ETSU Astrophysics 3415: “The Concordance Model in Cosmology: Should We Believe It?…” Martin Hendry Nov 2005 AIM:To review the current status of cosmological models and currently accepted values of cosmological parameters

What do we mean by the “Concordance Model” anyway? Since the late 1990s a remarkably (spookily?) consistent picture has emerged from all sorts of different observations. (This picture is not particularly simple or elegant!) The Universe began with a Big Bang, about 15 billion years ago, and has been expanding ever since It has a flat geometry (prediction of inflation) Energy budget – 1: 30% gravitating matter (a few percent is baryonic, the rest known as CDM – but we don’t know what that is) Energy budget – 2: 70% ‘dark energy’ – we really don’t know what that is but it is now causing the expansion of the Universe to accelerate, and probably has something to do with the energy of the vacuum. Energy budget – 3: a few percent probably also comes from massive neutrinos (but those can’t be the CDM) Large Scale Structure in the Universe grew from tiny quantum fluctuations (probably generated during inflation), first seen in the CMBR, under the influence of gravity.

What do we mean by the “Concordance Model” anyway?

From Lineweaver (1998)

What’s the problem with the “Concordance Model”?  Lack of elegance  Lack of observational evidence  A theoretician’s headache  It gives us nothing to argue about!  The lessons of history…

Modelling the Universe:- Background cosmological model described by the Robertson-Walker metric

Modelling the Universe:- Background cosmological model described by the Robertson-Walker metric Metric describes the geometry of the Universe

Closed Open Flat

General Relativity:- Geometry matter / energy “Spacetime tells matter how to move and matter tells spacetime how to curve” Einstein’s Field Equations Einstein tensor Ricci tensor Metric tensor Curvature scalar Energy-momentum tensor of gravitating mass-energy

General Relativity:- Geometry matter / energy “Spacetime tells matter how to move and matter tells spacetime how to curve” Einstein’s Field Equations Given can compute and ; These are generated by

Treat Universe as a perfect fluid Solve to give Friedmann’s Equations Four-velocity PressureDensity N.B.

Einstein originally sought static solution i.e. :- But if can’t have

Einstein originally sought static solution i.e. :- But if can’t have However, GR actually gives Can add a constant times to Einstein’s cosmological constant Covariant derivative

Friedmann’s Equations now give:- Can tune to give but unstable (and Hubble expansion made idea redundant)

Einstein’s greatest blunder?

Friedmann’s Equations now give:- Can tune to give but unstable (and Hubble expansion made idea redundant) But Lambda term could still be non-zero anyway !

Can instead think of Lambda term as added to energy- momentum tensor:- But what is ?… Particle physics motivates as energy density of the vacuum but scaling arguments suggest:- So historically it was easier to believe

Re-expressing Friedmann’s Equations:- For Define It follows that, at any time

Re-expressing Friedmann’s Equations:- Consider pressureless fluid (dust); assume mass conservation and More generally:- Expansion rate dominated by different terms at different redshifts Matter 3 Radiation 4 Curvature 2 Vacuum 0

“Concordance model” predicts:- But at redshift, At redshift, And in about another 15 billion years

Value of Present-day If the Concordance Model is right, we live at a special epoch. Why?…