# Cosmological Constant Problem

1. Jun 15, 2008

### NYSportsguy

I am new to the world of theoretical physics and was wondering if anyone can explain "vacuum energy" to me? What does it have to do with the expansion of our universe? Something about a "cosmological constant" is also involved.

If someone can give me a concise and accurate version of what all these three terms have to do with each other it would be much appreciated. I know "virtual particles" also have something to do with this.

2. Jun 18, 2008

### robousy

Hey NYSportsguy.

The solution to Einsteins equations require a 'fudge' factor to account for the current expansion of the universe. This is the cosmological constant $$\Lambda$$. We do not really know 'what' $$\Lambda$$ is, merely that it is required to fit theory with observation.

A number of theories exist as to the fundamental physical nature of $$\Lambda$$. One model is that it is the quantum vacuum energy as you mentioned. Here's the main idea. Forget everything you think you know about what an atom is, or an electron, or light or anything like that. In the language of Quantum Field Theory (QFT), one of the most succesful theories of physics, ALL matter and energy is fundamentally an excitation of a quantum field which is modelled as a HARMONIC OSCILLATOR. The harmonic oscillator is ubiquitous, ie it exists at all points in space. According to quantum mechanics no oscillator can be at rest due to the Heisenberg Uncertainty Principle. This implies that all the oscillator's in the universe are vibrating with some 'zero point' energy with a potentially infinte number of degrees of freedom (meaning each oscillator can vibrate at frequencies ranging from zero to infinity). When you calculate the energy of these vibrations one acquires the so called 'vacuum energy'.

To avoid infinite answers one usually applies some cutoff to the energy integral - around 100 GeV which is an expression of our 'faith' in QFT up to this energy. Even after applying this cutoff one obtains a vacuum energy around $$10^{120}$$ larger than the experimentally 'measured' value of the Cosmological constant $$\Lambda$$. This is a problem... : ) . It has been called the worst prediction of theoretical physics.

There are ways to tackle this but this is probably too much detail already. Hope this helps!

Last edited: Jun 18, 2008