Theorists have developed elaborate models to describe the opening moments of the universe and how it evolved after the Big Bang, but can these models be constrained by observing the universe as we see it today? This has been the thrust in recent years of work by William Stoeger and his collaborators. As has been recognized for decades, the universe today appears homogeneous – smooth – on very large length scales. The very early universe, in contrast, must have been very inhomogeneous – lumpy. When the size of the observable universe, a fraction of a moment after the Big Bang, was not all that different from the size of an atom, what is called the Planck era, then the inherent “graininess” of space described by quantum physics would have resulted in quantum fluctuations at the very earliest moments of its existence.
But in a system controlled by gravity, lumpiness almost always increases with time; only very rarely and then only under special conditions does it decrease. So where did our present homogeneity come from?
Usually a very early inflationary period (an extremely brief period of exponentially rapid expansion) – almost immediately after the Big Bang – is invoked to homogenize the universe. However, inflation itself requires a small perfectly smooth patch to get started. What process could make that initial inflationary patch smooth?
During his three-month visit from March to May, visiting Fulbright Fellow Krzysztof Bolejko (Nicolaus Copernicus Astronomical Center, Warsaw, Poland) worked with Stoeger to examine this question. They showed that, for large densities in the early universe, significantly broad initial conditions
involving viscous shear and pressure gradients can produce homogeneous regions from inhomogeneous ones rather quickly. An essay outlining the details of this work won 5th prize for the Gravity Foundation 2010 Awards for Essays on Gravitation.
But does the observed smoothness of the universe extend beyond the regions of space that we can observe today? We can only observe what we can see with light, and so we are limited in our observations (such as galaxy redshifts, the average overall mass and number of the galaxies, and their angular-diameter or luminosity distances) to that region of space within our “light cone”: that part of the universe close enough to us that light can have reached us within the age of the universe. For a 14 billion year old universe, this is a volume inside 14 billion light years from us.
For a number of years, Stoeger, Marcelo de Araújo (Universidade Federal do Rio de Janeiro) and their co-workers have been developing a framework for using astronomical observations to reveal the detailed structure and evolution of the universe without presupposing that it is spatially homogeneous (smooth and not lumpy) on the largest scales. Towards the end of last year Stoeger and de Araújo finally succeeded in demonstrating within this framework how to move the solution to the Einstein field equations (the mathematical description of the shape of the universe as expressed in Einstein’s theory of General Relativity) on our past light cone to all earlier times. This allows theorists to use those data – to the extent they are reliable
– to model precisely the structure and evolution of that part of the universe to which we have observational access.
As part of this approach the density of vacuum energy (dark energy) can also be determined, if we have data giving us the maximum of the angulardiameter distance and the redshift at which that occurs. Acquiring such data is just beginning to be possible with space telescopes measuring the light curves of distant type Ia Supernovae (at redshifts higher than 1.5).
More recently, de Araújo and Stoeger have succeeded in incorporating the drift of cosmological redshifts into this solution framework. These cannot be measured yet. But with the advent of extremely large telescopes and very high precision spectrographs, such crucial data will eventually be available to us. Redshift drift is the degree to which the redshift of a distant galaxy changes with time – the redshift of such a galaxy will, in general, be slightly different in, say, 10 years from what it is now.
It turns out that redshift drift is a parameter that can give us a lot of useful information about the nature of the universe. The famous cosmologists Alan Sandage and George McVittie first realized in 1962 that it gives us the mass-energy density of the universe at each redshift, independently of any details about galaxy counts, average masses, or evolution, or assumptions about dark matter content. But in the course of their research, de Araújo and Stoeger have also discovered that using redshift drift as a key element in their data set (instead of galaxy number counts and average mass per galaxy counted) also lets us quickly determine the functional relationship between redshift and the radial coordinate measure of light down our past light cone.
That is the key first step in determining the structure of the universe from data. At present it can only be done in a somewhat imprecise way, using estimates of galaxy masses along with galaxy number counts together with angular-diameter distances. Currently de Araújo and Stoeger are in the process of comparing the advantages and disadvantages of their technique with those of the methods previously used by cosmologists to approach this problem.
The Bolejko essay can be found in General Relativity and Gravitation 42: 2349-2356 (2010) and available online at arxiv.org: 1005.3009v1. The work by de Araújo and Stoeger has been published in Physical Review D 80, 123517 (2009) [with an erratum in Physical Review D 81, 049903(E) (2010)], and on the internet at arxiv: 1009.2783v1.
Gabriele Gionti, who joined the staff of the Observatory following his ordination in June, is now continuing his research on topics of Quantum Gravity.
Our current best understanding of the nature of gravity, one of the fundamental forces of the universe, is Einstein’s theory of General Relativity. This theory has a singularity, a point where it is clear that classical concepts of physics no longer hold, corresponding to the origin of the universe – what is popularly known as The Big Bang. This singularity suggests the necessity of a quantum mechanical approach to gravity, Quantum Gravity, in the same way that quantum mechanics underpins our understanding of the other fundamental forces of nature.
There are two main approaches to Quantum Gravity: Loop Quantum Gravity and String Theory. Loop Quantum Gravity has a “conservative” approach to quantum gravity; it treats gravity as an independent force from other interactions. On the other hand, String Theory attempts to unify all physical interactions, hypothesizing that there exist one-dimensional objects (called “strings”) more fundamental than particles, which propagate in time.