Physical Cosmology 1/4/2016
Docente: Alessandro Melchiorri
alessandro.melchiorri@roma1.infn.it
Suggested textbooks
http://www.astro.caltech.edu/~george/ay21/readings/Ryden_IntroCosmo.pdf
Barbara Ryden, Introduction to Cosmology
Suggested textbooks
An introduction to General Relativity, Sean Carroll
Suggested textbooks
Modern Cosmology, Scott Dodelson
Suggested textbooks
T. Padmanabhan, structure formation in the universe
Distance-redshift relation
Distance-redshift relation
When considering a single redshift, luminosity distances are larger for open and lambda dominated models respect to
flat, matter dominated, models.
http://www.icosmos.co.uk/index.html
Flat, matter only model.
Open model Blue: Flat, Lambda dominated
Degeneracy between Matter density and a
cosmological constant.
At first order, we measure the deceleration parameter from luminosity
distances of SN-Ia:
Line at constant q0=-0.5
SN-Ia catalogs sample up to redshift 2.
The degeneracy is close but no exactly along
q=-0.5
Line of degeneracy
In red,
current preferred region at 95% c.l.
from CMB and galaxy surveys.
We need a
cosmological constant !!
Cosmological Constant
What is a cosmological constant ?
Negative Pressure Costant Energy Density Very small: 0.2 atoms
per cube metre
Cosmological Constant
Zel’dovich in 1968 propose a connection with vacuum fluctuations in quantum mechanics.
http://users.camk.edu.pl/akr/zeldoedibiopap.grg.pdf
Cosmological Constant
In QM this diverges ! If we stop at Planck scale we have:
123 orders of magnitude difference !
Cosmological Constant
Matter and cosmological constant evolve very differently in time:
In the past, we had the two component equal at redshift:
Quite recent ! approximately 3.2 Gyrs ago ! This introduces another problem: “Why now ?” problem Matter/Lambda
equality
Dark Energy
Instead of considering a cosmological constant we can consider a generic equation of state:
From the second Friedmann equation:
We can have acceleration with w<-1/3 (if this is the only component).
Goal: to falsify a cosmological constant. We need a value of w different from -1 !
Dark Energy
If we consider a 2 components universe the acceleration parameter is:
Assuming:
We can have acceleration if:
Considering the continuity equation:
Assuming a multiple component flat universe:
The luminosity distance (neglecting radiation)can be written as:
Constraints on w (from Riess et al., 2004)
“Degeneracy”. with the matter density
Cosmological constant
No indication for w different from -1 !!!
Quintessence
A possible alternative to a cosmological constant is a scalar field. Under some conditions we can have an accelerating
Universe. Observationally we should have w different from -1 and evolving with z.
Tracking Quintessence
Several quintessence models have been proposed.
One interesting property of some of them is to follow the dominant energy component (tracking).
This helps in alleviating the Why Now ? problem.
http://arxiv.org/pdf/astro-ph/0403324v3.pdf
Phantom models
Models with w <-1 are compatible and also slightly preferred by current SN-Ia data.
These models are called “Phantom"and have quite dramatic consequences.
for w<-1 in the
future (z<0) this term
could diverge in a finite time.
Phantom models
In these models the scale factor grows as:
(teq is the time of dark energy-matter equality)
And diverges in a finite amount of time !
Phantom models
For w=-1.1 …
Dynamical Dark Energy
One could try a different parametrization introducing an equation of state that evolves with time.
A possible (old) parametrization is:
(not good, diverges at high redshifts!)
In this case the luminosity distance is (try at home):
Results from
SN-Ia from Riess et al, 2004 plus prior
on matter density.
Black dot
is a cosmological constant.
Parametrization of Chevallier-Polarski-Linder (CPL) Is, in practice, a Taylor expansion in a at first order:
At high redshift, small a, converges to w0+wa The continuity equation can be written as:
Integrating, we have that the energy density follows:
This parametrization could seem trivial…
…but sometimes trivial things work well, these CP+L papers are extremely well cited !!!
Recent
constraints from Planck 2015
Again, no evidence for something different from a
cosmological constant. But constraints on the evolution of w are weak !
The ESA Euclid satellite experiment,
expected to launch in 2020, by measuring
galaxy clustering and
Lensing should determine these parameters with
the following accuracy:
i.e. more than one order of magnitude better than what we have now.
Other parametrizations…
Chaplygin gas.
Introduced in aerodynamics in 1904.
Assuming , we get from the continuity equation:
This is a first example of Unified Dark Energy - Dark Matter model. At high redshift behaves as matter, at small redshift as a cosmological constant.
Another extremely well cited
paper…
Chaplygin Gas
Chaplygin gas with
alfa=1 is excluded from structure formation.
Excluded
Excluded
Excluded Excluded
http://arxiv.org/pdf/astro-ph/0301308.pdf
Cardassian Universe
We can modify the Friedmann equation by hand:
and we get acceleration even if we have just ordinary matter.
