A crack in Einstein's equation can be found for processes with constant negative pressure. Einstein's equations predict an exponential expansion which is adiabatic (no increase in entropy). Rather, thermodynamics predicts that systems exhibiting a negative pressure will spontaneously contract or implode. This is the only case where systems exhibiting a zero-point energy tend to condense.
Inflation, and all its modified forms, were proposed as a panacea for answering the nagging problems of standard cosmology:
(i) Why is space so homogeneous and isotropic on the large scale?
(ii) What is the origin of the primeval inhomogeneities there we observe on the small scale like that of stars, galaxies, and clusters?
(iii) Why does the universe appear spatially flat and the parameters are so fined-tuned?
(iv) Where have all the unwanted relics gone, like magnetic monopoles?
Many years ago Richard Feynman, building on a suggestion of Dirac's that the phase of the wave function should be given by the classical action of a particle, developed his path integral formulation of quantum mechanics, better known as a "sum over histories";. At first this was hotly contested by the same Dirac because once we know the position of a particle, the inevitable interaction between detector and particle modifies it so that it was not the same particle before detection.
Boltzmann, in his popular lectures, contemplated that the universe will end in a heat death. When bodies at different temperature are placed into thermal contact, heat is transferred from the hotter to the colder body thereby increasing the entropy. Thermal interactions will continue to occur between unevenly heated bodies, thereby producing ever increasing amounts of entropy until the universe will arrive at a state of thermal equilibrium where everything has reached the same temperature so that the 'fuel' for change has been exhausted.
There has been much ado about the Bekenstein expression for the entropy of a black hole, and the Hawking expression for its temperature. There has been less ado about the Unruh temperature that sets the temperature proportional to the acceleration of dectectors to detect particles that would otherwise go undetected if at rest, or in uniform motion. This relation supposedly is related to Einstein's principle of equivalence, which, in is most sweeping form, says that the effects of acceleration and gravity are identical. Here I will show that
Relativity abounds in paradoxes. The paradoxes themselves are the result of deceptive wording in the gedanken experiments conjured up by Einstein. Nothing can be deduced in a gedanken experiment that was not originally planted there. Many others have followed the same path.
Inflation has been described as a drug to cure the flatness, horizon, and smoothness problems of the big bang scenario with dangerous side effects [New Scientist 02/07/2012]. The horizon problem arises from the prediction that the universe is homogeneous and isotropic. When traced back to the big bang it would mean that causally disconnected regions would have to have been nearly the same so that it would explain the present day homogeneity. This is highly unlikely.