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1

As you state, conformal time is defined as $$ \eta(t) = \int_0^t\frac{\text{d}t'}{a(t')}. $$ Using $$ \dot{a} = \frac{\text{d}a}{\text{d}t}, $$ this can be written in the form $$ \eta(a) = \int_0^a\frac{\text{d}a}{a\dot{a}} = \int_0^a\frac{\text{d}a}{a^2H(a)}, $$ with $$ H(a) = \frac{\dot{a}}{a} = H_0\sqrt{\Omega_{R,0}\,a^{-4} + \Omega_{M,0}\,a^{-3} + ...


0

The Casimir Effect constrains the available wavelength of quantum fluctuations within the space between two conducting plates. So the answer to your last question is "Yes" - some places have more than others. However, in free (flat) space the answer is probably "No". They are not totally unpredictable because otherwise people would not be able to (say) ...


1

I created this site early in 2014: SpecialRelativity.net The site was built specifically for people who aren't keen on math.


2

From here: Before proceeding, it should be mentioned that the statistical significance of the result is still under debate. While the asymmetry is significant at the ≳3σ level, some question whether it is simply a consequence of the “look-elsewhere” effect: i.e., we test for all kinds of anomalies in the CMB, and the investigated parameter space is so ...


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i would like to provide another answer (despite my comments on top or complementary to them) i would propose to use a historical account of the evolution of the concepts and ideas/methods in physics from Newtonian mechanics to Relativistic mechanics, including the specific problems that arised (this provides two things: 1. a perspective on the methods and ...


1

To measure the size and distance of stars you use a set of tools that build on each other. For distance, first there is parallax. Nearby stars have an apparent shift in position relative to distant stars or preferably, galaxies, in the 6 months it takes the Earth to go from one side of the Sun to the other. Triangulation gives the distance. Then a table ...


1

I have used: "Relativity: A very short introduction"; Russell Stannard, OUP, to teach relativity to (interested) members of the general public, with some success. http://ukcatalogue.oup.com/product/9780199236220.do It really is very short - only 128 pages, but covers the main ideas of both Special and General Relativity. I find the explanations very clear. ...


2

Cosmology usually adopts something called the "Cosmological Principle", which is that, on large scales. the universe is homogeneous and isotropic. Therefore the universe looks the same wherever you are and looks the same in all directions. Thus light emitted from our part of the universe travels outwards and is received by distant parts of the universe ...


-1

If this is so, then isn't light constantly getting past all matter in the universe and so being lost. It may be, but we have no way to know. We do not see far enough to see what happens on the edge of the material universe. Even if there is such edge and only vacuum beyond, energy of the material universe does not need to decrease, because there may ...


3

What caused the transition,[...] As the universe expands, the number of particles per unit volume goes down. But in addition to this, photons suffer a cosmological red-shift. So the density of mass-energy due to nonrelativistic particles goes down, and the density due to photons goes down, the latter goes down faster. By extrapolation, we predict that ...


4

Here is a good basic summary of the history of the steady-state theory and the observations that caused it to fall out of favor, mainly the second two mentioned by Kyle Kanos. One of these was the observation of intense radio sources that didn't seem evenly distributed throughout the universe, but were only seen at large distances (higher redshifts): The ...


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The following passage has been extracted from the book Parallel worlds: Finally, in Nature magazine in 1965, Hoyle officially conceded defeat, citing the microwave background and helium abundance as reasons for abandoning his steady state theory.


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The steady state theory fails to model a few observed features of the universe: the accelerated expansion of the universe radio galaxies and quasars that are only observed at high redshifts & not everywhere the existence of the microwave background light


-1

Our Big Bang produced only matter. 2. Big Bangs can produce either only matter or only antimatter. 3. Many universes (only two will not do) were formed. One half of them contain only matter. The other half contains only antimatter. The formation of universes will continue. It has no known beginning nor a known end.


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Ever heard of the cosmic microwave background? The CMB is a relic from when the universe became "opaque" - when, as Wikipedia says, protons and electrons combined to form neutral atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. So photons decoupled and the CMB was ...


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I've found this paper: Cosmological quantum entanglement, of E. Martin-Martinez and N. C. Menicucci. (last revised 19 Oct. 2012) Abstract We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of expanding universes. We discuss recent theoretical results reporting on the ...


1

To my mind, the Big Bang doesn’t refer to a distinct event but to a cosmogonic theory as a whole, that “predicts” ( should we say “retrodicts”?) many different events of the deep past. For example, there is such established term as “Big Bang nucleosynthesis” that describes an epoch several seconds past the Beginning of Time. The Beginning of Time in the ...


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The main problem with this hypothesis is that Penrose–Hawking singularity theorems state existence of cosmological singularity at the beginning of time, unless (at great matter densities) either some mysterious fields intervene or General Relativity fails at all. Cosmological singularity is a thing definitely distinct from a supernova explosion, whichever ...


0

We may be Boltzmann Brains of the type that run simulations ie more of a "Boltzmann State Machine". 1 kg of mass converted to energy can execute approximately 10^50 operations, and that's assuming non-reversible classical computing. Which is quite enough to realistically simulate all of us on Earth, if not the rest of the universe in detail. The fact that we ...


0

$H$ tells us how fast the universe is expanding, relative to how much it has already expanded. It has units of inverse time. For example, if $H=0.1\ \mathrm{s}^{-1}$, then the universe is expanding by 10% every second. Suppose that the density of mass-energy in the universe was so small that deceleration was negligible, and suppose that at $t=1$ s, we have ...


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You have to consider entropy to answer this question. The idea of the Boltzamnn brain presupposes an expectation of a universe at thermal equilibrium, or maximally high entropy. In order to create the initial state from which the natural processes you describe (evolution, development etc.) require to operate, the universe has to first start in a state of ...


2

Your questions are in no way challenging. The answer to both questions is the same: it could be, we do not know. Actually, you could also ask the opposite: how do we know that physical space is equivalent to the continuum (the real line) instead of being a larger infinite (by this a mean an ordered field of larger cardinality, such as the surreal line)


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Um, a snarky answer is that now neither is proper. As Anna notes, the $r=0.20$ value assumes no contribution from galactic dust polarized emissions ("foregrounds"), while $r=0.16$ results from BICEP2's indirect estimate of such foregrounds. However, now Planck has published a much more direct measurement of these dust emissions, and they're much higher ...


0

Thus, the two primary options for flat finite space "shapes" are 3-D torus or video-game-screen. Not true. It's possible that the universe has a nontrivial topology, but there is no evidence for it, and it's not the most common assumption. The most common assumption is that if the universe is closed, it has the topology of a 3-sphere. I do not ...


3

So I've done some further research into this question and the result I found is quite surprising. There truly is no set definition. Some cosmologists will tell you (as John Rennie mentioned) to avoid using the term "Big Bang" unless you absolutely have to. However, that is a luxury not afforded to all cosmologists. The more surprising thing is that among ...


3

The total energy of the universe is a vexed issue since different commentators have different views about what the concept means. See the question Total energy of the Universe for a sampling of the various viewpoints. If you Google for zero energy universe you'll find several papers purporting to show that the total energy is zero. However since their ...


4

All statements like "when the universe was the size of a grapefruit" refer to the currently observable universe. As the universe has a finite age and light travels at a finite speed (and there is nothing infinite going on with expansion), the observable universe is a finite patch. I discussed some of the different notions of horizons in answering another ...


3

If we take the simple approach of determining the state of the "jerk" today by assuming an exponential expansion (e.g., $a(t)\sim\exp(H_0 t)$), then $$ \dot a=H_0a\tag{1} $$ The derivative of this is then, $$ \frac{d^2a}{dt^2}=H_0\dot{a}=H^2_0a $$ And now for the "jerk," $$ \frac{d^3a}{dt^3}=H^2_0\dot{a}=H^3_0a\tag{2} $$ The Hubble constant is already pretty ...


2

At what speed does our universe expand? This question doesn't make sense in the form in which it was posed. To see why, let's start by thinking about how we know the universe is expanding. The expansion of the universe was originally discovered by Lemaître and Hubble, who found that the redshifts of galaxies were proportional to their distances from ...


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As I stated in my comment, our observable universe is much larger than the Hubble radius: we can observe galaxies that are receding from us faster than the speed of light. I refer to this post of mine and links therein for more info: http://physics.stackexchange.com/a/63780/24142 Also, in the standard cosmological model, where the density of dark energy is ...


3

I had a quick look at the paper - its mostly nonsense. The intrinsic light from a quasar is completely dominated by its emission line spectrum and a mostly featureless continuum. The emission lines give the true redshift of the quasar. Absorption lines in quasar spectra are predominantly due to foreground gas clouds at lower redshifts than the more distant ...


0

If I understand correctly your question, you are essentially asking why is it, that we always see a potential of this form: Rather than a, say $V=-\phi^2 +\lambda \phi^4$ graph. Where in the first case the coordinate can roll-down only one direction, whereas in the other case it can roll down the other direction as well. It doesn't matter which you ...


1

There is no definite SIZE to the universe as such. There is however a size to the OBSERVABLE universe. These are very different. And indeed the observable universe is defined by Einstein information caveat where information cannot propagate faster than light. Now, it is in this sense, that Newtonian mechanics fails us, as newtonian gravity (and grav. ...


2

Only in the case of a static spacetime is the metric derivable from a scalar potential. Cosmological spacetimes aren't static, so they can't be derived from a potential.


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Here is a short description of Big Bang: Over the years, proponents of the big bang have tried heroically to change the name. They are dissatisfied with the common, almost vulgar connotation of the name and the fact that it was coined by its greatest adversary. Purists are especially irked that it was also factually incorrect. First, the big ...


1

Ulitimately the Universe's expansion is due to the initial conditions, unfortunately explaining why these initial conditions exist is beyond the scope of classical big bang theory as they exist as parameters than can be adjusted. However the expansion of the Universe is not independent of the matter it contains and the Friedmann equations link the rate of ...


3

The basic reason for cosmological expansion is simply inertia. Because the universe was in an expanding state soon after the big bang, it kept expanding. This is roughly analogous to Newton's first law of motion. In addition to this, dark energy is currently causing a significant acceleration of the expansion. (Its effect was not dominant in the past, and ...


0

You are apparently comparing with the expansion of some object, which is being heated. Well, such an object consists of particles, atoms in a lattice maybe, and each of those vibrate. More thermal energy makes them vibrate more violent, which make them fill more space. If all atoms require more space, the object expands, since they all "push" at each ...


4

One. The inflationary period is thought to have lasted from around $t = 10^{-36}$ seconds to $t = 10^{-33}$ seconds after the Big Bang. So while you're technically correct to say it lasted less than a second that's a bit of an understatement. Two. See my answer to What was the density of the universe when it was only the size of our solar system? for the ...



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