles" e.g. DM as massive particle DR as massless particle > "Static" form of

I. Motivation / Question * In this talk, I will show a story where plays a crucial role in cosmology CFT

I. Motivation / Question * In this talk, I will show a story where plays a crucial role in cosmology CFT * No notion of "particle" with scale-inv.

I. Motivation / Question * In this talk, I will show a story where plays a crucial role in cosmology CFT * No notion of "particle" with scale-inv. > mostly "non-particles" => hot CFT > "varying" form of

I. Motivation / Question * In this talk, I will show a story where plays a crucial role in cosmology CFT * No notion of "particle" with scale-inv. > mostly "non-particles" => hot CFT > "varying" form of > dynamical description of light DM => mass gap via SM phase transitions

Outline II. Basic idea / Big picture III. Conformal Freeze-in IV. Light DM from COFI

II. Basic idea / Big picture O O M pl CFT SM ~ CFT D-4 CFT CFT T R D = d + d CFT SM v EW MeV (BBN) eV (CMB)

II. Basic idea / Big picture O O M pl CFT SM ~ CFT D-4 CFT CFT T R D = d + d CFT SM v EW * want to study SM <-> CFT MeV (BBN) dynamics at fi nite T eV (CMB)

II. Basic idea / Big picture * In order to see (i) why this set up is useful (ii) possible challenges

II. Basic idea / Big picture Note : (i) For any QFT, exists. T In particular, exists. T CFT

II. Basic idea / Big picture Note : (i) For any QFT, exists. T In particular, exists. T CFT homogeneity + isotropy => T = -P CFT -P -P 1 = Scale invariance => P 3 CFT

II. Basic idea / Big picture Note : 1 4 = => CFT ~ T (i-1) P 3 CFT . + 3 H ( + P) = C cf) CFT CFT (i-2) d can be non-integer CFT cf) d > j + j +2- CFT 2 j j ,0 1 1 2

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT * In usual particle case, (a) n = N/V well-de fi ned, (b) SM <=> DS at fi nite T by scattering and/or (inverse) decay

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT * In usual particle case, (a) n = N/V well-de fi ned, (b) SM <=> DS at fi nite T by . 2 2 n + 3 H n = - < v> (n - n ) eq

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT * In cases with CFT, (a) n = N/V not de fi ned, (b) SM <=> CFT at fi nite T requires <O O > at fi nite T CFT CFT

II. Basic idea / Big picture O O O CFT SM ( ) ~ ~ e ff CFT D-4 CFT SM SM CFT SM SM ~ <O O > CFT CFT SM SM vs T=0 T= fi nite

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT * In cases with CFT, (a) n = N/V not de fi ned, . . + 3 H ( + P) = + 4 H = C CFT CFT CFT CFT

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT * In cases with CFT, . (a) + 4 H = C CFT CFT <O O > fi nite T (b) In d>2, general CFT CFT Not known (cf. holographic CFT)

II. Basic idea / Big picture (ii) possible challenges O O CFT SM ~ CFT D-4 CFT * In cases with CFT, . (a) + 4 H = C CFT CFT (b) Calculable case: << SM CFT

II. Basic idea / Big picture . (a) + 4 H = C CFT CFT Calculable case: (b) << SM CFT => backreaction CFT->SM can be ignored => C = C(SM->CFT)

II. Basic idea / Big picture . (a) + 4 H = C CFT CFT Calculable case: (b) << SM CFT => backreaction CFT->SM can be ignored => C = C(SM->CFT) * assume: No Pauli-blocking/stimulated emission

III. Conformal Freeze-in * For concreteness, consider SM1 + SM2 -> CFT (only channel) = + SM CFT tot . + 3 H ( + P ) = 0 tot tot tot

III. Conformal Freeze-in * For concreteness, consider SM1 + SM2 -> CFT (only channel) = + SM CFT tot . + 3 H ( + P ) = 0 tot tot tot . + 4 H = 0 (RD) SM-{SM1,SM2} SM-{SM1,SM2} . + 4 H = -n n < v E > 1+2 2 1 1+2->CFT SM1+SM2 SM1+SM2

III. Conformal Freeze-in . + 4 H = +n n < v E > 1+2 1 2 1+2->CFT CFT CFT

III. Conformal Freeze-in . + 4 H = +n n < v E > 1+2 1 2 1+2->CFT CFT CFT *As usual, Naive Dim. Analysis can teach us essence of relevant physics. O O 2D-9 T C ~ 6 T => CFT 2 SM ~ CFT 2D-8 D-4 CFT CFT CFT

III. Conformal Freeze-in . + 4 H = +n n < v E > 1+2 1 2 1+2->CFT CFT CFT *As usual, Naive Dim. Analysis can teach us essence of relevant physics. O O 2D-3 CFT T C ~ 2 => CFT SM ~ CFT D-4 2D-8 CFT CFT

III. Conformal Freeze-in . + 4 H = +n n < v E > 1+2 1 2 1+2->CFT CFT CFT *As usual, Naive Dim. Analysis can teach us essence of relevant physics. O O 2D-3 CFT T C ~ 2 => CFT SM ~ CFT D-4 2D-8 CFT CFT *Detailed calculation to determine O(1) factor

III. Conformal Freeze-in . 2D-3 CFT T + 4 H = 2 2D-8 CFT CFT CFT

III. Conformal Freeze-in . 2D-3 CFT T + 4 H = 2 2D-8 CFT CFT CFT 1 1/2 T 2 H = = g (RD) * 2t 2 M pl . 2 3/2-D + = A t t CFT CFT D-3/2 2 M pl A= CFT 2D-8 D-3/2 1/2 (2g ) * CFT

III. Conformal Freeze-in . 2D-3 CFT T + 4 H = 2 2D-8 CFT CFT CFT 1 1/2 T 2 H = = g (RD) 2t * M pl . 2 3/2-D + = A t t CFT CFT -2 9/2-D CFT = t (A/( -D) t + B) 9 2

III. Conformal Freeze-in -2 9/2-D CFT = t (A/( -D) t + B) 9 2 8 T = 10 GeV CFT = 1 R 9 = 10 GeV CFT D=8/2 D-3/2 2 M pl A= CFT 2D-8 D-3/2 (2g ) 1/2 * CFT

III. Conformal Freeze-in 9/2-D -2 CFT = t (A/( -D) t + B) 9 2 8 T = 10 GeV CFT = 1 R 9 = 10 GeV CFT D=8/2 D=10/2 D-3/2 2 M pl A= CFT 2D-8 D-3/2 (2g ) 1/2 * CFT

III. Conformal Freeze-in -2 9/2-D CFT = t (A/( -D) t + B) 9 2 * We need : CFT << 1 => << CFT SM D<9/2 d > j + j +2- j j ,0 1 2 CFT 1 2 => d =non-integer CFT

III. Conformal Freeze-in * Freeze-in ends via (i) mass gaps m f e.g.) SM mass: M Dynamical mass gap: Gap

III. Conformal Freeze-in * Freeze-in ends via (i) mass gaps m f e.g.) SM mass: M Dynamical mass gap: Gap (ii) Phase transitions e.g.) SM sector: EWPT, QCD-PT

III. Conformal Freeze-in * Freeze-in ends via (i) mass gaps m f e.g.) SM mass: M Dynamical mass gap: Gap (ii) Phase transitions e.g.) SM sector: EWPT, QCD-PT CFT sector: conformality lost

IV. Light DM from COFI * We consider O = HQ q O = H H SM SM (Q,q=quarks)

IV. Light DM from COFI * We consider O = HQ q O = H H SM SM (i) SM PTs trigger COFI,

IV. Light DM from COFI * We consider O = HQ q O = H H SM SM (i) SM PTs trigger COFI, (ii) SM PTs terminate COFI,

IV. Light DM from COFI * We consider O = HQ q O = H H SM SM (i) SM PTs trigger COFI, (ii) SM PTs terminate COFI, (iii) SM PTs `generate' mass gap in CFT

IV. Light DM from COFI * We consider O = HQ q O = H H SM SM (i) SM PTs trigger COFI, (ii) SM PTs terminate COFI, (iii) SM PTs `generate' mass gap in CFT (vi) COFI provides dynamical description for light (10 keV - 10 MeV) DM !

IV. Light DM from COFI O = HQ q (1) SM M pl O O CFT SM ~ CFT D-4 CFT CFT T R D = d + d CFT v SM EW MeV (BBN) eV (CMB)

IV. Light DM from COFI O = HQ q (1) SM M pl O O CFT SM ~ CFT CFT D-4 CFT T R D = d + d CFT v SM EW * two parameters: MeV (BBN) CFT d CFT , eV D-4 (CMB) CFT

IV. Light DM from COFI O = HQ q (1) SM M pl O O CFT SM ~ CFT CFT D-4 CFT T R D = d + d CFT v SM EW * two parameters: MeV (BBN) => M CFT d CFT , Gap eV D-4 (CMB) CFT

IV. Light DM from COFI O = HQ q (1) SM M pl CFT T R v EW MeV (BBN) eV (CMB)

IV. Light DM from COFI O = HQ q (1) SM M pl O O CFT SM ~ CFT CFT D-4 T CFT R < 9/2 D = d + d CFT v SM EW MeV (BBN) eV (CMB)

IV. Light DM from COFI O = HQ q (1) SM M pl O O CFT SM ~ CFT CFT D-4 T CFT R < 9/2 D = d + d CFT v SM EW * T> v D > 4+1 = 5 EW MeV (BBN) eV (CMB)