Your SlideShare is downloading. ×
Non-Gaussian perturbations from mixed inflaton-curvaton scenario
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Saving this for later?

Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime - even offline.

Text the download link to your phone

Standard text messaging rates apply

Non-Gaussian perturbations from mixed inflaton-curvaton scenario

840
views

Published on

Published in: Technology, Business

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
840
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Non-Gaussian perturbations from mixed inflaton-curvaton scenario José Fonseca - University of Portsmouth Based on a paper with David Wands arxiv:1101.1254/Phys. Rev. D 83, 064025 (2011) and current work 13-Feb at AIMSQuarta-feira, 15 de Fevereiro de 12
  • 2. The Plan • Motivation; • Perturbations from inflation in a nutshell; • Curvaton Scenario; • Mixed perturbations; • Constraints on curvaton dominated theories; • Including inflation perturbations; • SummaryQuarta-feira, 15 de Fevereiro de 12
  • 3. This is a pic of the Cosmic Microwave Background, aka CMB! Power Spectrum of primordial density perturbations ✓ ◆ns (k0 ) 1 k P⇣ (k) = ⇣ (k0 ) 2 k0 1 k0 = 0.002Mpc 2 +0.091 9 (k0 ) = (2.430 0.091 ) ⇥ 10 +0.012 ns (k0 ) = 0.968 0.012 E. Komatsu et al, Seven-year WMAP Observations: Cosmological Interpretation - arXiv:1001.4538v1Quarta-feira, 15 de Fevereiro de 12
  • 4. This is a pic of the Cosmic Microwave Background, aka CMB! Power Spectrum of Bispectrum from quadratic primordial density corrections perturbations ✓ ◆ns (k0 ) 1 k 3 P⇣ (k) = ⇣ (k0 ) 2 ⇣ = ⇣1 + fnl (⇣1 2 2 h⇣1 i) k0 5 1 k0 = 0.002Mpc 2 +0.091 9 (k0 ) = (2.430 0.091 ) ⇥ 10 10 < fnl < 74 +0.012 ns (k0 ) = 0.968 0.012 E. Komatsu et al, Seven-year WMAP Observations: Single field inflation is Cosmological Interpretation perfectly fine but... - arXiv:1001.4538v1Quarta-feira, 15 de Fevereiro de 12
  • 5. Perturbations from inflation in a nutshellQuarta-feira, 15 de Fevereiro de 12
  • 6. INFLATON 3H ˙ ⇥ V SCALAR FIELD LIVING IN A FRW UNIVERSE THAT DRIVES INFLATION. 2 V( ) H 3m2 l P PERTURBATIONS FROM INFLATION IN A NUTSHELL STANDARD INFLATION = INFLATON + SLOW ROLLQuarta-feira, 15 de Fevereiro de 12
  • 7. INFLATON 3H ˙ ⇥ V SCALAR FIELD LIVING IN A FRW UNIVERSE THAT DRIVES INFLATION. 2 V( ) H 3m2 l P SLOW ROLL ✓ ◆2 THE FIELD HAS AN OVER-DAMPED EVOLUTION, I.E., IT 1 2 V ✏ ⌘ mP l ⌧1 ROLLS DOWN THE POTENTIAL SLOWLY. 2 V THE EXPANSION IS ALMOST EXPONENTIAL. KINETIC ENERGY DOES NOT VARY WITHIN 1 HUBBLE 2 V TIME. |⌘ |⌘ mP l ⌧1 V THE POTENTIAL NEEDS TO BE FLAT. PERTURBATIONS FROM INFLATION IN A NUTSHELL STANDARD INFLATION = INFLATON + SLOW ROLLQuarta-feira, 15 de Fevereiro de 12
  • 8. SPLIT QUANTITIES BETWEEN BACKGROUND AND 1ST O R D E R P E R T U R B AT I O N ( G A U S S I A N VA C U U M ⇥(t, x) = ⇥(t) + ⇥(t, x) FLUCTUATIONS) ✓ ◆ EQ. OF MOTION FOR THE FIELD PERTURBATIONS (IN ¨ ˙ ⇥k + 3H ⇥k + k2 + m2 ⇥k = 0 FOURIER SPACE) FOR A “MASSLESS” FIELD. a2 ⇥ ⇤2 POWER SPECTRUM OF FIELD PERTURBATIONS AT H P ⇥ HORIZON EXIT 2 k=aH PERTURBATIONS FROM INFLATION IN A NUTSHELL POWER SPECTRUM OF PERTURBATIONS FOR A MASSLESS FIELD DURING INFLATIONQuarta-feira, 15 de Fevereiro de 12
  • 9. 0 THE “SEPARATE UNIVERSE” PICTURE SAYS 2 SUPER- HORIZON REGIONS OF THE UNIVERSE EVOLVE AS IF t2 THEY WERE SEPARATE FRIEDMANN-ROBERTSON- W A L K E R U N I V E R S E S W H I C H A R E L O C A L LY -1 cH s HOMOGENEOUS BUT MAY HAVE DIFFERENT DENSITIES AND PRESSURE. t1 a b Wands et al., astro-ph/0003278v2 THE CURVATURE PERTURBATION ZETA IS THEN GIVEN BY THE DIFFERENCE OF THE INTEGRATED EXPANSION ⇥ = N FROM A SPATIALY-FLAT HYPERSURFACE TO A UNIFORM-DENSITY HYPERSURFACE . 1 00 2 DIFFERENT PATCHES OF THE UNIVERSE WILL HAVE N = 0 N ⇤⇤ + N ⇤⇤ DIFFERENT EXPANSION HISTORIES DUE TO DIFFERENT 2 INITIAL CONDITIONS PERTURBATIONS FROM INFLATION IN A NUTSHELL DELTA N FORMALISM AND THE SEPARATE UNIVERSE PICTUREQuarta-feira, 15 de Fevereiro de 12
  • 10. POWER SPECTRUM AND SCALE DEPENDENCE ✓ ◆2 POWER SPECTRUM OF CURVATURE PERTURBATIONS 1 H⇤ P⇣ ⇤ W H I C H R E M A I N S C O N S TA N T F O R A D I A B AT I C 2✏⇤ 2⇡mP l PERTURBATIONS ON LARGE SCALES d ln P⇣ TILT n⇣ 1⌘ d ln k ns 1⇥ 6 + 2⇥ dn⇣ RUNNING ↵⇣ ⌘ s ⇥ 24⇥2 + 16⇥ ⇤ 2⌅ 2 d ln k PERTURBATIONS FROM INFLATION IN A NUTSHELL OBSERVATIONAL PREDICTIONS FOR SINGLE FIELDQuarta-feira, 15 de Fevereiro de 12
  • 11. POWER SPECTRUM AND SCALE DEPENDENCE ✓ ◆2 POWER SPECTRUM OF CURVATURE PERTURBATIONS 1 H⇤ P⇣ ⇤ W H I C H R E M A I N S C O N S TA N T F O R A D I A B AT I C 2✏⇤ 2⇡mP l PERTURBATIONS ON LARGE SCALES d ln P⇣ TILT n⇣ 1⌘ d ln k ns 1⇥ 6 + 2⇥ dn⇣ RUNNING ↵⇣ ⌘ s ⇥ 24⇥2 + 16⇥ ⇤ 2⌅ 2 d ln k GRAVITATIONAL WAVES ✓ ◆2 2 H⇤ TENSOR-TO-SCALAR RATIO rT ⌘ PG /P⇣ rT = m2 l P⇣ P 2⇡ PERTURBATIONS FROM INFLATION IN A NUTSHELL OBSERVATIONAL PREDICTIONS FOR SINGLE FIELDQuarta-feira, 15 de Fevereiro de 12
  • 12. POWER SPECTRUM AND SCALE DEPENDENCE ✓ ◆2 POWER SPECTRUM OF CURVATURE PERTURBATIONS 1 H⇤ P⇣ ⇤ W H I C H R E M A I N S C O N S TA N T F O R A D I A B AT I C 2✏⇤ 2⇡mP l PERTURBATIONS ON LARGE SCALES d ln P⇣ TILT n⇣ 1⌘ d ln k ns 1⇥ 6 + 2⇥ dn⇣ RUNNING ↵⇣ ⌘ s ⇥ 24⇥2 + 16⇥ ⇤ 2⌅ 2 d ln k GRAVITATIONAL WAVES ✓ ◆2 2 H⇤ TENSOR-TO-SCALAR RATIO rT ⌘ PG /P⇣ rT = m2 l P⇣ P 2⇡ NON-GAUSSIANITY CONSERVED CURVATURE PERTURBATION REMAINS 5 GAUSSIAN fnl = (2 ⇤ ⇥ )⌧1 6 PERTURBATIONS FROM INFLATION IN A NUTSHELL OBSERVATIONAL PREDICTIONS FOR SINGLE FIELDQuarta-feira, 15 de Fevereiro de 12
  • 13. Curvaton ScenarioQuarta-feira, 15 de Fevereiro de 12
  • 14. IT IS AN INFLATIONARY MODEL. THE INFLATON DRIVES THE ACCELERATED EXPANSION Lyth&Wands: hep-th/0110002 Enqvist&Sloth: hep-ph/0109214 WHILE THE CURVATON PRODUCES THE STRUCTURE IN Moroi&Takahashi: hep-ph/0110096 THE UNIVERSE. THE CURVATON IS A LIGHT FIELD DURING INFLATION, WEAKLY COUPLED AND LATE DECAYING, I.E., DECAYS H⇤ > m > INTO RADIATION AFTER INFLATION. CURVATON SCENARIO MAIN PRINCIPLESQuarta-feira, 15 de Fevereiro de 12
  • 15. IT IS AN INFLATIONARY MODEL. THE INFLATON DRIVES THE ACCELERATED EXPANSION Lyth&Wands: hep-th/0110002 Enqvist&Sloth: hep-ph/0109214 WHILE THE CURVATON PRODUCES THE STRUCTURE IN Moroi&Takahashi: hep-ph/0110096 THE UNIVERSE. THE CURVATON IS A LIGHT FIELD DURING INFLATION, WEAKLY COUPLED AND LATE DECAYING, I.E., DECAYS H⇤ > m > INTO RADIATION AFTER INFLATION. DURING INFLATION SUBDOMINANT COMPONENT ⌧1 SINCE IT IS EFFECTIVELLY MASSLESS IT IS IN AN OVER-DAMPED REGIME. THEREFORE OBEYS TO THE ⌧1 , ⇥ ⌧1 SLOW-ROLL CONDITIONS ✓ ◆2 AND ACQUIRES A SPECTRUM OF GAUSSIAN FIELD H⇤ PERTURBATIONS AT HORIZON EXIT P 2 CURVATON SCENARIO MAIN PRINCIPLESQuarta-feira, 15 de Fevereiro de 12
  • 16. AFTER INFLATION THE CURVATON IS AN ENTROPY DIRECTION, SO THE CURVATURE PERTURBATION ON UNIFORM DENSITY ˙ 6= 0 ⇣ HYPER-SURFACES IS NO LONGER CONSERVED CURVATON SCENARIO MAIN IDEASQuarta-feira, 15 de Fevereiro de 12
  • 17. AFTER INFLATION THE CURVATON IS AN ENTROPY DIRECTION, SO THE CURVATURE PERTURBATION ON UNIFORM DENSITY ˙ 6= 0 ⇣ HYPER-SURFACES IS NO LONGER CONSERVED THE FIELD STARTS COHERENT OSCILLATIONS IN THE BOTTOM OF THE POTENTIAL AND BEHAVES LIKE A Hm MATTER FLUID. CURVATON SCENARIO MAIN IDEASQuarta-feira, 15 de Fevereiro de 12
  • 18. AFTER INFLATION THE CURVATON IS AN ENTROPY DIRECTION, SO THE CURVATURE PERTURBATION ON UNIFORM DENSITY ˙ 6= 0 ⇣ HYPER-SURFACES IS NO LONGER CONSERVED THE FIELD STARTS COHERENT OSCILLATIONS IN THE BOTTOM OF THE POTENTIAL AND BEHAVES LIKE A Hm MATTER FLUID. DECAYS INTO RADIATION AND TRANSFERS ITS PERTURBATIONS H CURVATON SCENARIO MAIN IDEASQuarta-feira, 15 de Fevereiro de 12
  • 19. DURING AND AFTER INFLATION, THE CURVATON IS AN S ⌘ 3 (⇣ ⇣ ) ENTROPY PERTURBATION ZETA IS THE CURVATURE PERTURBATION ON UNIFORM H ⇢ ⇣= DENSITY HYPERSURFACES ⇢ ˙ MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 20. DURING AND AFTER INFLATION, THE CURVATON IS AN S ⌘ 3 (⇣ ⇣ ) ENTROPY PERTURBATION ZETA IS THE CURVATURE PERTURBATION ON UNIFORM H ⇢ ⇣= DENSITY HYPERSURFACES ⇢ ˙ LOCAL CURVATON ENERGY DENSITY ⇢ = ⇢ eS = m2 ¯ 2 osc MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 21. DURING AND AFTER INFLATION, THE CURVATON IS AN S ⌘ 3 (⇣ ⇣ ) ENTROPY PERTURBATION ZETA IS THE CURVATURE PERTURBATION ON UNIFORM H ⇢ ⇣= DENSITY HYPERSURFACES ⇢ ˙ LOCAL CURVATON ENERGY DENSITY ⇢ = ⇢ eS = m2 ¯ 2 osc EXPAND LOCAL VALUE OF THE FIELD DURING 1 00 0 2 OSCILLATION IN TERMS OF ITS VEV AND FIELD osc g+g ⇤+ g ⇤ FLUCTUATIONS DURING INFLATION 2 G ACCOUNTS FOR NON-LINEAR EVOLUTION OF CHI osc ⌘ g( ⇤) MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 22. DURING AND AFTER INFLATION, THE CURVATON IS AN S ⌘ 3 (⇣ ⇣ ) ENTROPY PERTURBATION ZETA IS THE CURVATURE PERTURBATION ON UNIFORM H ⇢ ⇣= DENSITY HYPERSURFACES ⇢ ˙ LOCAL CURVATON ENERGY DENSITY ⇢ = ⇢ eS = m2 ¯ 2 osc EXPAND LOCAL VALUE OF THE FIELD DURING 1 00 0 2 OSCILLATION IN TERMS OF ITS VEV AND FIELD osc g+g ⇤+ g ⇤ FLUCTUATIONS DURING INFLATION 2 G ACCOUNTS FOR NON-LINEAR EVOLUTION OF CHI osc ⌘ g( ⇤) ✓ ◆ 1 gg 00 2 S = SG + 1 SG 4 g 02 THE ENTROPY PERTURBATION IS g0 SG ⌘ 2 ⇤ g MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 23. THE FINAL CURVATON POWER SPECTRUM COMES ✓ 0 ◆2 FROM THE MODES EXCITED DURING INFLATION AND g H⇤ FROM NON-LINEAR EVOLUTION OF THE FIELD UNTIL PS = 4 DECAY. g 2⇡ MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 24. THE FINAL CURVATON POWER SPECTRUM COMES ✓ 0 ◆2 FROM THE MODES EXCITED DURING INFLATION AND g H⇤ FROM NON-LINEAR EVOLUTION OF THE FIELD UNTIL PS = 4 DECAY. g 2⇡ ⇥ AT DECAY ON UNIFORM TOTAL ENERGY DENSITY (1 ⌦ ) e4(⇣ ⇣) + HYPERSURFACES WE HAVE ⇢ = ⇢r + ⇢ ⇤ +⌦ e3(⇣ ⇣) =1 MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 25. THE FINAL CURVATON POWER SPECTRUM COMES ✓ 0 ◆2 FROM THE MODES EXCITED DURING INFLATION AND g H⇤ FROM NON-LINEAR EVOLUTION OF THE FIELD UNTIL PS = 4 DECAY. g 2⇡ ⇥ AT DECAY ON UNIFORM TOTAL ENERGY DENSITY (1 ⌦ ) e4(⇣ ⇣) + HYPERSURFACES WE HAVE ⇢ = ⇢r + ⇢ ⇤ +⌦ e3(⇣ ⇣) =1 AFTER THE DECAY ZETA IS CONSERVED ON SUPER- R2 HORIZON SCALES. WE DEFINE R AS THE TRANSFER P⇣ = P⇣ + PS EFFICIENCY AT DECAY. 9 MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 26. THE FINAL CURVATON POWER SPECTRUM COMES ✓ 0 ◆2 FROM THE MODES EXCITED DURING INFLATION AND g H⇤ FROM NON-LINEAR EVOLUTION OF THE FIELD UNTIL PS = 4 DECAY. g 2⇡ ⇥ AT DECAY ON UNIFORM TOTAL ENERGY DENSITY (1 ⌦ ) e4(⇣ ⇣) + HYPERSURFACES WE HAVE ⇢ = ⇢r + ⇢ ⇤ +⌦ e3(⇣ ⇣) =1 AFTER THE DECAY ZETA IS CONSERVED ON SUPER- R2 HORIZON SCALES. WE DEFINE R AS THE TRANSFER P⇣ = P⇣ + PS EFFICIENCY AT DECAY. 9 3 FOR A SUDDEN DECAY APPROXIMATION R ,dec = 4 dec MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 27. 2 THE WEIGHT OF THE CURVATON CONTRIBUTION TO R /9 P⇣ THE FINAL POWER SPECTRUM w ⌘ P⇣ MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 28. 2 THE WEIGHT OF THE CURVATON CONTRIBUTION TO R /9 P⇣ THE FINAL POWER SPECTRUM w ⌘ P⇣ ✓ ◆2 CRITICAL EPSILON FOR THE CURVATON. DEFINES THE 9 1 H⇤ FRONTIER BETWEEN RELEVANT CONTRIBUTIONS OF ✏c ⌘ 2 R P⇣ 2⇡ THE CURVATON TO THE TOTAL POWER SPECTRUM MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 29. 2 THE WEIGHT OF THE CURVATON CONTRIBUTION TO R /9 P⇣ THE FINAL POWER SPECTRUM w ⌘ P⇣ ✓ ◆2 CRITICAL EPSILON FOR THE CURVATON. DEFINES THE 9 1 H⇤ FRONTIER BETWEEN RELEVANT CONTRIBUTIONS OF ✏c ⌘ 2 R P⇣ 2⇡ THE CURVATON TO THE TOTAL POWER SPECTRUM ✓ ◆✓ ◆2 T H E P O W E R S P E C T R U M O F C U R V AT U R E 1 1 1 H⇤ P⇣ = + PERTURBATIONS IN TERMS OF EPSILON CRITICAL 2 ✏⇤ ✏c 2⇡mP l MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 30. 2 THE WEIGHT OF THE CURVATON CONTRIBUTION TO R /9 P⇣ THE FINAL POWER SPECTRUM w ⌘ P⇣ ✓ ◆2 CRITICAL EPSILON FOR THE CURVATON. DEFINES THE 9 1 H⇤ FRONTIER BETWEEN RELEVANT CONTRIBUTIONS OF ✏c ⌘ 2 R P⇣ 2⇡ THE CURVATON TO THE TOTAL POWER SPECTRUM ✓ ◆✓ ◆2 T H E P O W E R S P E C T R U M O F C U R V AT U R E 1 1 1 H⇤ P⇣ = + PERTURBATIONS IN TERMS OF EPSILON CRITICAL 2 ✏⇤ ✏c 2⇡mP l T H E C U R V AT O N I S T H E M A I N S O U R C E O F PERTURBATIONS IF ✏⇤ ✏c MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 31. SCALE DEPENDENCE OF POWER SPECTRUM n⇣ 1 = w (nS 1) + (1 w )(n⇣ 1) TILT = 2✏⇤ + 2⌘ w + (1 w )( 4✏⇤ + 2⌘ ) 2 RUNNING ↵⇣ = w ↵S + (1 w )↵⇣ + w (1 w ) nS n⇣ MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONS: OBSERVABLE QUANTITIESQuarta-feira, 15 de Fevereiro de 12
  • 32. SCALE DEPENDENCE OF POWER SPECTRUM n⇣ 1 = w (nS 1) + (1 w )(n⇣ 1) TILT = 2✏⇤ + 2⌘ w + (1 w )( 4✏⇤ + 2⌘ ) 2 RUNNING ↵⇣ = w ↵S + (1 w )↵⇣ + w (1 w ) nS n⇣ GRAVITATIONAL WAVES TENSOR-TO-SCALAR RATIO rT = 16w ✏c = 16✏⇤ (1 w ) MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONS: OBSERVABLE QUANTITIESQuarta-feira, 15 de Fevereiro de 12
  • 33. SCALE DEPENDENCE OF POWER SPECTRUM n⇣ 1 = w (nS 1) + (1 w )(n⇣ 1) TILT = 2✏⇤ + 2⌘ w + (1 w )( 4✏⇤ + 2⌘ ) 2 RUNNING ↵⇣ = w ↵S + (1 w )↵⇣ + w (1 w ) nS n⇣ GRAVITATIONAL WAVES TENSOR-TO-SCALAR RATIO rT = 16w ✏c = 16✏⇤ (1 w ) NON-GAUSSIANITY 5N ✓ ◆ 5 gg 00 (g/g 0 )R0 2R FNL fnl = w2 fnl = 1 + 02 + w2 6 N2 4R g R ⌧nl 36 TNL 2 = 25w fnl MIXED PERTURBATIONS TRANSFER OF LINEAR PERTURBATIONS: OBSERVABLE QUANTITIESQuarta-feira, 15 de Fevereiro de 12
  • 34. CONSTRAINS ON CURVATON DOMINATED THEORIES Fonseca & Wands arxiv:1101.1254Quarta-feira, 15 de Fevereiro de 12
  • 35. Numerical Studies Solve the Friedmann and the curvaton field evolution equations prior to decay for diferent potential; Ensure that the curvaton starts subdominant and overdamped; We match it with fluid description of the curvaton decay studied by Malik et al (2003) and Gupta et al (2004). m In principle there are 4 free parameters: ⇤ ✏⇤ H⇤ But the COBE normalisation of the power spectrum fixes the Hubble scale during inflation. In the curvaton limit the observables becomes independent of epsilon.Quarta-feira, 15 de Fevereiro de 12
  • 36. Curvaton Limit 18.5 18 -1 Quadratic potential 17.5 1 1 rT 10 1 2 2 17 30 0.1 V( )= m /GeV 100 2 16.5 0.01 fN L * Tensors and non- 10 16 0.001 log linearities can be used 15.5 in a complementary 15 way to constrain the 14.5 model parameters. 14 3 4 5 6 7 8 log 9 m/ 10 11 12 13 14 10 ( 4 4.7 ⇥ 10 q⇤ for ⇤ ( /m)1/4 mP l H⇤ 3 m2 l 1/4 < 5.7 ⇥ 1017 GeV 1.5 ⇥ 10 P for ⇤ ⌧ ( /m) mP l ⇤ ( m ⇤ ✓ ◆2 5/4 for ( /m)1/4 mP l ⇤ q ⇤ < 0.023 fN L m2 l 1/4 m mP l 3.9 m P2 for ⇤ ⌧ ( /m) mP l ⇤Quarta-feira, 15 de Fevereiro de 12
  • 37. rg . 0.1 Curvaton Limit 18.5 18 -1 Quadratic potential 17.5 1 1 rT 10 1 2 2 17 30 0.1 V( )= m /GeV 100 2 16.5 0.01 fN L * Tensors and non- 10 16 0.001 log linearities can be used 15.5 in a complementary 15 way to constrain the 14.5 model parameters. 14 3 4 5 6 7 8 9 10 11 12 13 14 log 10 m/ fnl . 100 ( 4 4.7 ⇥ 10 q⇤ for ⇤ ( /m)1/4 mP l H⇤ 3 m2 l 1/4 < 5.7 ⇥ 1017 GeV 1.5 ⇥ 10 P for ⇤ ⌧ ( /m) mP l ⇤ ( m ⇤ ✓ ◆2 5/4 for ( /m)1/4 mP l ⇤ q ⇤ < 0.023 fN L m2 l 1/4 m mP l 3.9 m P2 for ⇤ ⌧ ( /m) mP l ⇤Quarta-feira, 15 de Fevereiro de 12
  • 38. 15 x 10 3 100 30 10 2.8 2.6 0.01 0.001 0.1 1 2.4 Axion potential /GeV 2.2 1 * 2 log10 4 V = M (1 cos( /f )) 1.8 1.6 fN L rT 1.4 1.2 f = 1015 GeV 1 3 4 5 6 7 8 9 10 11 12 13 14 log m/ 10 17 16 x 10 x 10 3 0.01 3 2.8 2.8 f = 1016 GeV 2.6 2.6 0.01 1 0.1 0.001 0.1 2.4 2.4 /GeV 2.2 /GeV 2.2 * * 2 2 10 log10 log 1.8 1.8 1 1.6 1.6 1 1.4 1.4 100 30 10 1 10 1.2 30 f = 1017 GeV 1.2 1 1 3 4 5 6 7 8 9 10 11 12 13 14 3 4 5 6 7 8 9 10 11 12 13 14 log m/ log m/ 10 10Quarta-feira, 15 de Fevereiro de 12
  • 39. 15 x 10 5 4.5 f = 1015 GeV 4 0.01 0.001 1 0.1 Hyperbolic-cosine potential 3.5 /GeV * 3 10 -1000 log 4 V = M (cosh( /f ) 1) 2.5 -100 -10 2 0 fN L rT 1.5 1000 100 10 1 3 4 5 6 7 8 9 10 11 12 13 14 log m/ 10 17 16 x 10 x 10 5 5 -1000 16 1 4.5 4.5 f = 10 GeV -100 0.1 4 4 -1000 3.5 3.5 /GeV /GeV * * 3 1 3 -100 -10 10 10 log log 0.01 2.5 2.5 -10 2 2 0 0 1.5 0.1 1.5 17 10 0.001 10 f = 10 GeV 1000 100 1 1 3 4 5 6 7 8 9 10 11 12 13 14 3 4 5 6 7 8 9 10 11 12 13 14 log10 m/ log10 m/Quarta-feira, 15 de Fevereiro de 12
  • 40. When is the curvaton limit valid?Quarta-feira, 15 de Fevereiro de 12
  • 41. INCLUDING INFLATION PERTURBATIONSQuarta-feira, 15 de Fevereiro de 12
  • 42. Limits of Epsilon critical ✓ ◆2 Quadratic Potential 1 H⇤ ✏c 18.5 P⇣ = 2✏c 2⇡mP l 18 1 ✓ ◆2 17.5 9 g 1 ✏c = 17 8 g 0 mP l R2 /GeV 0.01 16.5 * 10 16 Curvaton limit log 0.0001 15.5 ✏⇤ ✏c 15 Inflaton contributions 14.5 ✏⇤ . ✏c 14 3 4 5 6 7 8 log 10 9 m/ 10 11 12 13 14 We need to fix the first slow-roll parameter to identify each region.Quarta-feira, 15 de Fevereiro de 12
  • 43. For ✏⇤ ⌘ ⌘ and w 1 we expect ✏⇤ = 0.02 from n⇣ 17.5 0.24 17 ✏c = 0.02 0.1 −1 16.5 0 0.01 In the curvaton /GeV 1 16 limit region * 0.001 10 15.5 10 rT 16✏c log 30 2 15 ✏⇤ = 0.02 ↵⇣ 2 (n⇣ 1) 100 14.5 fN L rT 14 7 8 9 10 11 12 13 14 log m/ 10Quarta-feira, 15 de Fevereiro de 12
  • 44. For ✏⇤ ⇠ ⌘ and w 1 we expect (✏⇤ ⌘ ) 0.02 from n⇣ 17.5 ✏c = 0.1 17 This case requires fine 0.24 −1 0 0.1 tuning of the slow roll 16.5 0.01 parameters /GeV 16 * 0.001 No inflation 10 15.5 log 1 dominated power 15 ✏⇤ = 0.1 10 spectrum allowed 14.5 30 fN L rT 100 14 6 7 8 9 10 11 12 13 14 log m/ 10Quarta-feira, 15 de Fevereiro de 12
  • 45. 18.5 17.5 18 -1 17 0.24 −1 1 0 1 17.5 0.1 10 16.5 17 30 0.1 0.01 /GeV /GeV 100 0.01 16 16.5 * * 0.001 10 10 16 0.001 15.5 log log 15.5 1 15 15 ✏⇤ = 0.1 10 30 14.5 14.5 100 14 14 3 4 5 6 7 8 9 10 11 12 13 14 6 7 8 9 10 11 12 13 14 log m/ log m/ 10 10 17.5 0.24 17 0.1 −1 16.5 0 0.01 /GeV 1 16 * 0.001 10 15.5 10 log 30 15 ✏⇤ = 0.02 100 14.5 14 7 8 9 10 11 12 13 14 log10 m/Quarta-feira, 15 de Fevereiro de 12
  • 46. Summary • The curvaton is an inflation model to source structure in the universe and predicts non-Gaussianities; • The tensor-to-scalar ration and fnl can be used in a complementary way to constrain the curvaton model; • Studied inflation contributions to the power spectrum and in which regimes are important.Quarta-feira, 15 de Fevereiro de 12
  • 47. Summary • The curvaton is an inflation model to source structure in the universe and predicts non-Gaussianities; • The tensor-to-scalar ration and fnl can be used in a complementary way to constrain the curvaton model; • Studied inflation contributions to the power spectrum and in which regimes are important. Thanks!Quarta-feira, 15 de Fevereiro de 12