Recent content by Safinaz

Where ##\delta \phi## is the first-order perturbation of a scalar field, ##\Phi## is the first-order perturbation of the space-time metric, and ##H## is the universe’s scale factor. It’s mentioned that this relation is given in reference: https://arxiv.org/pdf/1002.0600.pdf But I can't find...

Thanks so much for the answer : )

Hi, thanks for reply. What range does the index ##i## run over: ##\left( 1,2,3\right)## or ##\left( 0,1,2,3\right)## or something else? Ans.: ##\left( 0,1,2,3\right)## What explicitly are the variables ##w^i## that you are differentiating with respect to, i.e...

Does this equation mean that: ## x+y =z ##, and ## x = y##? I mean ## \delta_{ij} ## terms in the LHS of the eqaution equal those at the RHS ? with knowing that ## \partial_i \partial_j x ## term dose not vanish for ## \delta_{ij}=1 ## Any help is appreciated!

So there is no any way to simplify ## \partial_i \partial_j \phi ## ?

How can the following term: ## T_{ij} = \partial_i \partial_j \phi ## to be written in terms of Kronecker delta and the Laplacian operator ## \bigtriangleup = \nabla^2 ##? I mean is there a relation like: ## T_{ij} = \partial_i \partial_j \phi = ?? \delta_{ij} \bigtriangleup \phi.## But...

So can it written as: ## Eq = e^{ -ht} ( e^{t\sqrt{x}} + e^{-t\sqrt{x}} ) = 2 e^{ -ht} Cosh ( t \sqrt{x}) ##?

The eqution can be written as: ## Eq= e^{t( -h + \sqrt{ x} )} + e^{t( -h -\sqrt{ x} )} ## Can this be written in terms of Cosh x ?

I try to figure out the identity that leads to equation (27) in the menstioned paper. and writting ##F(k_1)## or ##F(k_2)## just to simplify. So that I'm asking about the correct identity of Dirac Delta

In a previous step in the paper, a transformation has been done from ##x## space to ##k## space by fourier-transforming

I need help to understand how equation (27) in this paper has been derived. The definition of P(k) (I discarded in the question ##\eta## or the integration with respect for it) is given by (26) and the definition of h(k) and G(k) are given by Eq. (25) and Eq. (24) respectively. In my...

I know how to solve similar ODEs like ## \frac{\partial^2 x}{ \partial t^2} + b \frac{\partial x}{ \partial t} + C x =0 ## Where one can let ## x = e^{rt}##, and the equation becomes ## r^2 + b r + C =0 ## Which can be solved as a quadratic equation. But now the problem is that there is...

My solution: Let ## \phi (x, t) = F(x) A(t) ##, then Eq. (1) becomes ## \frac{1}{A(t)} \frac{\partial^2}{\partial t^2} - \frac{1}{F(x)} \frac{\partial^2}{\partial x^2} = 0 ## So that : ## \frac{\partial^2}{\partial t^2} = k^2 ~A (t)##, and ## \frac{\partial^2}{\partial x^2} = k^2 ~F...

Hello. Thanks so much for your answer. I was trying to find proper IC and BC to find ## \phi(t,x)## . Assuming: ## bc={\phi[t,0]==1,(D[\phi[t,x],x]/.x->Pi)==0} ## ## ic={\phi[0,x]==0,(D[\phi[t,x],t]/.t->0)==1} ## Also ## \phi(t,x)## obays the Klein Gordon’s equation : ## \left(...

Okay. But now how to get the definition of ##f(x)## and ##a(t)## ?