Recent content by AHSAN MUJTABA

I am facing a problem while wanting ##\phi## dynamics in a cubic potential; ##g\phi^{3}##. The equation of motion I get for my case is(this follows from the usual Euler-Lagrange equations for ##\phi## in cosmology--Briefly discussed in Carol's Spacetime Geometry, inflation chapter)...

Sorry, the slow-roll parameter is: ##\epsilon_{H}=\frac{\dot{H}}{H^{2}}##.

I have recently studied the slow-roll inflation model. In it, slow-roll inflationary conditions are mentioned in a lot of places(these conditions needed to be satisfied for inflation to happen). I don't really understand the meaning and purpose of slow-roll inflation. I want to know a very...

We study metrics, in them, we take time as a coordinate. I mean to say that if time is a coordinate then in normal mathematical language, we can have negative coordinate values as well. This confuses me a lot as I want to see and understand the concept from the true physicist's perspective...

I am a bit confused regarding the concept of the horizon problem. I have studied that the background radiation data implies that the radiations were not in causal contact at the beginning of the universe as from the big bang model. I want to know that how inflation is solving that problem? To...

Yes, now I am clear about that. Thanks.

According to this article, it is seen that ##L=ct## is right because to convert dimensions of time into length, we set c=1. Secondly, we know Compton's wavelength relation, and from that, we can have ##(mass)^{-1}## dimensions of both time and length.

Just one little question, does defining length in terms of mass dimensions by using the relation ##L=ct## is legit or not? In natural units i.e. c=1, the time and length would have the same dimensions.

Just check my work to find dimensions of ##a(t)##. I have written the metric as, ##ds^{2}=dt^{2}+a(t)^{2}dx^{2}.## Now, I am aware of the dimensions of the quantities as: ##ds^{2}=[L]^{2}##, ##dt^{2}=[L]^{2}##( I am defining it in terms of length by L=ct, taking c=1.) and ##dx^{2}=[L]^{2}##. I...

Would you please elaborate a little? Thanks.

I know the formula for Hubble's parameter, ##\frac{\dot{a}}{a}##, but I cannot infer any dimension of ##a(t)## from it. Please guide me. Thanks.

I need to understand these dimensions as I am making some equations dimensionless for my tasks.

Does that imply that the dimension of momentum eigenvalue becomes inverse of mass? You say that we measure mass in terms of GeV. So, due to that unit(GeV), does the dimension of momentum become (mass)##^{-1}##?

I am studying polymer quantum mechanics. In it, they say that the momentum, ##p## eigenvalue, has the dimensions of ##(mass)^{-1}## and similarly ##\omega## has the dimensions of ##mass##. How it is possible, please someone explain that to me. Even a little hint would work. I don't get it...

One thing that bothers me regarding the phase portraits, if I plot a phase portrait, then all my possible solutions (for different initial conditions) are included in the diagram? In other words, a phase portrait of a system of ODE's is its characteristic diagram?