Some Conceptual Some Conceptual Problems in CosmologyProblems in Cosmology

Prof. J. V. NarlikarProf. J. V. Narlikar

IUCAA, PuneIUCAA, Pune

1.1.Dark Matter and Dark EnergyDark Matter and Dark Energy

Dark MatterDark Matter

mv2/r = GM(r) m /r2 constant v implies M(r) r

Why is dark matter needed?To explain flat rotation curves

Since visible mass is confined to r < rG , we need dark matter beyond the visible radius rG .

The amount of dark matter may exceed the amount of visible matter.

If clusters are in dynamical equilibrium the virial theorem applies:

2T + = 0.

Why is dark matter needed?To make up for potential energy

in clustersComa Cluster

Observationally what is found is that the kinetic energy is large compared to the potential energy. The difference is made up by postulating dark matter more or less at rest.

Again, the amount of dark matter exceeds that actually observed in the form of galaxies, stars, hot gas, etc.

Why is dark matter needed?To make up for potential energy

in clusters

How much dark matter is needed?

Define closure density by

C = 3H2/ 8G

The matter density is denoted by m = m C

If we were limited to visible matter only, we would have m 0.04 only.

The presence of dark matter means that the value of density is greater than this.

The problem of deuterium

If all the dark matter were baryonic, the

observed abundance of deuterium cannot

be explained by primordial nucleosynthesis.

For primordial process to work we need the

following inequality to hold:

m h02 0.02.

[Hubble’s constant is taken as 100 h0 km/s/Mpc.]

The problem of deuterium

Cluster / galaxy data suggests

m h02 0.15 h0

1.5 / (1 + 0.55

h01.5)

Thus there is conflict with deuterium abundance data.

Inflationary cosmology predicts that the spatial

part of the spacetime is ‘flat’, i.e., m= 1.

There is therefore a large gap between the

density of matter (including dark matter) and

the inflationary prediction.

The problem with inflation

The problem with matter density so large as required by inflation (whether dark or visible) is that in forming large scale structures with the observed level of inhomogeneity, it leaves large signatures on CMBR.

The problem with structure formation

Solution

Make the following assumptions: Dark matter is mostly non-baryonic.

This helps in two ways: it does not affect deuterium abundance and its signatures on CMBR are very minute.

Assume that inflation occurred,

i.e., m= 1 Assume that matter + energy is mainly in

these two modes, m= b+nb

This view prevailed till the 1990s. Vide quote by Malcolm Longair in the 1986

Beijing IAU Symposium on Observational Cosmology:

“There is no evidence that 0, and I find the classical Friedmann models to have the great appeals of simplicity and elegance…”

[Beijing Conference Proceedings p. 828.]

However, this did not turn out to be the last word! The assumptions made above were not sufficient.

A new concept was necessary.

Dark EnergyDark Energy

First introduced into GR by Einstein

via the -term-term:

Rik - ½gik R +gik = - {8G/c4} Tik .

The extra term on the l.h.s. has a constant and that is permitted by the covariance of

the equations. [ a variable will not do! ]

The advantage of this extra parameter is that it enables more theoretical models within the overall big bang scheme.

Dark Energy

One can define

a ‘density’ parameter for , by

= c2/3H02

In a generalized framework this concept

today is called “dark energy”.

Dark Energy

The age problem

The age of the ‘flat’(k = 0) Friedmann

model is 2/3H0-1,

which works out at

6.6 h0-1 109 yrs.

This is too short a time span to accommodate old galaxies. However, with , one gets models with longer ages.

The density problem

The ‘flatness condition’ required too much by way of density of nonbaryonic dark matter. Now we can write:

b + nb + = 1

(0.04) (0.23) (0.73) .

and pass on the lion’s share to .

The supernova problem

The models given by dark energy give a better fit to the redshift-magnitude relation for Type 1a Supernovae.

Some problems with non-baryonic dark matter and dark energy

1. As yet no candidate for NBDM has been found in the terrestrial lab or in astronomy.

2. Even finding a possible supersymmetric particle in the lab does not guarantee that it is a NBDM candidate until one shows that it exists in the cosmos with the right abundance.

Some problems with non-baryonic dark matter and dark energy

3. If dark matter is present in a cluster, why does it not collapse towards the centre under its own gravity? What keeps it in dynamical equilibrium.

[For NBDM the normal pressure option is not there.]

4. Dark energy models today are highly speculative and have no other direct support in any astronomical observation.

Some problems with non-baryonic dark matter and dark energy

5. Dark energy models, except for the of Einstein have no natural relationship to any existing and established theoretical framework, like GUTs, SUSY, etc….

On aesthetic grounds

one may question the propriety of placing

faith in so much speculation based on so

few direct observations.

Is this physics ?

or a new version of

the Emperor’s New Clothes?

Emperor's New Clothes?