One of the predictions of General Relativity are the gravitational waves. It was announced in February 2016 that the gravitational waves were finally observed for the first time in the history. It means that we obtain completely new window for the observation of the Universe. Before that event we observed the Universe almost only in electromagnetic radiation. But we have only theoretical models, what happened in the first second of the evolution of the Universe, because we are not able to detect any radiation from this epoch of evolution. But if we are able to detect primordial gravitational waves, this situation will change. Gravitational waves were already observed at LIGO and VIRGO terrestrial observatories. People prepare so called LISA observatory in space, it will be prepared for launch around 2029. And the next generation of observatories are BBO, which will be already able to detect primordial gravitational waves. I try to explain in this lecture, how we describe gravitational waves in modified gravities.
One of the biggest puzzles of modern cosmology is the accelerated expansion of the Universe, which was observed at the beginning of the 21st century. One of the possibilities, how to obtain a model, is to add the cosmological constant into the Einstein equations. Second possibility is to change the theory of gravity. There are many ways, how to do it. We were investigating so called f(R)-theories. General Relativity is one example of these theories for f(R) = R. Here is my talk.
It was announced a result in 2012 that people measured neutrinos, which had the velocity bigger than the velocity of light. I tried to explain, why it was impossible to have such tachyons in Nature, so there had to be a mistake in the experiment. And really, there was an error in the experimental setting. Here are all slides in Czech (pictures are taken from web).
We could study General Relativity, when we consider d spatial dimensions (instead of 3). Then the computations are much more involved and there are many open issues in perturbation theory. Of course, such an extended theory is not realized in Nature, because we don’t observe extended extra dimensions. But people are still trying to search for small curved extra dimensions. Here is the presentation (pictures are taken from web).
Sometimes it looks mysterious, what is it the variational derivative and what is it the physical term variation. I try to give a simple explanation, how is the connection with the weak derivative.
Cross-product has interesting properties and exists only in dimension 3. I try to explain why.