Loop quantum cosmology and the early universe

Over the history of mankind, the understanding of our Universe has evolved and matured, thanks to remarkable advancements both on theoretical and experimental fronts in the fields of quantum mechanics and general relativity (GR).

Quantum mechanics describes the physics at small scales such as the scale of sub-atomic particles, while gravity is weak and remains practically inert. On the other hand, the large scale structure of the universe is dictated by gravity, which is governed by GR, while quantum mechanics plays no role. Both theories have proved to be robust in their own territory under various theoretical and experimental tests. Unfortunately, it turns out that, as they are, GR and quantum mechanics do not play well with each other when brought under the same umbrella. This leaves us clueless about the situations when the size of the system is small enough for quantum physics to be important and at the same time gravity is so strong that it cannot be neglected anymore.

The very early stage of our own Universe is an example of such a situation, where neither GR nor quantum mechanics can alone be trusted. Although the large scale structure of the universe is very well explained by Einstein’s theory of general relativity (GR), it fails to provide a consistent picture of the early stages of the universe, due to the presence of cosmological singularities such as the big bang. Evolving Einstein’s equations backwards in time from the conditions observed in a large macroscopic universe today, we see that the universe keeps contracting and the space-time curvature keeps increasing, until the universe reaches an extremely high curvature regime where the classical GR description is not reliable. In fact, if one naively continues evolving Einstein’s equations in this regime, one encounters the big bang singularity.

To gain a reliable understanding of the physics in such cases one needs an amalgamation of ideas from both GR and quantum mechanics: a quantum theory of gravity.

Visualization of quantum structure of space-time in LQG. (Credits: Albert Einstein Institute)

Loop quantum gravity (LQG) is one of the leading approaches to quantum gravity, which gives a consistent picture of the discrete quantum structure of space-time geometry (as opposed to the continuum description given by GR). The quantum space-time geometry provided by LQG opens up new avenues to explore the physics of the early universe and cosmological singularities under the paradigm of loop quantum cosmology (LQC). One of the key features of the discrete quantum geometry of LQG is that when the space-time curvature is sub-Planckian, equations of LQC are extremely well approximated by those of classical GR. The difference becomes important when the space-time curvature becomes significant for quantum discreteness to kick in. This leads to the resolution of the big-bang singularity via a quantum bounce, which serves as a smooth quantum geometric bridge between the current expanding branch of our universe and a contracting phase that should have existed in the far past (Fig.2).

Schematic impression of early universe in LQC. (Credit: APS/Alan Stonebraker)

In the paradigm of LQC, the history of the Universe is different from that in the standard GR. As shown in Fig.2, there exists a quantum geometric pre-inflationary phase. The origin of quantum perturbations which result in the formation of cosmic microwave background (CMB), and that of the large scale structure observed today, can now be traced all the way back to the quantum gravity regime. Due to a modified pre-inflationary dynamics of LQC, these quantum fluctuations experience a different background evolution than in the standard paradigm, which can in principle have observational imprints on the temperature and the polarization power spectrum observed in the CMB. Understanding the evolution of the quantum fluctuations and extracting out loop quantum geometric imprints in the recent observational data are among the main directions of research pursued by the scientists at IGC.

In forthcoming articles, I will describe different aspects of LQC and its connection with observations, in particular, with the CMB anomalies observed by the recent Planck and WMAP missions.

Brajesh Gupt

Author: Brajesh Gupt

Brajesh Gupt is a postdoctoral fellow at IGC. His current research interest lies in understanding the very early stages of our Universe and studying its relation to current observation using the techniques of loop quantum gravity. His research interest extends to inflationary paradigm and CMB anomalies. Brajesh was born in Deoria, a small town in the eastern part of the state of Uttar Pradesh, India and earned bachelor’s degree in electronics and communication engineering from Birla Institute of Technology Mesra, Ranchi, India in June 2009. He then enrolled in the doctoral degree program in the physics and astronomy department at the Louisiana State University and joined IGC in August 2014. When not thinking about the mysteries of the Universe, Brajesh likes to travel, read, write, cook, and listen to music.