Cosmology Definition and 951 Threads

I am trying to replicate the space time plot (the 2nd plot with Proper distance vs Time) as in this thread: space-time I wrote everything in python using the astropy cosmology package. Everything went smooth, but I am stuck at plotting the light path on the 'purple path', as per the above...

Considering the FLWR metric in cartesian coordinates: ##ds^2=-dt^2+a^2(t)(dx^2+dy^2+dz^2)## With ##a(t)=t##, the trace of the extrinsic curvature tensor is ##-3t##. But why is it negative if it's describing an expanding universe, not a contracting one?

[Mentor Note -- thread moved from the schoolwork forums to the technical forums] Homework Statement:: Tentative Note and summary on the origin and the evolution of information in the universe. Relevant Equations:: none As a teacher of physics I got many questions asked by my students when...

Imagine we attach an imaginary cosmological scale rope to an object that is very far away from us. Before attaching the string, the object would be receding from us due to spacetime expansion. After attaching it, tension would form in the string and we would eventually stop the object. After...

I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales. At some point (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic...

I was reading this paper from George Smoot (https://arxiv.org/abs/1003.5952) where he assumes the holographic principle as true and conjectures that our universe would be encoded on the "surface" of an apparent horizon as the weighted average of all possible histories. In that way, there would...

We assume two galaxy population, ##\mathrm{A}## and ##\mathrm{B}##; the corresponding maps have the following ##a_{\ell m}## : ## \begin{aligned} &a_{\ell m}^{A}=b_{A} a_{\ell m}^{M}+a_{\ell m}^{p A} \\ &a_{\ell m}^{B}=b_{B} a_{\ell m}^{M}+a_{\ell m}^{p B} \end{aligned} ## Here, ##b_{A}## and...

0:00 Gravitational lensing 23:19 Cosmology 33:00 Robertson-Walker spacetime 38:20 FLRW universe 1:01:35 Big Bang

I know I should not study cosmology from books that are too dated. Can you recommend an up-to-date cosmology book? I am studying GR from Carroll's book. Do I need to study astrophysics first or other topics?

In the ADM decomposition, like in the construction of the FRW metric, the coordinates are defined to be co-moving, so we know $$d\tau = dt$$ (i.e. the lapse function is normalized away) Starting from a five-dimensional embedded hyperboloid (as in carroll pg. 324) ## -u^2 + x^2 + y^2 + z^2 + w^2...

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

I found an article by James Bjorken (https://arxiv.org/abs/hep-th/0210202) which argues that universes with different size would have different physics (like different Standard Model parameters). When applying this reasoning to our own universe, Is this pure conjecture? Or is there some truth...

I know for sure PICO will be measuring polarization anisotropies with high fidelity. In addition, the PICO science paper shows that it will make full-sky Compton-y maps but the plots are mostly limited to l=1000. Will PICO be able to measure kSZ temperature anisotropy at l=3000?

I am trying to understand this graph but I am confused about the distance definitions. So there's an object located at a comoving distance ##r##. The proper distance of the object at ##z'## can be written as $$d(z{'}) = \frac{1}{1+z{'}}\int_0^{z{'}} \frac{dz{'}}{H(z{'})}$$ In this case...

but I could not develop, is it really possible to represent this way?

I have come across an old formula from my notes and I have no reference for it but it is using truncated digits in its formula to calculate the redshift for decoupling. The formula is nearly as accurate as the observed data from Planck 2018. So I would like to figure out the derivation of those...

Greetings everyone, I'm looking for ideas about what areas of math I should do to prepare for a PhD in Cosmology. (So far I have an undergrad math & stats degree). I personally love pure math and view it as a series of puzzles; but somehow cosmology sounds more "applied". Anyway there are so...

Greetings everyone, It's lovely to be here and I decided to join because I thought I might be able to get ideas about what math I should do to prepare for a PhD in Cosmology. (All I have so far is an undergrad math & stats degree). I mean I love pure math and view it as a series of puzzles...

A 1-sphere exists in 2D space. It is a circle in flat space. A 2-sphere is a 1-sphere embedded in 3D space. Its surface is non flat and 2 dimensional. A 3-sphere is a 2-sphere embedded in 4D space. Its surface is non flat and 3 dimensional. What does this last sentence mean in...

It is very amazing help8ng and encouraging forum. I am a research student of MS PHYSICS at COMSATS UNIVERSITY ISLAMABAD. I hope this firum will be much helpful to help me finding some tedious numerical solutions of a research paper.

Reference: https://scitechdaily.com/breaking-cosmology-too-many-disk-galaxies-a-significant-discrepancy-between-prediction-and-reality/ The following are quotes from the reference. 1. The Standard Model of Cosmology describes how the universe came into being according to the view of most...

The definition of power spectrum of matter density field is given by eq(1). I have also seen definitions of power spectra given by eq(2) . Does this mean (2\pi^3) has been absorbed in the correlation function? $$P_{xx}(k)=(2\pi^3)\delta(k-k^\prime)<x(k)x(k^\prime)>$$ .. (1)...

I was browsing YouTube (again) and stumbled upon this set of lectures by Ta-Pei Cheng. (I've seen the cover of the textbooks... but I'm not familiar with the author-lecturer or the details of the texts... but this looks interesting.) http://www.umsl.edu/~chengt/...

Hello all! I have been taking an academic break from school for certain mental health reasons that I won't waste your time talking about. Now, I am only a freshman in college. My school's physics department currently offers 2 majors: Physics and Physics/Astronomy. Obviously, I have lots of time...

Hi all, I just graduated from my master's program in theoretical physics. I did 60% of the coursework in high energy physics and rest in condensed matter theory plus a few experimental physics courses. I did my master's thesis in what can be called as theoretical cosmology, studying particle...

$$n_\vec{k} = \omega a^2(\vec{k})\tag{1}$$ One way is to write the inverse Fourier transforms of the terms above. So, eqn (1) becomes $$\int\mathrm{d}^3x\ n(\vec{x})e^{-i\vec{k}\cdot\vec{x}} = \omega \int\mathrm{d}^3x^\prime\ a(\vec{x^\prime})e^{-i\vec{k}\cdot\vec{x^\prime}}...

So. It was late night, the limpid sky a near cloudless darkness, somewhat lightened by the waxing moon. I being somewhat stoned and looking at the stars and constellations as I sometimes do, and it came to seem to me, in my imagination, that In the spaces between the stars, I was observing (in...

I’ve really been struggling with this book since I started it a couple of days ago. It’s essentially a problem book designed to teach you about astrophysics, structure formation, radiation, fluid dynamics, etc. through a curated set of questions. Some of the questions take a ridiculously long...

It is in cosmology context but actually, but it is also a mathematics/statistical issue. From spherical harmonics with Legendre deccomposition, I have the following definition of the standard deviation of a ##C_\ell## noised with a Poisson Noise ##N_p## : ## \begin{equation}...

What is the Compton Drag in cosmology?

In the following lectures: Prof. Susskind writes the terms ##\exp(3Ht_n)## and ##\exp(3ht_n)##. If I understand correctly he computes ##R(t)=R_0 \exp[\int^{t_n}H(t')dt']## where ##R(t)## is the scale factor of the Universe and ##H(t')## is Hubble's parameter. What I still don't understand is...

The error on photometric galaxy clustering under the form of covariance which is actually a standard deviation expression for a fixed multipole ##\ell## : ## \sigma_{C, i j}^{A B}(\ell)=\Delta C_{i j}^{A B}(\ell)=\sqrt{\frac{2}{(2 \ell+1) f_{\mathrm{sky}} \Delta \ell}}\left[C_{i j}^{A...

I have been studying cosmology, quantum field theory, and inflation all by myself, taking notes, solving the equations, and when I write down my work, it looks like a book. I think of self-publishing it; I believe it could be useful to others interested in the field. However, I am only a...

I know it says Universe is eternal, how does that work with gravity? If all the stars and galaxies had infinite time to attract each other why are they still apart? I guess this is a naïve question because no one talks about it but I can't figure it out. Thank you for answers!

Summary:: A Standard Model for Fantasy Role-Playing? Greetings fellow nerds. I am an amateur when it comes to cosmology. I know little in terms of cosmology beyond what I've seen on documentaries, of which I have watched dozens, if not hundreds. I've read Hyperspace by Michio Kaku and Black...

The number of visible galaxies is to vanish in the long-term future with the ##\Lambda##CDM model (book and papers of L. Krauss et al). I am interested in a quantitative study on how the population of galaxies decreases; I could not find one so I do it myself: The scale factor...

I am trying to follow a calculation from the book of William C. Saslaw, The Distribution of the Galaxies: Gravitational Clustering in Cosmology. The calculation is shown on the pages following page 122 in chapter 14 where the author talks about the Correlation function. I am able to reproduce...

Hello, I would like to know the right expression for the expression of variance of Shot noise in spectroscopic probe. Sometimes, I saw ##\sigma_{SN,sp}^{2} = 1/n_{sp}## with ##n_{sp}## the average density of galaxies, whereas my tutor tells me that ##\sigma_{SN,sp}^{2} = 1/n_{sp}^{2}## , so I...

I cite an original report of a colleague : 1) I can't manage to proove that the statistical error is formulated like : ##\dfrac{\sigma (P (k))}{P(k)} = \sqrt{\dfrac {2}{N_{k} -1}}_{\text{with}} N_{k} \approx 4\pi \left(\dfrac{k}{dk}\right)^{2}## and why it is considered like a relative error ...

Apart from Frank Wilczek, Kip Thorne, and perhaps Gerard 't Hooft, are there any more (living) Nobel laureates in physics who are open to the possibility that multiple universes exist?

I'm currently a fresh grad student in theoretical physics, and I'm still deciding to choose which research group to join. My current understanding (maybe I'm wrong) is the PhD theme pretty much determines the topic for future post-doc research so I kinda need to choose very carefully. I'm...

I was reading recently about string theory recently which postulates that there are 11 dimensions representing all possibilities for everything. This is an interesting theory, although very difficult to prove and therefore somewhat speculative in my opinion. [Ed.: personal speculation removed]...

a) For a flat universe ##(k=0)##, so ##(1)## simplifies to ##\dot a^2 = \frac{C_r}{a^2}##. The solution to this first order, separable ODE (given the I.C. ##a(0) = 0##) is \begin{equation*} a(t) = \left( 4 C_r\right)^{1/4} t^{1/2} \tag{2} \end{equation*} We switch to conformal time by...

Good evening, I have a question on a cosmology problem I have solved from Barbara Ryden’s Introduction to Cosmology 2nd Edition. I believe I have answered the question correctly, resulting in the following linear redshift relation when using separation by variables and some algebra manipulation...

This post is slightly different from a previous post sent to mathematical forum : this is because I talk about here the MATLAB function "eig" with 2 arguments but this concerns actually the combination between 2 biased tracers in Cosmology context. I am looking for a common basis of...

The Canadian physicist, Lee Smolin proposed in the 90's that laws of nature may evolve and change over time. He begun proposing that only the constants of nature would evolve, while the most fundamental laws would remain the same, but recently he has change a little bit his ideas and has...

There are several models of brane cosmology (https://en.wikipedia.org/wiki/Brane_cosmology) and several physicists working in this field (e.g Lisa Randall and Raman Sundrum), but as you will notice, apparently they are all directly related to string theory. This has several consequences, for...

One of the distance measures in cosmology is angular diameter distance, that can be used to determine a distance to objects whose actual (spatial) size is known, i.e. standard rulers. Beside baryonic acoustic oscillations, do we know other objects (or maybe I should better say structures) that...

I am curious about space. How it works, what does it contain, all different sorts of things. Any suggestions on what books to read for a beginner so that this curiosity do not fade away with time.

In the wikipedia article of the observable universe I have read the following: "Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe". This can be justified on the grounds that we can never know anything by direct...