Cosmology Course Gustavo Niz

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1 Cosmology Course Gustavo Niz Camille Flammarion L'atmosphère: météorologie populaire

2 Content Brief history & scales Observations & the Understanding the CMB Inflation and the early Universe (EFTs in cosmology & the cosmic accelerator) CDM Model

3 Word of caution 1 2 Bayesian analysis

4 History & Scales

5 Cosmology until the twentieth century Universe is finite and with the size of our galaxy (the milky way) How to measure distances not well understood

6 Cepheids Discovered by E.Pigott & J. Goodricke, 1784

7 Cepheids Real luminocity depends on period (Henrietta Swan Leavitt, 1908) Apparent luminocity (the one we measured on Earth) tell us what the distance is

8 A bigger Universe Edward Hubble (1924) measured distance to Cepheids and found them in Andromeda's Galaxy Mount Wilson Observatory Cepheids = steps on the distance ladder

9 Universe is not static Doppler effect

10 Universe is not static Redshift

11 Universe is not static E. Hubble (1929) Velocity = H * Distance

12 An old Universe Velocity = Ho * Distance Now

13 Parsecs? Parsec = 3.08x1016 m 1 Pc 1 AU 1''

14 Parsecs? Parsec = 3.08x1016 m = 3.2 light years Andromeda 0.78 Mpc (2.5 million light-years) ~ pc 30 kpc ~ 1,000,000,000,000,000,000 km ~ 100,000 light years Mpcs Radius of visible Universe (particle horizon) 14.0 Gpc (~ 46 billion light years)

15 Observations & The CDM model

16 Hubble diagram today Now we know: 0) Empty 1) Big 2) Expanding (E. Hubble off by factor ~10)

17 The big bang theory Universe was HOT and DENSE in the past Pillars 0) FRWL metric + perts. 1) Hubble diagram 2) Nucleosynthesis 3) Cosmic Microwave Radiation

18 Thermal history Half size z=0 z=1 z=

19 Expansion Misconceptions No explosion Not an expansion into something else Expansion may be faster than c

20 Thermal history

21 Thermal history 300,000 years

22 Cosmic Microwave Background (CMB) radiation

23 CMB T=2.7 K Error 1K

24 CMB Radiation is Isotropic and Homogeneous

25 CMB

26 CMB ~scale invariant Gaussian

27 CMB Seeds of Large Scale Structure (LSS)

28 Other key observations Dark Matter

29 Dark matter We do not understand what it is! Only acts gravitationally and does not emit light Best candidate: a weakly interacting particle that we have not seen yet Or have we?

30 Dark matter Some experiments (Dama, CoGeNT, CDMS, etc.) have signals, hard to explain with known physics, but others (Xenon, LUX) have not seen anything in the same regions.

31 Dark matter Or, could it be a modification of gravity?

32 Dark Energy There are other objects (called supernovae IA) which also belong to the distance ladder. The supernovae are big star explosions. Remanente de SN 1572 SN 1987A

33 Dark Energy Hubble diagram with supernovas IA: the Universe presents accelerated expansion (5-sigma detection)

34 Dark Energy We understand even less what it is! Only acts gravitationally, but in a repulsive way Best candidate: Cosmological Constant Vacuum energy value?

35 Cosmic Pie (energy content) 5% 27%?? Visible Dark Matter Dark Energy 68%

36 Building the theory Important concepts: Isotropy and homogeneity

37 Building the theory On sufficiently large scales (>200Mpc) the Universe is isotropic and homogeneous Filaments Voids SDSS

38 Theory Cosmological Principle Assume an isotropic and homogeneous metric FRWL Scale factor Open Flat Closed

39 Theory Friedmann equations Einstein equations with a perfect fluid reduce to Open k = -1 Flat k = 0 Closed k = +1 Energy conservation From two above Or Bianchi id.

40 Theory Critical Mass Define in terms of critical mass Friedmann eqn reduces to

41 Theory One matter component (dust p=0)

42 Theory Scale factor evolution Dark energy p=-1 p=1/3 Radiation p=0 Matter t

43 Theory Scale factor evolution Dark energy Radiation Matter Model fits ALL observations to great accuracy t

44 Perturbation Theory But this is only the background! What happens to perturbations? Density perturbations Vector perturbations Tensor perturbations Linear scales Vs Non-linear scales Initial conditions? (later)

45 Perturbation Theory But this is only the background! What happens to perturbations? Density perturbations Vector perturbations Tensor perturbations Linear scales Vs Non-linear scales Initial conditions? (later)

46 r=ho^(-1) r=2gm Other effects Linear theory Non-linear theory Strongly coupled NL theory Relativistic effects

47 Perturbation Theory Density perturbations Assume a perfect fluid, use the Newtonian limit And that Expanding on and solving iteratively

48 Perturbation Theory Correlation function In Fourier space power spectrum

49 Tegmark, M. et al. 2004

50 r=ho^(-1) r=gm Linear theory

51 Understanding the CMB

52 CMB Convenient to expand CMB anisotropies in spherical harmonics The power spectrum is defined as

53 CMB

54 CMB

55 ~.25

56 CMB What are these oscillations?

57 CMB What are these oscillations?

58 CMB

59 UNIVERSE IS FLAT (error < 0.1%) Planck, 2013

5% Other peaks account for Visible Matter, Dark Planck, 2013

60 5% Other peaks account for Visible Matter, Dark Planck, % Visible Dark Matter Dark Energy Matter and Dark Energy 68% ~.25

61 Other effects in the CMB Gravitaional lensing Planck 2015

62 E & B modes E B Polarisation Equivalent to Electric and Magnetic fields Divergence Curl

63 E & B modes RECALL Unpolarised light Surface Linear polarisation

64 E & B modes

65 E & B modes

66 E & B modes

67 E and B Non-local relations Spin raising and Lowering operators Zaldarriaga and Seljak, 1997

68 E & B modes Using spin two spherical harmonics (like usual spherical harmonics with additional U(1)) Zaldarriaga and Seljak, 1997 Stokes parameters

69 E & B modes Spin raising/ lowering Zaldarriaga and Seljak, 1997

70 E & B modes SMALL SIGNAL! EE BB

$primordial fraction$

71 Modos E y B Amplitude depends on primordial fraction of gravitational waves TT EE BB

72 E & B modes SMALL SIGNAL! r=0 EE BB r=0.3

73 E & B modes B modes only Before BICEP2 Foregrounds

74 E & B modes BICEP 2

75 BICEP2 bites the dust... Planck dust 2014

76 BICEP's Talk (John Kovac)

77 B modes TO QUANTUM GRAVITY

78 The early Universe (inflation)

79 Problems of the Big Bang Theory 1) Magnetic monopoles With many phase transitions why there are not any topological relics? 2) Horizon problem Why disconnected region of space have same CMB temperature 3) Size 4) Flatness Expansion 13.7 Gyrs

80 Problems of the Big Bang Theory Problems 1) Magnetic monopoles With many phase transitions why there are any 5) The initial (big bang) singularity topological relics? 2) Horizon problem Why disconnected region of space have same CMB temperature 3) Size 4) Flatness Expansion 13.7 Gyrs

81 Inflationary mechanism Phase of exponential acceleration -35 t=10 s

82 Inflationary mechanism Simplest realisation: canonical scalar field slowly rolling down a potential

83 Inflation Friedmann equations read If slow-roll is assumed (potential energy dominates over kinetic), then which imply the following solution

84 Inflation Solves the Problems 1) Magnetic monopoles Dilutes them 2) Horizon problem A small patch was enlarged beyond the Hubble horizon 3) Size 4) Flatness 5) Singularity problem remains

85 Inflation In order to solve problems inflation should last N =50-60 e-foldings

86 Inflation Slow-roll paramters Should be roughly <0.01 to achieve inflation. Measure when the approximation breaks down (inflation ends). After that one needs a mechanism of reheating.

87 Inflation Quantum fluctuations - BONUS

88 Inflation Quantum fluctuations - Evolution Baumann notes k R=1/(aH)

89 Inflation Scalar perturbations Changing variables

90 Inflation In slow-roll It is a harmonic oscillator! Can quantise provided a vacuum (e.g. Bunch-Davis) The two-point correlation function is Where is the curvature perturbations and k is wavenumber.

91 Inflation One obtains Which is complete agreement with the CMB Planck (2013) Remember scalar perturbations only produce E modes (Zaldarriaga & Seljak, 1997)

92 Inflation Tensor perturbations = gravity waves

93 Inflación Tensor perturbations = gravity waves Also obtain a harmonic oscillator, and their power spectrum would be given by We can define These tensor modes produce both E and B modes (Zaldarriaga y Seljak, 1997)

94 Inflation Tensor perturbations = gravity waves Another way to write the potential is r=0.01 results in GUT scale for inflation.

95 Inflation Tensor perturbations = gravity waves Generically, one gets a bound (Lyth) If r ~ 0.01 the field moves more than a Planck unit (large field models) Perturbation theory stops being valid and One needs to understand quantum gravity corrections

96 Inflation Tensor perturbations = gravity waves

97 Inflation. Problems But introduces new (or keeps) problems: No explanation of amplitude in the CMB anisotropies What is the inflaton (inflation's scalar field)? Why did we start at the top of the potential? Initial conditions (homogeneity and isotropy, the singularity)?

98 Alternatives to inflation 1. Horava's gravity Speed of light is infinite in the UV, thus leading to scale invariance. 2. Cyclic models The contraction phase (if fast) can generate scale invariant fluctuations 3. EFT ( Effective field theories of inflation) Write down all possible relevant operators in the quantum gravity scale which are consistent with the symmetries (cf. SM). Among others...

99 The Cosmic Accelerator (EFT of LSS)

100 EFT of LSS Program Inflation Matter Dark Energy Dark Matter Non-Gaussianity Modified Gravity Tracers Redshift Pajer's talk, 2015

101 r=ho^(-1) r=gm Non-linear theory EFT of LSS All possible operators to describe non-linear perturbations in LSS Capture small-large scale interactions (breaks perfect fluid approximation!) Fix parameters with sims or data

102 Cosmic accelerator 1) Most efforts in studying the propagator or two point correlation function (power spectrum) 2) What about higher correlation functions?

103 Higher correlation functions 1) More data to break degeneracies between theories, calculate errors, etc. 2) Direct understanding of the theory behind our Universe (RG, inflación, etc.) 3) Check small deviations from Gaussian (initial) conditions (f_nl).

104 Higher correlation functions 4) Consistency relations *Invariant under renormalization and baryon physics *Equivalence principle violations?

105 Grupo de GRAVITACIÓN Y FÍSICA MATEMÁTICA 8 Profesores 3 Postdocs 15+ Estudiantes de Posgrado UNIVERSIDAD DE GUANAJUATO Temas Cosmología Gravedad cuántica Teorías alternas Gravedad modificada Teoría de cuerdas (astropartículas y partículas)

modificada Teoría de cuerdas (astropartículas) Postdocs: PROMEP CONACyT Posgrados: MAESTRIA DOCTORADO

106 Grupo de GRAVITACIÓN Y FÍSICA MATEMÁTICA 8 Profesores 3 Postdocs 15+ Estudiantes de Posgrado UNIVERSIDAD DE GUANAJUATO Oportunidades Temas Cosmología Gravedad cuántica Teorías alternas Gravedad modificada Teoría de cuerdas (astropartículas) Postdocs: PROMEP CONACyT Posgrados: MAESTRIA DOCTORADO ( Competencia Internacional CONACYT) Website fisica.ugto.mx/~gfm Contacto Gustavo Niz (responsable) g.niz@ugto.mx

107 Extra slides: The singularity in GR Singularity theorems Initial data (assuming some energy conditions) can lead, unavoidable, to geodesically incomplete space-times. Penrose, Hawking (60-70's) Global statement. What about the analytical structure of fields near the singularity?

108 Extra slides: The singularity in GR Belinski, Khalatnikov and Lifshitz (BKL) Assumed ultralocality : spatial gradients are not as important as time derivatives! System reduces to 1d, but may have strong dependence on the initial conditions! Chaos Big Bang (e.g. Mixmaster)

109 Extra slides: The singularity in GR All depends on matter content: *scalar fields tend to remove chaos *gauge fields (p-forms) may restore it Cosmological billiards Hamiltonian: Damour et al '03 Near t=0,

110 Extra slides: The singularity in GR Away from walls: Kasner metric

111 Extra slides: The singularity in GR *General Relativity (d<11) *Low energy limits of 5 string theories and M theory Kac Moody algebras (formally integrable)

112 Extra slides: The singularity in GR Note that there are potentials for the scalar fields which can overtake this oscillating behaviour, providing a deterministic evolution of the Universe. However, for generic cases, we found a unpredictable behaviour of the metric near the spacetime singularity. We can even forget a description of the singularity itself.

General Relativity (2nd part)

General Relativity (2nd part) Electromagnetism Remember Maxwell equations Conservation Electromagnetism Can collect E and B in a tensor given by And the charge density Can be constructed from and current