According to the current interpretation of the big bang theory, the universe began some 13.8 billion years ago when space, time, matter, and energy arose spontaneously in an infinitesimally small region of space called a singularity. luckily for us, this tiny speck inflated, starting a journey of cosmic expansion that continues to this day. for the first 380,000 years of its existence, the space, time, matter, and energy of the universe were so dense that everything was effectively opaque. light and other electromagnetic waves were tightly bound to the matter of the universe, much like the electrons in a wire are tightly bound to the metallic network of the metal from which it was constructed. (have you ever been shocked while passing an electrical outlet in your house? no, of course not. and why not? because the electrons are bound to the atoms of the solid metal conductor quite tightly.) after expanding for roughly 380,000 years, temperatures reduced to a relatively cool 3,000 k and the universe finally became diffuse enough for light and matter to live independent lives. when we look out at the universe around us now, all the radiation we see is at least 380,000 years younger than the universe as a whole. everything before this moment is lost in time. this is also the time when nearly every free electron joined up with a hydrogen or helium nucleus - the period of recombination. in the intervening 13,799,620,000 years since recombination the oldest radiation has been stretched by the expansion of space-time to the point where it is no longer visible, but instead lies wholly within the microwave part of the spectrum. this cosmic microwave background radiation (cmb) has been chilled to a mere 2.725 k by the overall expansion of the universe. determine the following quantities at the moment of recombination in comparison to their current value for the currently observable a. its volume b. its radius c. its density