COSMOLOGICAL GRAVITATIONAL WAVES DANIEL G. FIGUEROA IFIC, Valencia, - - PowerPoint PPT Presentation

COSMOLOGICAL GRAVITATIONAL WAVES

September 23-27 2019, Kavli-RISE ‘summer' school on Gravitational Waves

DANIEL G. FIGUEROA

IFIC, Valencia, Spain

[LIGO & Virgo Scientific Collaborations]

[LIGO & Virgo Scientific Collaborations (arXiv:1602.03841)]

Straight to the point …

Gravitational Waves (GWs) detected ! [by LIGO/VIRGO]

[LIGO & Virgo Scientific Collaborations]

Straight to the point …

Gravitational Waves (GWs) detected !

Einstein 1916 … LIGO/VIRGO 2015/16/17

[LIGO & Virgo Scientific Collaborations (arXiv:1602.03841)]

[by LIGO/VIRGO]

m i l e s t

• n

e i n p h y s i c s

[LIGO & Virgo Scientific Collaborations]

Straight to the point …

Gravitational Waves (GWs) detected ! [by aLIGO]

* O(10) Solar mass Black Holes (BH) exist * We can observe the Universe through GWs * … * We can further test General Relativity (GR)

[so far no deviation]

m i l e s t

• n

e i n p h y s i c s

* We can test the BH's paradigm and Neutron Star physics

Straight to the point …

* O(10) Solar mass Black Holes (BH) exist * We can observe the Universe through GWs * … * We can further test General Relativity (GR)

[so far no deviation]

Extremely interesting ! but … … I will focus

• n something else !

(binaries)

* We can test the BH's paradigm and Neutron Star physics

Straight to the point …

* O(10) Solar mass Black Holes (BH) exist * We can observe the Universe through GWs * … * We can further test General Relativity (GR)

[so far no deviation]

Extremely interesting ! but … … I will focus

• n something else !

(binaries)

* We can test the BH's paradigm and Neutron Star physics

Stay tuned ! many results guaranteed to come …

Straight to the point …

* O(10) Solar mass Black Holes (BH) exist * We can observe the Universe through GWs * … * We can further test General Relativity (GR)

[so far no deviation]

Extremely interesting ! but … … I will focus

• n something else !

(binaries)

* We can test the BH's paradigm and Neutron Star physics

* O(10) Solar mass Black Holes (BH) exist * We can observe the Universe through GWs * … * We can further test General Relativity (GR)

[so far no deviation]

* We can test the BH's paradigm (or Neutron Star physics)

Extremely interesting ! but … … We will focus

• n something else !

(binaries)

Stay tuned ! more fun guaranteed to come …

* We can observe the Universe through GWs

* We can observe the Universe through GWs

* Cosmology with GWs

* We can observe the Universe through GWs

* Cosmology with GWs

* Late Universe: Hubble diagram from Binaries * Early Universe: High Energy Particle Physics

* We can observe the Universe through GWs

* Cosmology with GWs

* Late Universe: Hubble diagram from Binaries * Early Universe: High Energy Particle Physics

* We can observe the Universe through GWs

* Cosmology with GWs

* Late Universe: Hubble diagram from Binaries * Early Universe: High Energy Particle Physics

Can we really probe High Energy Physics using Gravitational Waves (GWs) ? How ?

GWs: probe of the early Universe

Cosmic Defects

Motivation ?

1

WEAKNESS of GRAVITY: ADVANTAGE: GW DECOUPLE upon Production DISADVANTAGE: DIFFICULT DETECTION

2

ADVANTAGE: GW → Probe for Early Universe → ⇢ Decouple → Spectral Form Retained Specific HEP ⇔ Specific GW

3

Physical Processes: 8 > > < > > : Inflation Reheating Phase Transitions Turbulence

GWs: probe of the early Universe

Cosmic Defects

@ Early Universe

1

WEAKNESS of GRAVITY: ADVANTAGE: GW DECOUPLE upon Production DISADVANTAGE: DIFFICULT DETECTION

2

ADVANTAGE: GW → Probe for Early Universe → ⇢ Decouple → Spectral Form Retained Specific HEP ⇔ Specific GW

3

Physical Processes: 8 > > < > > : Inflation Reheating Phase Transitions Turbulence

GWs: probe of the early Universe

Cosmic Defects

@ Early Universe

What processes of the early Universe ?

Particle Production

(∆t . 1s)

Cosmic Defects Quantum Fluctuations Phase Transitions

The Early Universe

Particle Production Phase Transitions

(∆t . 1s)

Quantum Fluctuations Cosmic Defects

The Early Universe

Particle Production Phase Transitions

(∆t . 1s)

Cosmic Defects Quantum Fluctuations

The Early Universe

Particle Production

(∆t . 1s)

Phase Transitions

GWs

The Early Universe

Cosmic Defects Quantum Fluctuations

Particle Production

(∆t . 1s)

Phase Transitions

Probe of the early Universe

GWs

The Early Universe

Cosmic Defects Quantum Fluctuations

Particle Production

(∆t . 1s)

Phase Transitions

Probe of the early Universe

GWs

The Early Universe

Cosmic Defects Quantum Fluctuations

‘Holy Grail’ of Stochastic GW Backgrounds

(N. Christensen, Moriond'19)

0) GWs in Cosmology (def.) OUTLINE 1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects Early Universe

Gravitational Waves in Cosmology

• GW: ds2 = a2(dη2 + (δij + hij)dxidxj),

TT : ⇢ hii = 0 hij,j = 0

FRW:

Transverse-Traceless (TT)

Gravitational Waves in Cosmology

• GW: ds2 = a2(dη2 + (δij + hij)dxidxj),

TT : ⇢ hii = 0 hij,j = 0

FRW: ⇢ Eom: h00

ij + 2Hh0 ij r2hij = 16πGΠTT ij ,

Πij = Tij hTiji

FRW

Transverse-Traceless (TT) dof carry energy out of the source!!

Source: Anisotropic Stress

Creation/Propagation GWs

Transverse-Traceless (TT)

Gravitational Waves in Cosmology

• GW: ds2 = a2(dη2 + (δij + hij)dxidxj),

TT : ⇢ hii = 0 hij,j = 0

FRW:

• GW Source(s): ( SCALARS

, VECTOR , FERMIONS ) ΠT T

ij

/ {∂iχa∂jχa}T T , {EiEj + BiBj}T T , { ¯ ψγiDjψ}T T

⇢ Eom: h00

ij + 2Hh0 ij r2hij = 16πGΠTT ij ,

Πij = Tij hTiji

FRW

Transverse-Traceless (TT) dof carry energy out of the source!!

Source: Anisotropic Stress

Creation/Propagation GWs

Transverse-Traceless (TT)

0) GW definition

Gravitational Waves as a probe of the early Universe

OUTLINE 1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects Early Universe

COSMIC INFLATION

1 cm 10 cm

28

Needed for Consistency of the Big Bang theory

a ∼ eH∗t & e60

Inflation (basics)

Irreducible GW background from Inflation

gµν = g(B)

µν + δgµν

[δgµν]TT = hij

⇢ hii = 0 ∂ihij = 0

, ;

Irreducible GW background from Inflation

Quantum

Fluctuations

gµν = g(B)

µν + δgµν

[δgµν]TT = hij

⇢ hii = 0 ∂ihij = 0

, ;

Irreducible GW background from Inflation

Quantum

Fluctuations

D hij(~ k, t)h⇤

ij(~

k0, t) E ≡ (2⇡)3 2⇡2 k3 ∆2

h(k)(~

k − ~ k0)

D hij(~ k, t) E = 0

gµν = g(B)

µν + δgµν

[δgµν]TT = hij

⇢ hii = 0 ∂ihij = 0

, ;

Irreducible GW background from Inflation

Quantum

Fluctuations

D hij(~ k, t)h⇤

ij(~

k0, t) E ≡ (2⇡)3 2⇡2 k3 ∆2

h(k)(~

k − ~ k0)

D hij(~ k, t) E = 0

gµν = g(B)

µν + δgµν

[δgµν]TT = hij

⇢ hii = 0 ∂ihij = 0

, ;

energy scale

∆2

h(k) = 2

π2 ✓ H mp ◆2 ✓ k aH ◆nt

nt ≡ −2✏

Irreducible GW background from Inflation

∆2

h(k) = 2

π2 ✓ H mp ◆2 ✓ k aH ◆nt

energy scale

nt ≡ −2✏

Irreducible GW background from Inflation

Ω(o)

GW(f) ≡

1 ρ(o)

c

✓d log ρGW d log k ◆

• = Ω(o)

Rad

24 ∆2

h∗(k)

∆2

h(k) = 2

π2 ✓ H mp ◆2 ✓ k aH ◆nt

}

T(k) ∝ k0(RD)

Transfer Funct.:

energy scale

nt ≡ −2✏

Irreducible GW background from Inflation

Ω(o)

GW(f) ≡

1 ρ(o)

c

✓d log ρGW d log k ◆

• = Ω(o)

Rad

24 ∆2

h∗(k)

∆2

h(k) = 2

π2 ✓ H mp ◆2 ✓ k aH ◆nt nt ≡ −2✏

• 18.0
• 14.0
• 10.0
• 6.0
• 2.0

2.0 6.0 10.0 Log[f]

• 16.0
• 14.0
• 12.0
• 10.0
• 8.0
• 6.0

Log[h0

2ΩGW]

scale-invariant (RD modes) (MD modes)

ΩGW ∝ 1/k2

r e d t i l t e d ( q u a s i

• )

s c a l e

• i

n v a r i a n t ( R D m

• d

e s )

}

T(k) ∝ k0(RD)

Transfer Funct.: aLIGO LISA

energy scale

Quantum

Fluctuations

Irreducible GW background from Inflation

Ω(o)

GW(f) ≡

1 ρ(o)

c

✓d log ρGW d log k ◆

• = Ω(o)

Rad

24 ∆2

h∗(k)

∆2

h(k) = 2

π2 ✓ H mp ◆2 ✓ k aH ◆nt nt ≡ −2✏

• 18.0
• 14.0
• 10.0
• 6.0
• 2.0

2.0 6.0 10.0 Log[f]

• 16.0
• 14.0
• 12.0
• 10.0
• 8.0
• 6.0

Log[h0

2ΩGW]

scale-invariant (RD modes) (MD modes)

ΩGW ∝ 1/k2

r e d t i l t e d ( q u a s i

• )

s c a l e

• i

n v a r i a n t ( R D m

• d

e s )

}

T(k) ∝ k0(RD)

Transfer Funct.: aLIGO LISA

energy scale

Quantum

Fluctuations

Not Observable !

Irreducible GW background from Inflation

Ω(o)

GW(f) ≡

1 ρ(o)

c

✓d log ρGW d log k ◆

• = Ω(o)

Rad

24 ∆2

h∗(k)

∆2

h(k) = 2

π2 ✓ H mp ◆2 ✓ k aH ◆nt nt ≡ −2✏

• 18.0
• 14.0
• 10.0
• 6.0
• 2.0

2.0 6.0 10.0 Log[f]

• 16.0
• 14.0
• 12.0
• 10.0
• 8.0
• 6.0

Log[h0

2ΩGW]

scale-invariant (RD modes) (MD modes)

ΩGW ∝ 1/k2

r e d t i l t e d ( q u a s i

• )

s c a l e

• i

n v a r i a n t ( R D m

• d

e s )

}

T(k) ∝ k0(RD)

Transfer Funct.: aLIGO LISA

energy scale

Quantum

Fluctuations

e x c e p t ( p e r h a p s ) i n d i r e c t l y , i n C M B …

Not Observable !

Irreducible GW background from Inflation

Dashed Line Theoretical Inflation Expectation

r ∼ 10−2 − 10−3 ⇒ E∗ ∼ 5 · 1015GeV

r ≡ ∆t/∆s < 0.07 (2σ) (!) Planck/Keck next goal

2 2

⌦ E2↵ , ⌦ B2↵ → ⌦ |elm|2↵ ≡ CE

l ,

⌦ |blm|2↵ ≡ CB

l

B- MODE: Depends only

• n Tensor Perturbations !

Search of B-modes @ CMB, might be only change to detect Inflationary Tensors !

Ground: AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G Balloons Satellites EBEX 10k, Spider CMBPol, COrE, LiteBIRD,

Irreducible GW background from Inflation

⌦ E2↵ , ⌦ B2↵ → ⌦ |elm|2↵ ≡ CE

l ,

⌦ |blm|2↵ ≡ CB

l

B- MODE: Depends only

• n Tensor Perturbations !

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

=

{

Primordial perturbations

Tensor Scalar Irreducible GW Background

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

=

{

Scenarios Primordial perturbations

Tensor Scalar Irreducible GW Background Enhanced GWs Enhanced Scalar Pert. Extra species/symmetries Modified Gravity, spectator fields, graviton mass, …

{

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

=

{

Scenarios Primordial perturbations

Tensor Scalar Enhanced GWs Enhanced Scalar Pert. Extra species/symmetries Modified Gravity, spectator fields, graviton mass, …

{

Irreducible GW Background

INFLATIONARY MODELS

• Shift symmetry φ ! φ + C on c

inflaton = pseudo-scalar axion

ϕ V (ϕ) + α f Fµν ˜ F µν

Freese, Frieman, Olinto ’90; . . .

aine

during lue

Axion-Inflation

ϕ → ϕ + const.

• ⇤ Not the QCD axion;

ϕ

INFLATIONARY MODELS

• Shift symmetry φ ! φ + C on c

[J. Cook, L. Sorbo (arXiv:1109.0022)] [N. Barnaby, E. Pajer, M. Peloso (arXiv:1110.3327)]

inflaton = pseudo-scalar axion

ϕ

Chiral instability

∂2 ∂τ 2 + k2 ± 2kξ τ

• A±(τ, k) = 0,

ξ ≡ α ˙ φ 2fH

Photon: ! 2 helicities

A+ / eπξ , |A−| ⌧ |A+|

A+ exponentially amplified, !

V (ϕ) + α f Fµν ˜ F µν

Freese, Frieman, Olinto ’90; . . .

aine

during lue

Axion-Inflation

ϕ → ϕ + const. ϕ

˙ ϕ

INFLATIONARY MODELS

chiral GWs !

: h00

ij + 2Hh0 ij r2hij = 16πGΠTT ij , ,

{EiEj + BiBj}T T

∝ Chiral Aµ GW left-chirality only !

inflaton = pseudo-scalar axion

ϕ V (ϕ) + α f Fµν ˜ F µν

• Shift symmetry φ ! φ + C on c

Freese, Frieman, Olinto ’90; . . .

aine

during lue

ϕ → ϕ + const.

Axion-Inflation

ϕ

INFLATIONARY MODELS

Gauge fields ! source a! Blue-Tilted ! + Chiral! + Non-G! GW background GW energy spectrum today

vacuum fluctuations LISA

Axion-Inflation

Bartolo et al ’16, 1610.06481 Critical view: Ferreira et al, 1512.06116

INFLATIONARY MODELS

Gauge fields ! source a! Blue-Tilted ! + Chiral! + Non-G! GW background GW energy spectrum today

vacuum fluctuations LISA

Axion-Inflation

L I S A c a n d e t e c t t h i s b a c k g r

• u

n d !

Bartolo et al ’16, 1610.06481 Critical view: Ferreira et al, 1512.06116

What if there are arbitrary fields coupled to the inflaton ?

(i.e. no need of extra symmetry)

large excitation of fields !?

will they create GWs?

−Lχ = (∂χ)2/2 + g2(φ φ0)2χ2/2,

Lψ = ¯ ψγµ∂µψ + g(φ φ0) ¯ ψψ,

L = 1

4FµνF µν |(∂µ gAµ)Φ)|2 V (Φ†Φ) [ iθ

Scalar Fld Fermion Fld Gauge Fld

• |

d Φ = φeiθ

( )

e inflaton φ

V (φ)

INFLATIONARY MODELS

What if there are arbitrary fields coupled to the inflaton ?

(i.e. no need of extra symmetry)

large excitation of fields !?

will they create GWs?

INFLATIONARY MODELS

s m = g(φ(t) φ0) v

All 3 cases:

s ˙ m m2,

∆tna ⇠ 1/µ , µ2 ⌘ g ˙ φ0 ,

during

⇠ s non-adiabatica

reads nk = Exp{π(k/µ)2}

Non-adiabatic field excitation (particle creation)

e inflaton φ

V (φ)

GW

INFLATIONARY MODELS

∆Ph Ph ⌘ P(tot)

h

P(vac)

h

P(vac)

h

⌘ P(pp)

h

P(vac)

h

⇠ few ⇥ O(10−4) H2 m2

pl

W(kτ0) ⇣ µ H ⌘3 ln2(µ/H) ,

• 18.0
• 14.0
• 10.0
• 6.0
• 2.0

2.0 6.0 10.0 Log[f]

• 16.0
• 14.0
• 12.0
• 10.0
• 8.0
• 6.0

Log[h0

2ΩGW]

scale-invariant (RD modes) (MD modes)

ΩGW ∝ 1/k2

r e d t i l t e d ( R D m

• d

e s )

∆k ∼ µ

∆Ph Ph

µ2 ⌘ g ˙ φ0

( Sorbo et al 2011, Peloso et al 2012-2013, Caprini & DGF 2018)

INFLATIONARY MODELS

∆Ph Ph ⌘ P(tot)

h

P(vac)

h

P(vac)

h

⌘ P(pp)

h

P(vac)

h

⇠ few ⇥ O(10−4) H2 m2

pl

W(kτ0) ⇣ µ H ⌘3 ln2(µ/H) ,

• 18.0
• 14.0
• 10.0
• 6.0
• 2.0

2.0 6.0 10.0 Log[f]

• 16.0
• 14.0
• 12.0
• 10.0
• 8.0
• 6.0

Log[h0

2ΩGW]

scale-invariant (RD modes) (MD modes)

ΩGW ∝ 1/k2

r e d t i l t e d ( R D m

• d

e s )

∆k ∼ µ

∆Ph Ph

for every model !

∆Ph Ph

⌧ 1

µ2 ⌘ g ˙ φ0

( Sorbo et al 2011, Peloso et al 2012-2013, Caprini & DGF 2018)

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

Cosmological Pple

'cures' hBB =

{

Scenarios Primordial perturbations

Tensor Scalar Irreducible GW Background

Continuous GW production

Enhanced Scalar Pert. Extra species{

shift symm. arbitrary

Localized GW enhancement Observable Blue tilted (chiral) GWs negligible GW production

Modified Gravity, spectator fields, graviton mass, …

INFLATIONARY MODELS

INFLATION non-monotonic

IF { multi-field

{

∆2

R

possible to enhance (at small scales) Let us suppose ∆2

R ∆2 R

• CMB ⇠ 3 · 10−9 , @ small scales

ds2 = a2(η)[−(1 + 2Φ)dη2 + [(1 − 2Ψ)δij + 2F(i,j) + hij]dxidxj] (

INFLATIONARY MODELS

INFLATION non-monotonic

IF { multi-field

{

∆2

R

possible to enhance (at small scales) Let us suppose ∆2

R ∆2 R

• CMB ⇠ 3 · 10−9 , @ small scales

ds2 = a2(η)[−(1 + 2Φ)dη2 + [(1 − 2Ψ)δij + 2F(i,j) + hij]dxidxj] ( h′′

ij + 2Hh′ ij + k2hij = ST T ij

Sij = 2Φ∂i∂jΦ − 2Ψ∂i∂jΦ + 4Ψ∂i∂jΨ + ∂iΦ∂jΦ − ∂iΦ∂jΨ − ∂iΨ∂jΦ + 3∂iΨ∂jΨ − 4 3(1 + w)H2 ∂i(Ψ′ + HΦ)∂j(Ψ′ + HΦ) − 2c2

s

3wH [3H(HΦ − Ψ′) + ∇2Ψ] ∂i∂j(Φ − Ψ)

Phys.Rev. D81 (2010) 023527 Phys.Rev. D75 (2007) 123518

• D. Wands et al, 2006-2010

(2nd Order Pert.) ∼ Φ ∗ Φ

INFLATIONARY MODELS

INFLATION non-monotonic

IF { multi-field

{

∆2

R

possible to enhance (at small scales) Let us suppose ∆2

R ∆2 R

• CMB ⇠ 3 · 10−9 , @ small scales

ds2 = a2(η)[−(1 + 2Φ)dη2 + [(1 − 2Ψ)δij + 2F(i,j) + hij]dxidxj] (

Phys.Rev. D81 (2010) 023527 Phys.Rev. D75 (2007) 123518

• D. Wands et al, 2006-2010

Ωgw,0(k) = Frad Ωγ,0 △4

R(k) .

Frad = 8 3 2162 π3

• 8.3 × 10−3fns

∼ 1

∼ 30

h′′

ij + 2Hh′ ij + k2hij = ST T ij

(2nd Order Pert.) ∼ Φ ∗ Φ

INFLATIONARY MODELS

INFLATION non-monotonic

IF { multi-field

{

∆2

R

possible to enhance (at small scales)

Ωgw,0 < 1.5 × 10−5

△2

R < 0.1

Frad 30 − 1

2

.

Ωgw,0 < 6.9 × 10−6 .

△2

R < 0.07

Frad 30 − 1

2

.

Ωgw,0 < 10−13

△2

R < 3 × 10−4

Frad 30 − 1

2

1 × 10−5

Ωgw,0 < 10−17

△2

R < 3 × 10−7

Frad 30 − 1

2

Ωgw,0 < 4 × 10−8 .

△2

R < 5 × 10−3

Frad 30 − 1

2

BBN LIGO PTA LISA BBO

Phys.Rev. D81 (2010) 023527

INFLATIONARY MODELS

INFLATION non-monotonic

IF { multi-field

{

∆2

R

possible to enhance (at small scales) IF very enhanced ∆2

R

Primordial Black Holes (PBH) may be produced! PBH candidate for Dark Matter ?

Has LIGO detected PBH’s ?

Clesse & Garcia-Bellido, 2015-2017 Ali-Haimoud et al 2016-2017

See talks by Ali-Haimoud, Byrnes, Garcia-Bellido, Zumalacarregui, …

INFLATIONARY MODELS

INFLATION non-monotonic

IF { multi-field

{

∆2

R

possible to enhance (at small scales) IF very enhanced ∆2

R

Primordial Black Holes (PBH) may be produced! PBH candidate for Dark Matter ?

Has LIGO detected PBH’s ?

Clesse & Garcia-Bellido, 2015-2017 Ali-Haimoud et al 2016-2017

See talks by Ali-Haimoud, Byrnes, Garcia-Bellido, Zumalacarregui, …

‘We will know soon, determining mass and spin distributions’

(Maya Fishbach, Moriond'19)

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

=

{

Scenarios Primordial perturbations

Tensor Scalar Enhanced Scalar Pert. … Enhanced GWs Extra species/symmetries : Irreducible GWs

{

Reheating =

New GW production Matching inflation with Thermal Era

(

)

GWs from (p)Reheating

INFLATION − → REHEATING − → BIG BANG THEORY

SCALAR (P)REHEATING

Chaotic Scenarios: PARAMETRIC RESONANCE

1)

V (φ, χ) = V (φ) +

1 2m2 χχ2

+

1 2g2φ2χ2

(Chaotic Models) X00

k + [κ2 + m2(φ)]Xk = 0

(Fluctuations of Matter)

SCALAR (P)REHEATING

Chaotic Scenarios: PARAMETRIC RESONANCE

1)

V (φ, χ) = V (φ) +

1 2m2 χχ2

+

1 2g2φ2χ2

(Chaotic Models) X00

k + [κ2 + m2(φ)]Xk = 0

(Fluctuations of Matter)

SCALAR (P)REHEATING

Chaotic Scenarios: PARAMETRIC RESONANCE

1)

V (φ, χ) = V (φ) +

1 2m2 χχ2

+

1 2g2φ2χ2

(Chaotic Models) X00

k + [κ2 + m2(φ)]Xk = 0

(Fluctuations of Matter)

SCALAR (P)REHEATING

Chaotic Scenarios: PARAMETRIC RESONANCE

1)

V (φ, χ) = V (φ) +

1 2m2 χχ2

+

1 2g2φ2χ2

(Chaotic Models) X00

k + [κ2 + m2(φ)]Xk = 0

(Fluctuations of Matter)

SCALAR (P)REHEATING

Chaotic Scenarios: PARAMETRIC RESONANCE

1)

V (φ, χ) = V (φ) +

1 2m2 χχ2

+

1 2g2φ2χ2

(Chaotic Models) X00

k + [κ2 + m2(φ)]Xk = 0

(Fluctuations of Matter)

SCALAR (P)REHEATING

2)(Hybrid Scenarios): SPINODAL INSTABILITY

):

¨ φ(t) + (µ2 + g2|χ|2)φ(t) = 0 ¨ χk +

• k2+ m2 ⇣

φ2 φ2

c − 1

⌘ +λ|χ|2 χk = 0 9 > = > ; (k < m = √ λv) χk, nk ∼ e

√ m2−k2t

Hybrid Preheating

INFLATIONARY PREHEATING

Physics of (p)REHEATING: ¨ ϕk + ω2(k, t)ϕk = 0 ⇢ Hybrid Preheating : ω2 = k2 + m2(1 − V t) < 0 (Tachyonic) Chaotic Preheating : ω2 = k2 + Φ2(t) sin2 µt (Periodic) At ki: ϕki, nki ∼ eµ(k,t)t ⇒ Inhomogeneities: 8 > > > < > > > : Li ∼ 1/ki δρ/ρ & 1 v ≈ c (p)REHEATING: VERY EFFECTIVE GW GENERATOR

INFLATIONARY PREHEATING

Physics of (p)REHEATING: ¨ ϕk + ω2(k, t)ϕk = 0 ⇢ Hybrid Preheating : ω2 = k2 + m2(1 − V t) < 0 (Tachyonic) Chaotic Preheating : ω2 = k2 + Φ2(t) sin2 µt (Periodic) At ki: ϕki, nki ∼ eµ(k,t)t ⇒ Inhomogeneities: 8 > > > < > > > : Li ∼ 1/ki δρ/ρ & 1 v ≈ c (p)REHEATING: VERY EFFECTIVE GW GENERATOR

Easther, Giblin, Lim ’06-’08 DGF, Ga-Bellido, et al ’07-’10 Kofman, Dufaux et al ’07-’09

P r e h e a t i n g : V e r y E f f e c t i v e G W g e n e r a t

• r

!

Parameter Dependence (Peak amplitude)

Chaotic Models:

q ⌘ g2Φ2

i

ω2

⇤

.

ω2

⇤ ≡ V 00(ΦI)

(DGF, Torrentí 2017)

Resonance Param.

INFLATIONARY PREHEATING

Ω(o)

GW ∼ A2 ω6

ρm2

p

q−1/2

κ

Parameter Dependence (Peak amplitude)

Chaotic Models:

fo ∼ 108 − 109 Hz Ω(o)

GW ∼ 10−11 ,

@

Large amplitude ! … at high Frequency !

Very unfortunate… but unobservable !

INFLATIONARY PREHEATING

Parameter Dependence (Peak amplitude)

Chaotic Models:

fo ∼ 108 − 109 Hz Ω(o)

GW ∼ 10−11 ,

@

Large amplitude ! … at high Frequency !

ΩGW ∝ q−1/2

Spectroscopy of particle couplings ? different couplings … different peaks ?

INFLATIONARY PREHEATING

Parameter Dependence (Peak amplitude)

Chaotic Models:

fo ∼ 108 − 109 Hz Ω(o)

GW ∼ 10−11 ,

@

Large amplitude ! … at high Frequency !

Very unfortunate… no detectors there !

INFLATIONARY PREHEATING

Parameter Dependence (Peak amplitude)

Hybrid Models:

Ω(o)

GW ∝

✓ v mp ◆2 × f(λ, g2) fo ∼ λ1/4 × 109 Hz

,

Ω(o)

GW ∼ 10−11 ,

@

Large amplitude !

(for v ' 1016 GeV)

realistically speaking …

fo ∼ 108 − 109 Hz fo ∼ 102 Hz

{

λ ∼ 0.1 ( n a t u r a l )

λ ∼ 10−28

(fine-tuning)

INFLATIONARY PREHEATING

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

'cures' hBB =

{

Scenarios Primordial perturbations

Tensor Scalar Enhanced Scalar Pert. … Enhanced GWs Extra species/symmetries : Irreducible GWs

{

Reheating

Large GW production scalar Preheating gauge Preheating fermion Preheating (high freq)

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

'cures' hBB =

{

Scenarios Primordial perturbations

Tensor Scalar Enhanced Scalar Pert. … Enhanced GWs Extra species/symmetries : Irreducible GWs

{

Reheating

Large GW production scalar Preheating gauge Preheating fermion Preheating Large GW, peaks Large GW production (high freq) (high freq) (high freq)

INFLATIONARY COSMOLOGY

(

)

initial cond.

Inflation

'cures' hBB =

{

Scenarios Primordial perturbations

Tensor Scalar Enhanced Scalar Pert. … Enhanced GWs Extra species/symmetries : Irreducible GWs

{

Reheating

Large GW production scalar Preheating gauge Preheating fermion Preheating Large GW, peaks Large GW production (high freq) (high freq) (high freq)

1203.4943, 1306.6911 1006.0217, 1706.02365

0) GW definition

Gravitational Waves as a probe of the early Universe

OUTLINE 1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects Early Universe

true and false vacua quantum tunneling Universe expands, T decreases: phase transition triggered !

First order phase transitions

source: anisotropic stress

Πij Πij ∼ γ2(ρ + p) vivj

Πij ∼ (E2 + B2) 3 − EiEj − BiBj

Πij ∼ ∂iφ ∂jφ

true and false vacua quantum tunneling Universe expands, T decreases: phase transition triggered !

First order phase transitions

(Bubble wall collisions) (Sound waves/Turbulence) (MHD)

fc = f∗ a∗ a0 = 2 · 10−5 ✏∗ T∗ 1 TeV Hz

What is the freq. in 1st Order PhT’s ?

GW generation <—> bubbles properties

BUBBLE COLLISIONs

⇥ ' H∗ , H∗ R∗ fc = f∗ a∗ a0 = 2 · 10−5 ✏∗ T∗ 1 TeV Hz

SOUND WAVES & MDH TURBULENCE

What is the freq. in 1st Order PhT’s ?

GW generation <—> bubbles properties

: duration of PhT size of bubbles at collision

β−1 vb ≤ 1 R∗ = vb β−1

: speed of bubble walls

Parameters determining the GW spectrum

α = ρvac ρ∗

rad

κ = ρkin ρvac ρ∗

s

ρ∗

tot

= κ α 1 + α ⇥ ' H∗ , H∗ R∗ β H∗ , vb , T∗ fc = f∗ a∗ a0 = 2 · 10−5 ✏∗ T∗ 1 TeV Hz ΩGW ∼ Ωrad ✏2

∗

✓ ⇢∗

s

⇢∗

tot

◆2

Parameter List ! (not independent)

MHD turbulence

Example of spectrum

10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL

Caprini et al, arXiv:1512.06239

sound waves wall collision total

peak of fluid-related processes 1/R∗

β

peak of bubble collisions

MHD turbulence

Example of spectrum

10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL

Caprini et al, arXiv:1512.06239

sound waves wall collision total

peak of fluid-related processes 1/R∗

β

peak of bubble collisions

L I S A c a n d e t e c t t h i s b a c k g r

• u

n d !

Evaluation of the signal

• bubble collisions: analytical and numerical simulations
• sound waves: numerical simulations of scalar field and fluid
• MDH turbulence: analytical evaluation

(Huber and Konstandin arXiv:0806.1828) (Caprini et al arXiv:0909.0622) (Hindmarsh et al arXiv:1504.03291)

1304.2433

[ 1504.03291 ,1608.04735, 1704.05871 ] [ astro-ph/9310044, 0711.2593, 0901.1661 ]

Evaluation of the signal

• bubble collisions: analytical and numerical simulations
• sound waves: numerical simulations of scalar field and fluid
• MDH turbulence: analytical evaluation

(Huber and Konstandin arXiv:0806.1828) (Caprini et al arXiv:0909.0622) (Hindmarsh et al arXiv:1504.03291)

1304.2433

[ 1504.03291 ,1608.04735, 1704.05871 ] [ astro-ph/9310044, 0711.2593, 0901.1661 ]

C

• s

m

• l
• g

y a n d P a r t i c l e P h y s i c s i n t e r p l a y ! C

• n

n e c t i

• n

s w i t h b a r y

• n

a s y m m e t r y & d a r k m a t t e r LISA —> new probe of BSM physics! (complementary to particle colliders)

• LISA sensitive to energy scale 10 GeV - 100 TeV !
• LISA can probe the EWPT in BSM models …
• singlet extensions of MSSM (Huber et al 2015)
• direct coupling of Higgs to scalars (Kozackuz et al 2013)
• SM + dimension six operator (Grojean et al 2004)
• … and beyond the EWPT
• Dark sector: provides DM candidate and confining PT

(Schwaller 2015)

• Warped extra dimensions : PT from the dilaton/radion

stabilisation in RS-like models (Randall and Servant 2015)

(mHZ)

Models for EWPT and beyond

• LISA can probe the EWPT in BSM models …
• singlet extensions of MSSM (Huber et al 2015)
• direct coupling of Higgs to scalars (Kozackuz et al 2013)
• SM + dimension six operator (Grojean et al 2004)
• … and beyond the EWPT
• Dark sector: provides DM candidate and confining PT

(Schwaller 2015)

• Warped extra dimensions : PT from the dilaton/radion

stabilisation in RS-like models (Randall and Servant 2015)

• LISA sensitive to energy scale 10 GeV - 100 TeV !

(mHZ)

Big Problem: LHC is putting great pressure

• ver these scenarios

Models for EWPT and beyond

• LISA can probe the EWPT in BSM models …
• singlet extensions of MSSM (Huber et al 2015)
• direct coupling of Higgs to scalars (Kozackuz et al 2013)
• SM + dimension six operator (Grojean et al 2004)
• … and beyond the EWPT
• Dark sector: provides DM candidate and confining PT

(Schwaller 2015)

• Warped extra dimensions : PT from the dilaton/radion

stabilisation in RS-like models (Randall and Servant 2015)

LISA —> new probe of BSM physics! (complementary to particle colliders)

• LISA sensitive to energy scale 10 GeV - 100 TeV !

(mHZ)

Models for EWPT and beyond

Big Problem: LHC is putting great pressure

• ver these scenarios

MAGNETIC FIELD DYNAMICS: Hybrid Preheating (Abelian-Higgs)

[Dufaux, DGF, Ga-Bellido, PRD’10]

What about Cosmic Defects ? (aftermath products of a PhT)

Introduction to Cosmic Defects

→

Introduction to Cosmic Defects

→

x y

Introduction to Cosmic Defects

→

x y

Introduction to Cosmic Defects

→

x y

Introduction to Cosmic Defects

→

x y

Introduction to Cosmic Defects

→

x y

φ = v φ = v φ = v φ = v

Introduction to Cosmic Defects

→

x y

φ = 0

φ = v φ = v φ = v φ = v

Introduction to Cosmic Defects

DYNAMICS OF THE HIGGS: Hybrid Preheating (Abelian-Higgs)

[Dufaux, DGF, Ga-Bellido, PRD’10]

U(1) Breaking (after Hybrid Inflation)

Higgs Dynamics

Dufaux et al PRD 2010

Introduction to Cosmic Defects

Dufaux et al PRD 2010

U(1) Breaking (after Hybrid Inflation)

SNAPSHOT OF THE HIGGS (mt = 17)

Introduction to Cosmic Defects

Dufaux et al PRD 2010

U(1) Breaking (after Hybrid Inflation)

Magnetic Field energy density

Introduction to Cosmic Defects

→

Introduction to Cosmic Defects

→

O(2) O(3) O(4)

(M = G/H)

Vilenkin & Shellard, '94

Introduction to Cosmic Defects

!

DEFECTS: Aftermath of PhT !                 Domain Walls Cosmic Strings Cosmic Monopoles Non Topological DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT CAUSALITY & MICROPHYSICS ) Corr. Length: ξ(t) = λ(t) H1(t) (Kibble’ 76) SCALING:    λ(t) = const. ! λ ⇠ 1 ) k/H = kt hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

!

DEFECTS: Aftermath of PhT !                 Domain Walls Cosmic Strings Cosmic Monopoles Non Topological

Unequal Time Correlator (UTC)

ξ

ξ

ξ

Introduction to Cosmic Defects

!

DEFECTS: Aftermath of PhT !                 Domain Walls Cosmic Strings Cosmic Monopoles Non Topological DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT CAUSALITY & MICROPHYSICS ) Corr. Length: ξ(t) = λ(t) H1(t) (Kibble’ 76) SCALING:    λ(t) = const. ! λ ⇠ 1 ) k/H = kt hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

!

DEFECTS: Aftermath of PhT !                 Domain Walls Cosmic Strings Cosmic Monopoles Non Topological

λ(t) = const. → λ ∼ 1

k/H = kt

comoving momentum conformal time

!

DEFECTS: Aftermath of PhT !                 Domain Walls Cosmic Strings Cosmic Monopoles Non Topological DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT CAUSALITY & MICROPHYSICS ) Corr. Length: ξ(t) = λ(t) H1(t) (Kibble’ 76) SCALING:    λ(t) = const. ! λ ⇠ 1 ) k/H = kt hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

!

DEFECTS: Aftermath of PhT !                 Domain Walls Cosmic Strings Cosmic Monopoles Non Topological

λ(t) = const. → λ ∼ 1

k/H = kt

comoving momentum conformal time

Scaling

H−1 H−1 H−1

Cosmic Defects

DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT

GW spectrum: Expansion UTC

dρGW d log k(k, t) ∝ k3 M 2

pa4(t)

R dt1dt2 a(t1)a(t2) cos(k(t1 − t2)) Π2(k, t1, t2)

   hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

)) Π2(k, t1, t2)

UTC:

Comoving Conformal (Unequal Time Correlator)

GWs from a scaling network of cosmic defects

DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT

   hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

UTC:

SCALING

GW spectrum: Expansion UTC

dρGW d log k(k, t) ∝ k3 M 2

pa4(t)

R dt1dt2 a(t1)a(t2) cos(k(t1 − t2)) Π2(k, t1, t2)

))

V4 √t1t2 U(kt1, kt2)

SCALING

Comoving Conformal

GWs from a scaling network of cosmic defects

DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT

   hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

UTC:

GW spectrum: Expansion UTC

dρGW d log k(k, t) ∝ k3 M 2

pa4(t)

R dt1dt2 a(t1)a(t2) cos(k(t1 − t2)) Π2(k, t1, t2)

))

V4 √t1t2 U(kt1, kt2)

SCALING

dt2 t1t2

SCALING

• Rad. Dom

SCALING

Comoving Conformal

GWs from a scaling network of cosmic defects

DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT

   hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

UTC:

GW spectrum: Expansion UTC

dρGW d log k(k, t) ∝ k3 M 2

pa4(t)

R dt1dt2 a(t1)a(t2) cos(k(t1 − t2)) Π2(k, t1, t2)

))

V4 √t1t2 U(kt1, kt2)

SCALING

dt2 t1t2

GW spectrum: (xi ≡ kti) R.D. and SCALING

dρGW d log k(k, t) ∝

⇣

V Mp

⌘4

M 2

p

a4(t)

⇥R dx1dx2 √x1x2 cos(x1 − x2) U(x1, x2) ⇤

• Rad. Dom

SCALING Expansion UTC

: (xi ≡ kti)

GWs from a scaling network of cosmic defects

DEFECTS: GW Source ! {Tij}TT / {∂iφ∂jφ, EiEj, BiBj}TT

   hT TT

ij (k, t)T TT ij (k0, t0)i = (2π)3 V4 p tt0 U(kt, kt0)δ3(k k0)

UTC:

GW spectrum: Expansion UTC

dρGW d log k(k, t) ∝ k3 M 2

pa4(t)

R dt1dt2 a(t1)a(t2) cos(k(t1 − t2)) Π2(k, t1, t2)

))

V4 √t1t2 U(kt1, kt2)

SCALING

dt2 t1t2

GW spectrum: (xi ≡ kti) R.D. and SCALING

dρGW d log k(k, t) ∝

⇣

V Mp

⌘4

M 2

p

a4(t)

⇥R dx1dx2 √x1x2 cos(x1 − x2) U(x1, x2) ⇤

• Rad. Dom

SCALING Expansion UTC

: (xi ≡ kti)

dρGW d log k(k, t) ∝

⇣

V Mp

⌘4

M 2

p

a4(t) FU ,

FU ∼ Const. (Dimensionless)

}

GWs from a scaling network of cosmic defects

GW today: ∀ PhT (1st, 2nd, ...), ∀ Defects (top. or non-top.) Ω(o)

GW ≡ 1 ρ(o)

c

⇣

dρGW d log k

⌘

• = 32

3

⇣

V Mp

⌘4 Ω(o)

rad FU ,

(SCALE INV.!) Defect type Scaling @ RD VEV

FU ≡ Z x dx1dx2 √x1x2cos(x1 − x2)U(x1, x2)

DGF, Hindmarsh, Urrestilla, PRL 2013

GWs from a scaling network of cosmic defects

GW today: ∀ PhT (1st, 2nd, ...), ∀ Defects (top. or non-top.) Ω(o)

GW ≡ 1 ρ(o)

c

⇣

dρGW d log k

⌘

• = 32

3

⇣

V Mp

⌘4 Ω(o)

rad FU ,

(SCALE INV.!) Defect type Scaling @ RD VEV

y: ∀ PhT (1st, 2nd, ...), ∀ Defects (top. or non-top.)

FU ≡ Z x dx1dx2 √x1x2cos(x1 − x2)U(x1, x2)

DGF, Hindmarsh, Urrestilla, PRL 2013

GWs from a scaling network of cosmic defects

R D

h2Ω(o)

GW = h2Ω(o) rad

✓ V Mp ◆4 " F (R)

U

+ F (M)

U

✓keq k ◆2 #

M D

F (M)

U

≡ 32 3 ( √ 2 − 1)2 2 Z x

xeq

dx1dx2 (x1x2)3/2 cos(x1 − x2) UMD(x1, x2)

F (R)

U

≡ 32 3 Z x dx1dx2 (x1x2)1/2 cos(x1 − x2) URD(x1, x2)

T

• t

a l G W S p e c t r u m

GWs from a scaling network of cosmic defects

energy scale constants

h2Ω(o)

GW = h2Ω(o) rad

✓ V Mp ◆4 " F (R)

U

+ F (M)

U

✓keq k ◆2 #

10-19 10-14 10-9 10-4 10

[]

10-20 10-16 10-12 10-8

Ω

LISA configs v = 10−2Mp v = 10−3Mp v = 10−4Mp

N = 2 N = 3 N = 4

N = 8 N = 12 N = 20

More on GW from Defect Networks

Intercommutation Loops are formed !

What if Defects are Cosmic Strings ?

Loops are formed !

Gravitational Waves emitted ! (releasing the loops' tension)

Image Credit: Google

What if Defects are Cosmic Strings ?

Cosmic Strings Network: Loop configurations

Emission of a GW background !

(Vilenkin ’81)

Cosmic string loop (length l) oscillates under tension μ emits GWs in a series of harmonic modes

and many others !

Cosmic Strings Network: Loop configurations

∗

dρ(o) d f ≡ ΓGµ2 Z to

t∗

dt ✓a(t) ao ◆3 Z α/H(t) dlln(l, t) P((ao/a(t))fl)

number density length GW power emission expansion history

Cosmic string loop (length l) oscillates under tension μ emits GWs in a series of harmonic modes

∝ 1/(fl)q+1

features (kinks,cusps,…) GW power emission

Emission of a GW background !

(Vilenkin ’81) and many others !

15 10 5 5 10 9.0 8.5 8.0 7.5 7.0 log10f Hz log10gwh2

(RD) (MD)

Example of GW emission from Loops

Cosmic strings loops: GW background

e.g. Sanidas 2012

10-9 10-6 10-3 1 103 106 10-15 10-13 10-11 10-9 10-7 frequency (Hz) h2gw Pn from [53] using Model II 10-9 10-6 10-3 1 103 106 10-15 10-13 10-11 10-9 10-7 frequency (Hz) h2gw Pn n-43 using Model III

Blanco-Pillado, Olum, Shlaer Lorenz, Ringeval, Sakellariadou

Very large parameter space !

Cosmic strings loops: GW background

Gµ ∼ 10−11 − 10−17

LISA LISA

10-9 10-6 10-3 1 103 106 10-15 10-13 10-11 10-9 10-7 frequency (Hz) h2gw Pn from [53] using Model II 10-9 10-6 10-3 1 103 106 10-15 10-13 10-11 10-9 10-7 frequency (Hz) h2gw Pn n-43 using Model III

Gµ & 10−17

Very large parameter space !

Blanco-Pillado, Olum, Shlaer Lorenz, Ringeval, Sakellariadou

Cosmic strings loops: GW background

LISA LISA

CMB PTA (today) PTA (future) LISA improve:

O(1010) O(106) O(103)

Gµ & 10−17

*

Best constraints on Comic Strings

*

(actually only way to obtain them)

*

Discovery, or stringent constraints

{

LISA

GW background constrained by LISA

(v & 1010 GeV) Gµ ∼ 10−7 Gµ ∼ 10−11 Gµ ∼ 10−14

0) GW definition

Gravitational Waves as a probe of the early Universe

SUMMARY 1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects Early Universe

0) GW definition

Gravitational Waves as a probe of the early Universe

1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects Early Universe

Intensive search at the CMB High amplitude, unlike detection Possible Enhancement

SUMMARY

0) GW definition

Gravitational Waves as a probe of the early Universe

1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects Early Universe

High amplitude, unlike detection EWPT (1st)

• bservable*

[*At LISA if EWPT is strong 1st order]

GUT-PT

• bservable**

[**By PTA/LISA, If large loops present]

1) GWs from Inflation 2) GWs from Preheating 3) GWs from Phase Transitions 4) GWs from Cosmic Defects

Intensive search at the CMB Possible Enhancement

SUMMARY

Review on Cosmological Gravitational Wave Backgrounds

Caprini & Figueroa arXiv:1801.04268

Propaganda, Part I

Première Sept 28th 2018, @ CERN Globe

Propaganda, Part II

Almost Nothing

THANKS FOR YOUR ATTENTION !

Back Slides —————— ——————

LHC

• LISA sensitive to energy scale 10 GeV - 100 TeV !
• LISA can probe the EWPT in BSM models …
• singlet extensions of MSSM (Huber et al 2015)
• direct coupling of Higgs to scalars (Kozackuz et al 2013)
• SM + dimension six operator (Grojean et al 2004)
• … and beyond the EWPT
• Dark sector: provides DM candidate and confining PT

(Schwaller 2015)

• Warped extra dimensions : PT from the dilaton/radion

stabilisation in RS-like models (Randall and Servant 2015)

(mHZ)

Models for EWPT and beyond

• LISA can probe the EWPT in BSM models …
• singlet extensions of MSSM (Huber et al 2015)
• direct coupling of Higgs to scalars (Kozackuz et al 2013)
• SM + dimension six operator (Grojean et al 2004)
• … and beyond the EWPT
• Dark sector: provides DM candidate and confining PT

(Schwaller 2015)

• Warped extra dimensions : PT from the dilaton/radion

stabilisation in RS-like models (Randall and Servant 2015)

• LISA sensitive to energy scale 10 GeV - 100 TeV !

(mHZ)

Big Problem: LHC is putting great pressure

• ver these scenarios

Models for EWPT and beyond

• LISA can probe the EWPT in BSM models …
• singlet extensions of MSSM (Huber et al 2015)
• direct coupling of Higgs to scalars (Kozackuz et al 2013)
• SM + dimension six operator (Grojean et al 2004)
• … and beyond the EWPT
• Dark sector: provides DM candidate and confining PT

(Schwaller 2015)

• Warped extra dimensions : PT from the dilaton/radion

stabilisation in RS-like models (Randall and Servant 2015)

LISA —> new probe of BSM physics! (complementary to particle colliders)

• LISA sensitive to energy scale 10 GeV - 100 TeV !

(mHZ)

Models for EWPT and beyond

Big Problem: LHC is putting great pressure

• ver these scenarios

CMB SLIDES

Cosmic Microwave Background

Durrer, DGF, Kunz, JCAP 2014

5 10 50 100 500 1000 10 50 100 500 1000 5000

l lHl+1LCl

TTê2p @mK2D

Planck Best-fit H f10 = 0.00L f10 = 0.215 f10 = 0.130 f10 = 0.070 f10 = 0.055

Temp-anisotropies

l

200 300 150 3000 3500 4000 4500 5000 5500 6000

l lHl+1LCl

TTê2p @mK2D

f10 = 0.215 f10 = 0.130 f10 = 0.070 f10 = 0.055 f10 = 0.000

400. 500. 600. 700. 800. 900. 1600 1800 2000 2200 2400 2600

l lHl+1LCl

TTê2p @mK2D

f10 = 0.215 f10 = 0.130 f10 = 0.070 f10 = 0.055 f10 = 0.000

Temp-anisotropies

Cosmic Microwave Background

Durrer, DGF, Kunz, JCAP 2014

50 100 200 500 1000 2000 0.001 0.002 0.005 0.010 0.020 0.050 0.100

l lHl+1LCl

BBê2p @mK2D

INF: r = 0.2 + Lensing INF: r = 0.2, No Lensing SOSF: f10 = 0.055 + Lensing SOSF: f10 = 0.055, No Lensing INF: r = 0.0, Just Lensing

B-modes

Cosmic Microwave Background

Durrer, DGF, Kunz, JCAP 2014

10 20 50 100 200 500 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

l lHl+1LCl

BBê2p @mK2D

Inflation Hr = 0.2L SOSF vector SOSF tensor SOSF total Hf10 = 0.055L

B-modes

(SOSF = Defects)

Cosmic Microwave Background

Durrer, DGF, Kunz, JCAP 2014