Questions tagged [cosmological-inflation]
Cosmological inflation refers to an era of expansion that lasted for approximately $10^{-34}$ seconds, during which the universe expanded by a factor of approximately $10^{26}$ in every direction. This is different from ordinary space expansion and from the acceleration in expansion we experience now and questions tagged by inflation should pertain to this era and not be about the expansion of the universe in general.
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Questiong about comoving frame
From what I understand, in an expanding universe given by
$$ds^2=-dt^2+e^{2Ht}dx_{com}^2,$$ where I believe that $dx_{com}$ denotes a comoving spatial line element, the distance between a comoving ...
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Cosmological horizon and particle production
Typically, one studies particle production in de Sitter using a scalar field, and observing that one can rearrange the problem as one of a scalar field in Minkowski but with a time-dependent frequency ...
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2-Dimensional Cosmology and Power Spectrum
First, full disclosure, I am not even sure yet if this question makes sense, but I tried to derive some stuff, and would love some feedback.
First, recall that in $d=4$, we can write the de Sitter ...
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Why didn't inflation happen right after creation and it had to wait $10^{-36}$ seconds to occur?
What caused this minimum delay in the universe faster than light expansion?
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Why is it necessary the inflaton field?
The Friedmann equations read $(+---)$:
$$\frac{\dot{a}^2+kc^2}{a^2} = \frac{8\pi G\rho + \Lambda c^2}{3}$$
$$3\frac{\ddot{a}}{a} = \Lambda c^2 - 4\pi G \left(\rho + \frac{3p}{c^2}\right)$$
$$\dot{\rho}...
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Why does a scalar field with mass much greater than the Hubble parameter stay near its minimum during inflation?"
If a scalar field $\chi$ (not the inflaton) is present during inflation, and if the mass of this field is much larger than the Hubble parameter $H$ during inflation, the field will stay near its ...
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How does a non-zero slow roll parameter break the conformal invariance of the kinetic term in the scalar Lagrangian?
I am trying to understand how the introduction of a non-zero slow roll parameter ($\epsilon$) breaks the conformal invariance of the kinetic term in the scalar Lagrangian, particularly in the context ...
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Spatial Curvature of Universe at recombination vs now
From my understanding, we use the CMB data to measure the spatial curvature of the universe today. Why is it the value for today if the CMB data reflects the universe at recombination (380K years ...
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Cosmological numerical computations
I am unsure where to ask this question, whether here or in the Mathematica stackexchange, but either way, I was wondering what are some recommendations for cosmological computations specifically using ...
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OPE limit of four-point function in de Sitter space
I have been trying to read the paper 'Cosmological Collider Physics'. This paper studies several things, of
which the most interesting to me was studying the correlation function in de Sitter space by ...
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Multiple time dimensions in the eternal inflation model
From a lecture by Prof. Kaiser, I reckoned that according to the Eternal Inflation model, it is possible that all of the 10500 topologies posited by string theory could exist somewhere in the region ...
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Inflation in background free models of the universe
There are many authors who are attempting to construct a model of physics that doesn't rely on the objective existence of spacetime. This is part of the work in quantum gravity. This leads to things ...
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How to find the relation between flow-parameters and number of e-folds?
In models of single field inflation the Friedmann equation reads
$$ H(t)^2 = \frac{8\pi G}{3} \big(V(\varphi) + \frac{\dot{\varphi}^2}{2}\big) \tag{1}\label{eq1}. $$
In the slow-roll approximation one ...
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Feynman rule from dynamical Chern-Simons
Consider the following action that
\begin{equation}
S = \int d^4x\sqrt{-g}\left(-\frac{1}{2}(\partial\phi)^2 + V(\phi) + \frac{2R}{\kappa^2}
- \frac{\phi}{4f}{}^*RR\right)
\end{equation}
where
\...
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Inconsistency in numerical and slow-roll solutions of Mukhanov-Sasaki equation during Inflation
from my lectures in cosmological inflation, we derived the Mukhanov-Sasaki equation and its initial condition (Bunch-Davies). From here, it was of our interest to find a numerical solution of the ...
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A problem on cosmic inflation
I analyze inflation in this following scenario: Suppose that at some very early epoch, $t_1 ≤ t ≤ t_2$ (where $t_1 ≪ t_2 ≪ t_r$ and $t_r$ is the time at the recombination epoch), the universe resides ...
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What would an inter-universal medium be like?
I don't really believe in the Multiverse Theory, but hypothetically, if universes were like soap bubbles in a foam, what might that foam be like? I know this seems like an opinion-based question but ...
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Relation between energy of cosmic inflation and dark energy
Searching for "relation between inflation and dark energy" I found: "The energy scale of inflation is possibly 10^24eV, while the energy scale of dark energy is around 10^-3eV."
e....
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Horizon problem, what if our observable universe is roughly equal to the whole universe, especially in early times?
How do we know that at a time of 380.000 years, when CMB got free, the observable universe was not equal to the actual universe? Maybe they were roughly the same and couldn't that explain the horizon ...
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Question regarding the backreaction of a scalar field in curved spacetime
Lets assume that I start with the following action:
$$
{\mathcal L}_1 = \frac{1}{2} \sqrt{-g} \left( \partial_\mu \phi \partial^\mu \phi - m^2 \phi \right)
$$
where $g_{\mu \nu}$ is a FRW metric and $\...
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Cosmological Scalar Field Density Dilution
Consider a homogeneous free scalar field $\phi$ of mass m which has a
potential
$$V(\phi) = \frac{1}{2}m^2\phi^2$$
Show that, for $m ≫ H$, the scalar field undergoes oscillations with
frequency given ...
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If dark energy has constant density, would it still be subject to quantum variations; would increase/decrease be symmetrical, or would one take over?
There are different suggestions, but it stills seems like the basic scenario is for dark energy to have constant density, as a property of space (and as represented by the cosmological constant in ...
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Why is the comoving Hubble radius always increasing without inflation?
I have been told that the comoving Hubble radius $r_{H}(t)\equiv\frac{c}{\dot{a}}$ is increasing without inflation (and inflation was introduced as a period of time with decreasing $r_{H}$ in order to ...
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What was the entropy of the universe during inflation?
What was the entropy of the universe a) during inflation; b) at the end of inflation (at reheating, begin of the big bang)?
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Is time inflating proportionally to space?
We know space is expanding at a rate of roughly 432 miles/light-year/year. Since Einstein showed that time was intrinsically linked into the 4 dimensional structure of spacetime one would logically ...
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A question from a paper on general relativity
I try to read a paper on general relativity and perturbation theory:
https://arxiv.org/abs/2109.01398 page16
My question is about equation (3.16) in section (3.2):
$$
\delta \phi = -\sqrt{\frac{2}{\...
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How low can the scale of cosmological inflation be?
Usually, when we think of inflation we think of it happening at high energy scales, close to the bound set by CMB polarization measurements (with a Hubble scale of $H_I\sim 10^{14}$ GeV). However, ...
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Model of Quintessential Inflation
I have a question about how the potential for an inflaton field is selected. It is clear that there are limitations associated with number of e-folds, scalar-to-tensor relation and scalar spectral ...
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Does dark energy get used up in the expansion of the universe?
Now, I am a beginner in Cosmology, so I am not sure if this makes sense.
Since the universe is expanding at an accelerating rate, and thus distant objects are also accelerating away. In that sense, ...
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Black Hole Ripped Apart
Could a black hole be ripped apart if it passed directly between two other black holes that were millions of times bigger?
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Bunch-Davies initial condition
I have the Mukhanov-Sasaki equation in terms of $Q(t)$
\begin{align*}
Q''(t)+3HQ'(t)+k^2Q/a^2+\left(3\phi'(t)^2-\phi'(t)^4/2H^2+2\phi'(t)V_\phi/H+V_{\phi\phi}\right)Q=0,\ u=aQ
\end{align*}
and also ...
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What means Alan Guth's Free Lunch Principle for the universe?
Alan Guth calls the universe the ultimate free lunch. What does he mean by this?
Does he mean that the total energy of the universe is zero? So the total energy of all particles is the negative of the ...
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How big was the universe after inflation? [duplicate]
If we assume the universe is a closed 3-sphere, how big was the universe after inflation, compared to nowadays? Was, relatively, most space already there? If we envision the universe as a 2-sphere, a ...
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Intuitive explanation of COSMIC TIME?
I came across the following statement, while studying a Newtonian model for cosmic expansion:
"If $R(t)$ is the scaling factor, we can define the Hubble parameter as $H(t)=\frac{\dot{R(t)}}{R(t)}...
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Could cosmic inflation restart, even briefly?
Is it possible for a region of space in our universe to reenter an inflationary state? For example, if a particle accelerator collision of sufficiently high energy recreated conditions under which the ...
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Why is there an infinite supply of energy in slow-roll inflation?
The physical model of inflation includes a metastable false vacuum, or a slow-roll field on a flat potential. In either case, I just realized how this is completely insane. With the exponential growth ...
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Tachyonic instabilities [closed]
How to find tachyonic instabilities for some parameter ranges in the $f(R)$ gravity model? I have tried to find the parameter ranges for exponential $f(R)$ model, Starobinsky $f(R)$ model and ...
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Time evolution of scale factor for FRW solutions
I'm reading TASI Lectures on Inflation(https://arxiv.org/pdf/0907.5424.pdf). On page 20, it says
... also called the Friedmann Equations
$$\tag{21}
\boxed{H^2=\left(\frac{\dot{a}}{a}\right)^2=\frac13\...
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False Vacuum State (QFT)
I am wondering if someone can refer me to a proof that the false vacuum state is a natural consequence of scalar field theories? I see that being said in a lot of texts on cosmology when discussing ...
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Numerical solution for the Mukhanov-Sasaki equation with Bunch-Davies vacuum state
I have the Mukhanov-Sasaki equation in terms of $u_k$
\begin{align*}
u''_k(\tau)+\left(k^2-\frac{a''(\tau)}{a(\tau)}+f(\tau)\right)u_k(\tau)=0
\end{align*}
and also the initial condition from Bunch-...
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How to select proper values to solve Bunch-Davies initial condition?
I am trying to solve the Mukhanov-Sasaki equation for a Starobinsky potential $V(\phi(t))=3/4m^2M_P^2(1-e^{-\sqrt{2/3}\phi(t)})^2$. I could change the equations so that $m^2$ does not appear and chose ...
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"Boltzmann" equation for radiation (Reheating period)
These equations are given in many papers as the "Boltzmann equations" (without derivation) governing the reheating period, where $\rho_\phi$ is the energy density of the decaying inflaton ...
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Difference between new inflation and chaotic inflation
I'm trying to understand the difference between new inflation and Linde's chaotic inflation. From what I understand, according to the old inflation, during inflation empty space remains empty, so its ...
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What is the intuition behind the decrease in comoving Hubble radius during inflation and then its increase later on?
We know that the comoving Hubble radius decreases during inflation when the universe is exponentially expanding and then increases during matter and radius domination. What is the reason behind this? ...
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Does inflation theory assume a finite universe?
Inflation theory has it that the early universe was causally connected, and could “mix”, hence explaining relative homogeneity of the CMB. The universe then rapidly expanded and became causally ...
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What would the cosmic microwave background radiation look like in a hyperspherical universe?
I was thinking about what things would look like in a hyperspherical universe. How would galaxies look as they got closer to the other side of that hypersphere? It seems like if a galaxy were on the ...
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Does General Relativity, without Cosmic Inflation, predict a perfect blackbody for the CMB radiation?
My understanding is that the universe did not have enough time to thermalize before the epoch of recombination, so many patches of the sky were not in causal contact with each other, which means they ...
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Can either of LISA, NanoGrav or LIGO measure the polarization of gravitational wave background (GWB)?
Polarization in GWB should carry as much important information as in CMB. However, I've done some superfluous literature research and found little discussion. Is there any planned project for ...
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Do matrix models capture the string landscape?
Essentially what the title asks-- are matrix models, such as BFSS, believed to capture in any way the large possible space of false string vacua, for instance as saddles in the action with nonminimal ...
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Does the expansion of the universe affect small objects? [duplicate]
If the expansion of the universe happens uniformly, how does this affect small objects? For example, are the distances between protons and neutrons inside a nucleus actually expanding? Is the nucleus ...
