Cosmology Principles

CosmologyCosmologyCourseCourse

GustavoNizGustavoNiz

Camille Flammarion L'atmosphre: mtorologie populaire

Content

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

Word of caution

Bayesiananalysis

1

2

History&

Scales

Cosmology until the twentieth century

Universe is finite and with the size of our galaxy (the milky way)

How to measure distancesnot well understood

Cepheids

Discovered by E.Pigott & J. Goodricke, 1784

Cepheids

Real luminocity depends on period (Henrietta Swan Leavitt, 1908)

Apparent luminocity (the one wemeasured on Earth) tell us what the distance is

A bigger Universe

Edward Hubble (1924) measured distance to Cepheids and found them in Andromeda's Galaxy

Cepheids = steps on the distance ladder

Mount Wilson Observatory

Universe is not static

Doppler effect


Redshift

E. Hubble (1929)

Velocity = H * Distance


An old Universe

Velocity = Ho * Distance

Now

Parsecs?

Parsec = 3.08x1016 m

1 AU

1''1 Pc

Parsecs?Parsec = 3.08x1016 m

= 3.2 light years

Radius of visible Universe (particle horizon) 14.0 Gpc (~ 46 billion light years)

0.78 Mpc (2.5 million light-years)

30 kpc ~ 1,000,000,000,000,000,000 km~ 100,000 light years

Mpcs

~0.0000000001 pc

Andromeda

Observations&

TheCDMmodel

Hubble diagram today

Now we know:

0) Empty1) Big2) Expanding

(E. Hubble off by factor ~10)

The big bang theory

Universe was HOT and DENSE in the past

Pillars0) FRWL metric + perts.1) Hubble diagram2) Nucleosynthesis3) Cosmic Microwave Radiation

Thermal history

z=0 z=z=1

Half size

Expansion

Misconceptions

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

Thermal history

Thermal history

300,000 years

Cosmic Microwave Background (CMB) radiation

CMB

T=2.7 K

Error 1K

CMB

Radiation is Isotropic and Homogeneous

CMB

Gaussian~scale invariant

CMB

Seeds of Large Scale Structure

(LSS)

Other key observations

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?

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.

Dark matter

Or, could it be a modification of gravity?

Dark matter

There are other objects (called supernovae IA) which also belong to the distance ladder. The supernovae are big star explosions.

SN 1987ARemanentede SN 1572 SN 1987A

Dark Energy

Dark Energy

Hubble diagram with supernovas IA:

the Universe presentsaccelerated expansion

(5-sigma detection)

We understand even less what it is!

Only acts gravitationally, but in a repulsive way

Best candidate: Cosmological Constant

Vacuum energy value?

Dark Energy

5%

27%

68%

VisibleDark MatterDark Energy

??

Cosmic Pie (energy content)

Important concepts:Isotropy and homogeneity

Building the theory

On sufficiently large scales (>200Mpc) the Universe is isotropic and homogeneous

FilamentsVoids

SDSS

Building the theory

Theory

Cosmological PrincipleAssume an isotropic and homogeneous metricFRWL

Open

Flat

Closed

Scalefactor

TheoryFriedmann equationsEinstein equations with a perfect fluid reduce to

Open k = -1

Flat k = 0

Closed k = +1

From two aboveOr Bianchi id.

Energy conservation

Theory

Critical Mass

Define in terms of critical mass

Friedmann eqn reduces to

TheoryOne matter component (dust p=0)

Theory

Scale factor evolution

t

MatterRadiation

Dark energy

p=1/3p=0

p=-1

Theory

Scale factor evolution

t

MatterRadiation

Dark energy

Model fits ALL observations to great accuracy

Perturbation Theory

But this is only the background!

What happens to perturbations?

Linear scales Vs Non-linear scales

Initial conditions? (later)

Density perturbations

Vectorperturbations

Tensorperturbations

Linear theory

Othereffects

Non-linear theory

Relativistic effects

Strongly coupled NL theory

r=Ho^(-1) r=2GM

Assume a perfect fluid, use the Newtonian limit

And that

Expanding on and solving iteratively

Density perturbations

Perturbation Theory

Correlation function

In Fourier spacepower spectrum

Perturbation Theory

Tegmark, M. et al. 2004

Linear theory

r=Ho^(-1) r=GM

UnderstandingtheCMB

CMBConvenient to expand CMB anisotropies in spherical harmonics

The power spectrum is defined as

CMBWhat are these oscillations?

UNIVERSE IS FLAT(error < 0.1%)

Planck, 2013

~.25

Other peaks account for Visible Matter, Dark

Matter and Dark Energy

Planck, 20135%

27%

68%

VisibleDark MatterDark Energy

Other effects in the CMB

Gravitaional lensing

Planck2015

E & B modes

PolarisationEquivalent to Electric and

Magnetic fields

E B

Divergence Curl

E & B modesRECALL

Surface

Unpolarised light

Linear polarisation

E & B modes

E and B

Zaldarriaga and Seljak, 1997

Spin raising andLowering operators

Non-localrelations

E & B modesUsing spin two spherical harmonics (like usual spherical harmonics with additional U(1))

Stokes parametersZaldarriaga and Seljak, 1997

E & B modesSpin raising/ lowering

Zaldarriaga and Seljak, 1997

EE

BB

SMALL SIGNAL!

E & B modes

Modos E y B

EE

BB

Amplitude depends on primordial fraction of gravitational waves

TT

EE

BB

r=0

r=0.3

SMALL SIGNAL!

E & B modes

Before BICEP2Foregrounds

B modes only

E & B modes

BICEP 2

E & B modes

BICEP2 bites the dust...

Planck dust 2014

BICEP's Talk (John Kovac)

B modes

TO QUANTUM GRAVITY

TheearlyUniverse(inflation)

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 temperature3) Size

4) Flatness

Expansion13.7 Gyrs

Problems1) Magnetic monopoles With many phase transitions why there are any topological relics?2) Horizon problem Why disconnected region of space have same CMB temperature3) Size

4) Flatness

Expansion13.7 Gyrs

5) The initial (big bang) singularity

Problems of the Big Bang Theory

Inflationary mechanism

Phase of exponential acceleration

t=10 s-35

Inflationary mechanism

Simplest realisation: canonical scalar field slowly rolling down a potential

InflationFriedmann equations read

If slow-roll is assumed (potential energy dominates over kinetic), then

which imply the following solution

Inflation

Solves the Problems1) Magnetic monopoles Dilutes them2) Horizon problem A small patch was enlarged beyond the Hubble horizon 3) Size4) Flatness

5) Singularity problem remains

InflationIn order to solve problems inflation should last

N =50 - 60 e-foldings

Inflation

Slow-roll paramters

Should be roughly

Inflation

Quantum fluctuations - BONUS

Inflation

Quantum fluctuations - Evolution

k

R=1/(aH)

Baumann notes

Inflation

Scalar perturbations

Changing variables

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.

One obtains

Which is complete agreement with the CMB

Planck (2013)

Remember scalar perturbations only produce E modes (Zaldarriaga & Seljak, 1997)

Inflation

Tensor perturbations = gravity waves

Inflation


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)

Inflacin


Another way to write the potential is

r=0.01 results in GUT scale for inflation.

Inflation


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 validand

One needs to understand quantum gravity corrections

Inflation


Inflation

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)?

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...

TheCosmicAccelerator(EFTofLSS)

EFTofLSSProgram

Inflation

Matter

Tracers

RedshiftPajer's talk, 2015

Dark EnergyDark MatterNon-GaussianityModified Gravity

Non-linear theory

r=Ho^(-1) r=GM

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

Cosmic accelerator

1) Most efforts in studying the propagator or two point correlation function (power spectrum)

2) What about higher correlation functions?

Higher correlation functions

1) More data to break degeneracies between theories, calculate errors, etc.

2) Direct understanding of the theory behind our Universe (RG, inflacin, etc.)

3) Check small deviations from Gaussian (initial) conditions (f_NL).

Higher correlation functions

4) Consistency relations

*Invariant under renormalization and baryon physics*Equivalence principle violations?

UNIVERSIDADGUANAJUATODE

Grupode

GRAVITACINYFSICAMATEMTICA

8 Profesores3 Postdocs

15+ Estudiantes de Posgrado

Temas

CosmologaGravedad cunticaTeoras alternasGravedad modificadaTeora de cuerdas(astropartculas y partculas)

UNIVERSIDADGUANAJUATODE

Postdocs: PROMEP CONACyT

Posgrados: MAESTRIA DOCTORADO

(Competencia Internacional CONACYT)

Website fisica.ugto.mx/~gfmContacto Gustavo Niz (responsable) [email protected]

Temas

CosmologaGravedad cunticaTeoras alternasGravedad modificadaTeora de cuerdas(astropartculas)

Grupode

GRAVITACINYFSICAMATEMTICA

8 Profesores3 Postdocs

15+ Estudiantes de Posgrado

Oportunidades

Singularity theorems

Initial data (assuming some energy conditions) can lead, unavoidable, to geodesically incomplete space-times.

Global statement.

What about the analytical structure of fields near the singularity?

Penrose, Hawking (60-70's)

Extra slides: The singularity in GR

Belinski, Khalatnikov and Lifshitz (BKL)

Assumed ultralocality :

spatial gradients are not as important as time derivatives!

Big Bang

System reduces to 1d, but may have strong dependence on the initial conditions!

Chaos

(e.g. Mixmaster)


All depends on matter content: *scalar fields tend to remove chaos *gauge fields (p-forms) may restore it

Cosmological billiards

Damour et al '03Hamiltonian:

Near t=0,


Away from walls:

Kasner metric


*GeneralRelativity(d

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.


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Cosmology Principles