A short introduction to Cosmology

Surhud More (IUCAA)

Big questions

• How old is mankind?
• What are we made up of?
• How did we come into existence?
• What is the fate of mankind?

Age old questions in the domain of religion

Big questions

• How old is the Universe?
• What is it made up of?
• How did the Universe come into existence?
• What is the fate of the Universe?

Now can be addressed scientifically

The story of the Universe in a nutshell

Planck collaboration 2015

Different epochs - different observational probes

Planck collaboration 2015

General relativity: the cosmological crisis

• The geometry of the Universe related to its energy density content
• Simplest solutions of Einstein’s equations assuming homogeneity and isotropy predict a non-static Universe.
• The Universe has a scale factor, a(t), which changes all cosmological distances with time: D_phys = a(t) R
• v = d(aR)/dt = R da/dt + a dR/dt = D_phys a^-1da/dt + a dR/dt

Measure distances and velocities

Electromagnetic spectrum of extragalactic objects

Velocities can be measured with the shifts of standard lines

Distances: Standard candles and rulers

• Measure the flux of a standard candle
• Measure the angular size of a standard ruler

Pulsating stars

• Cepheid variables: kappa mechanism due to ionized Helium in the atmosphere
• Calibrate the period luminosity relation using parallaxes

The expansion of the Universe

• Galaxies receding away from each other
• Hubble’s discovery of the expansion of the Universe

Velocity proportional to the distance of galaxies.

Gravitational waves: independent distance measurement

The Friedmann equation

The past and the future of the Universe

Carroll, S. Lecture notes

Behaviour of different constituents

Total energy density dictates geometry of the Universe

The redshift is: a = 1/(1+z)

Fluctuations in the cosmic microwave background

The origin of the inhomogeneity of the Universe

COBE collaboration 1990

Planck collaboration 2015

Primordial sound waves

Typical size of CMB spots: a standard ruler

Hu & White (2004)

The power spectrum

• The location of the first peak informs us about the geometry of the Universe
• The relative heights of the peaks about dark matter and baryon densities

Geometry and the constituents in the early Universe

Hu & White (2004)

Fluctuations in the CMB

The mode which has maximum temperature fluctuations are those with wavelengths

The cosmological model

• The Universe is flat and has critical density
• Baryons make up about 15 percent of the matter sector, rest is dark matter.

Homogeneous Universe

Planck collaboration 2015

The evidence for dark matter

• Measured the velocities of galaxies in the Coma and Virgo clusters
• The baryon density cannot explain the large velocities

Dunkle materie: unseen matter holding cluster of galaxies

© AIP Emilio Segrè Visual Archives, Physics Today Collection

Zwicky

NASA/ESA Hubble Space telescope

The evidence for Dark matter

• Measured the rotation curves of gas around M31 and other spirals
• Non-Keplerian rotation curves

Dunkle materie: unseen matter holding galaxies

Vera Rubin

Growth of structure

• Structures grow at most as the scale factor in the linear regime
• Fluctuations in CMB of the order 10^-5 cannot form galaxies and clusters

Dark energy: evidence from Type Ia Supernovae

Baryon acoustic oscillations

The same physics as the CMB, but predicted in galaxy distribution at lower redshifts

Geometric probes

Distance redshift relation probing the geometry of the Universe

The competition between dark matter and dark energy

Growth of structure probes

• Galaxy clusters: abundance as a function of redshift
• Find galaxy clusters using the CMB, Xray, or optical surveys
• Redshift space distortions
• Growth of fluctuations with velocity measurement
• Cosmic shear
• Direct mapping of dark matter structure using gravitational lensing

Gravitational lensing

• General relativity predicts that light should get deflected by mass
• Comes in different forms: strong, weak and micro

Dark matter maps of the Universe

Summary

• The Universe really is an Un-known-iverse.
• We understand the particle physics behaviour of only 5 percent of the constituents of the Universe.
• Dark matter and dark energy dominate the energy budget of the Universe.
• Observations are making a rapid progress to fill the missing gaps in the puzzle
• Geometric probes
• Growth of structure probes
• It is an exciting era in Cosmology, where we move from speculations to observational tests.

Interstellar distances

• Distance to the star closest to the Sun: Proxima centauri?
• How to measure distances on these scales?

Parallaxes: distances in units of the Earth-Sun distance

Galactic distances

• Distance to the centre of the Milky way?
• What were we doing those many years ago?

Intergalactic distances

• The Andromeda galaxy and the local group of galaxies

The horizon and flatness problems

• If the sound horizon is finite, why does the cosmic microwave background have the same temperature over all of sky?
• Why is the Universe flat? It requires an extreme amount of fine tuning of the density of the Universe in the early Universe.

Fine-tuning or new physics in the early Universe

Inflation

• An exponential expansion in the beginning of the Universe
• Causally connected regions expanded beyond the horizon scale
• Dilutes the magnetic monopole number density
• Results in a flat Universe, quantum fluctuations provide seeds for structure formation with a nearly scale invariant spectrum

Framework to explain observed data, has its own issues

The history of the Universe

Planck collaboration 2015

Growth of structure in the early Universe

• The density fluctuations beyond horizon scales grow with the scale factor
• The growth of density fluctuations within the horizon stunted in radiation dominated era
• Generates a peculiar form for the density power spectrum

Measure the power spectrum of density fluctuations

• Blackboard derivations to understand the transfer function.

Distances within the country

• What is the order of magnitude of distances between these cities?
• How would you go about measuring these distances?

New Delhi

Kolkata

Chennai

Mumbai

~ 1000 kilometer

Distances in space

• Distance to the Hubble telescope?

• Distance to the moon?

Solar system scales

• Distance to the Sun?
• Distance to the outer planets?

Easier to measure in units of light travel time