Some Conceptual Problems in Cosmology Prof. J. V. Narlikar IUCAA, Pune

1. Dark Matter and Dark Energy Dark Matter

mv 2 /r = GM(r) m /r 2  constant v implies M(r)  r Why is dark matter needed? To explain flat rotation curves Since visible mass is confined to r < r G, we need dark matter beyond the visible radius r G. 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 clusters Coma ClusterComa 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 = 3H 2 / 8  G 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 h 0 2  [Hubble’s constant is taken as 100 h 0 km/s/Mpc.]

The problem of deuterium Cluster / galaxy data suggests  m h 0 2  0.15 h / ( h ) 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 Energy

First introduced into GR by Einstein -term via the -term: R ik - ½g ik R + g ik = - {8  G/c 4 } T ik. 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   = c 2 /3H 0 2 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 2/3H 0 -1, which works out at  6.6 h 0 -1  10 9 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?