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1

For inflation the potential energy of the field dominates the kinetic energy $\dot{\phi} \ll V(\phi)$ This limit is referred as slow roll and under such conditions the universe expands quasi exponentially $a(t) \propto \exp \left( H dt\right) = e^{-N} $ where we define the number of e-folds $N$ as: $dN = -H dt$ so that $N$ is large in the far past and ...


3

In the standard model of cosmology, we say that the universe we live in is an FRW-universe. The FRW part just refers to the initials of the guys who first wrote down the description. The equation that describes such a universe is: $$ds^2=a(t)^2\left[-d\tau^2+d\vec x^2\right]$$ Note: this is for a flat, homogeneous, isotropic FRW-universe. In the above ...


5

The cosmological constant has an interesting history behind it. Originally, when Einstein introduced his theory of general relativity in the early 20th century, the Einstein Field Equation, which was the equation for the gravitational field, described gravity as the effect of the curvature of space-time due to the presence of matter and energy. Perhaps you ...


3

The cosmological constant is important for at least two reasons. Our universe is currently asymptotically evolving towards a universe where a constant energy density dominates the total energy density. The cosmological constant can be interpreted as exactly this. Therefore, analysis of the current state of our universe relies heavily on the concept of a ...


0

I suspect that you cannot prove it purely from experimentally/observational, and I think that approach is useless. If you think that the whole universe as a single state in state space, then there is no way you can compare with any other state. You may think that there might be a phase space with (macroscopic) parameters $(V,\{\alpha_i\})$, so we can have a ...


2

Reheating is the decaying of the inflaton into the particles that we are currently observing. In the context of quantum field theory this happens simply because there is a coupling of the inflaton field to either the Standard Model (and possibly other, yet unobserved, particles) directly, or to a field $\chi$ which then couples to the Standard Model and ...


0

There's a difference between curvature of spacetime and curvature of space. Extrapolating from what we can see around us and assuming the cosmological constant lives up to its name, spacetime will eventually approach curved de Sitter geometry, in contrast to flat Minkowski geometry or anti-de Sitter geometry of opposite curvature. This is something of an ...


-2

I think this is an example,universe is rotating about its own central axis.if this is the case,take a curve beaker and a flat plate with some water in them.First shake clockwise the curved beaker and then flat plate.In which,beaker or plate did the circular motion was seen about its center?I guess curved one.So,our universe is curved.


0

What muddies the waters a bit are that when I tried to search for the borde-guth thing, the first result was a Christian site, and of course when it was discovered that the universe was expanding, the big bang was taken by many Christian scientists as the creation of the universe by God, and that is still the most likely explanation for why the universe ...


3

It is only in the absence of dark energy that the correspondence between geometrical curvature and the ultimate fate of the universe is as straightforward as you describe. Measurements (primarily of the cosmic microwave background) indicate that our universe is flat or very nearly so, which should be interpreted geometrically (i.e. in terms of the sum of ...


0

There are a few other reasons why we think the universe is expanding. Wikipedia lists and explains them far better than I will ever be able to. One thing though, your ruler is not expanding. The intermolecular forces are making sure the distance between molecules stays the same. Empty space is expanding, expanding essentially the distances between weakly ...


0

Wayne Hu (professor, Univ. Chicago) has a CMB website that seems to answer this question. It is stated that "The one-to-one mapping between wavenumber and multipole moment described in [a previous section] is only approximately true and comes from the fact that the spherical Bessel function is strongly peaked at $kD \approx l$" where $l$ is the ...


0

The BICEP2 data suggests that inflation happened, and in particular the data is compatible with chaotic inflation. Lubos Motl has a blog post on this here, and a quick Google found many related articles like this one. Chaotic inflation (almost?) invariably results in multiple causally disconnected regions. One of these would constitute our universe, and the ...


-1

Regarding question 1, Inflation was offered as a theory to explain why the universe seems more or less the same and has the same cosmic background radiation in all directions today. A multiverse can be suggested from a multiplicity of theoretical positions. One could say there could be an infinite number, etc. One can argue, for example, given our small ...


2

I think you are missing that the source is actually referring to he observable universe explicitly - just somewhat indirect: It is not obvious as it is talking about "visible/observable universe", but about "total mass of the visible matter" and "mass density of visible matter". As far as I can see, any references to mass etc in the universe are covered by ...


1

$\phi$ in this context is typically known as the "inflaton" (a somewhat silly name, I know, but we already have quarks), it is the scalar field that drives inflation. Any field may have a potential component, typically written as $V$. Then the Lagrangian can be written as the sum of kinetic term(s) with (the relevant covariant) derivatives and the potential ...


6

The time used in describing the evolution of the universe is comoving time. This is the time that would be measured by a freely moving observer on their wristwatch (assuming the high temperatures didn't melt both the observer and the wristwatch :-). Time is not a simple thing to define in general relativity, however we can always unambiguously define proper ...


19

This is a common point of confusion, not only with regards to inflation, but any time an expanding universe comes up... The "cosmic speed limit" as you call it says that no particle or signal can move through spacetime faster than the speed of light. Spacetime is a very specifically defined thing, described with a coordinate system. There is no restriction, ...



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