I've been reading about inflation and i encountered that one can always define the sound's speed as
c_s^2 \equiv \frac{\partial_X P}{\partial_X \rho}
where X \equiv \frac{1}{2} g^{ab} \partial_a \phi \partial_b \phi. In the case of a canonical scalar field P=X-V and \rho=X+V, so c_s^2=1...
In the standard inflationary scenario, the power spectrum is evaluated at the cosmological time when one assumes an equation of state $ P= \omega \rho$ , that is, one is assuming a particular radiation or matter dominated universe. Why does it has to be in these cosmological epochs? does it...
Hello, i was studying kerr black holes and i think i can understand most of the theory behind it but i was wondering how can you detect black holes that are actually rotating?. I thought like sending two light rays from the same point (like gravitational lensing) but since the black hole is...
Thanks for your reply, but now i have more questions
This is exactly where i am confused, as far as i know, when we measure the quantum mechanical spin of a particle, we need a time of measurement, a basis, and a measuring device. In the cosmological context i don't see these, so my...
Im trying to understand inflation, specially the part of structure formation, so I am following Mukhanov's Book. There he does an analysis on quantum fluctuations, more specifically he quantize the Newtonian potential and finds the power spectrum and turns out to be scale invariant. I kind of...
Im trying to solve (approximately) the following problem: Suppose that i have 2 planets with mass m1 and m2 orbiting around the sun and i take into account the following interactions:
a) Interaction between planet 1 and the sun
b) Interaction between planet 2 and the sun
c) Interaction...
Homework Statement
I need to prove that if two metrics are related by an overall conformal transformation of the form \overline{g}_{ab}=e^{a(x)}g_{ab} and if k^{a} is a killing vector for the metric g_{ab} then k^{a} is a conformal killing vector for the metric \overline{g}_{ab}Homework...
1. The problem statement
I need to prove that if two metrics are related by an overall conformal transformation of the form \overline{g}_{ab}=e^{a(x)}g_{ab} and if k^{a} is a killing vector for the metric g_{ab} then k^{a} is a conformal killing vector for the metric \overline{g}_{ab}Homework...