A GOLDILOCKS UNIVERSE

The values of many fundamental constants appear to lie  within narrow boundaries that allow life to exist. In 2000,  the UK’s Astronomer Royal Martin Rees boiled them down  to six in his book Just Six Numbers NUMBER N, the ratio of the strengths of two fundamental forces, electromagnetism  and gravity VALUE about 1036 IN WHAT WAY IS IT FINE-TUNED? “The existence of elements other than hydrogen, helium and lithium depends on a coincidence” N determines the minimum size of sunlike stars. It tells us how big an object must  be before its gravity can overcome the repulsive electromagnetic forces that keep atomic nuclei apart, igniting nuclear fusion. A larger value would not matter very much, but if N were lower, stars would be smaller and burn through their fuel more quickly, making the evolution of life unlikely. NUMBER , the proportion of the mass of a hydrogen atom that is released as energy when it is fused into helium inside a star VALUE 0.007 IN WHAT WAY IS IT FINE-TUNED? The fusion of hydrogen into helium is  the first step in forming heavier elements and thus makes complex chemistry, and life, possible. If  were slightly smaller, nuclear fusion would be impossible and the universe would consist only of hydrogen. If it were slightly larger, all the universe’s hydrogen would have been consumed during the big bang and stars would not exist. NUMBER , the ratio of the actual density of matter in the universe to the theoretical “critical density” which would cause the universe to collapse eventually under its own gravity VALUE about 0.3 IN WHAT WAY IS IT FINE-TUNED?  is one of the factors that determines how fast the universe expands. If it were higher, the universe would have collapsed long ago; if it were lower, expansion  would have been too rapid to allow stars and galaxies to form. NUMBER , the cosmological constant, or the  energy that arises from quantum fluctuations of the vacuum VALUE about 0.7 IN WHAT WAY IS IT FINE-TUNED?  is the leading contender for the mysterious force that is accelerating the expansion of the universe. A smaller value would not be a problem, but if it were much larger the universe would have expanded so rapidly that stars or galaxies would not have had time to form. NUMBER Q, the amount of energy it would take  to break up a galactic supercluster as a proportion of the total energy stored in  all of its matter VALUE about 10-5 IN WHAT WAY IS IT FINE-TUNED? Q is a proxy measure of the size of the  tiny fluctuations in the early universe  that were eventually amplified into stars and galaxies. If it were smaller the universe would be inert and structureless; larger and the universe would be dominated by black holes by now. Neither case would support life. NUMBER D, the number of spatial dimensions VALUE 3 IN WHAT WAY IS IT FINE-TUNED? With four spatial dimensions the orbits of planets would be unstable, while life would be impossible with just two.