# 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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### An exercise on the adiabatic initial condition from Daniel Baumann's new cosmology book

Additional info for those not familiar with cosmology: The $\delta$ s are the density contrast whose subscripts indicate species. It is defined as: $\delta_{a}=\frac{\delta\rho_{a}}{\bar{\rho}_{a}}$ ....
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### Harmonic (coherent or not) waves from inflation?

I am just wondering if inflation could produce harmonic (coherent or not) waves and what are they strength (in the limit of frictionless media) or amplitude now for each mode, and if we are searching ...
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### How are these equations derived?

This is from Wayne Hu's lecture slides on cosmology Pg.20 (http://background.uchicago.edu/~whu/Presentations/crete1.pdf) He starts out with a diffusion/conservation equation for comoving photon number ...
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### Why is the flatness problem called the "flatness" problem? What is its connection to geometry?

My understanding of the flatness problem is that it says that if we leave out dark energy and inflation, then the density parameter $\Omega(t)$ tends to $\infty$ or $0$ unless we have $\Omega(t) = 1$ ...
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### Why is the current cosmological constant insufficient to solve the flatness problem?

The flatness problem can be very succinctly summarized by the fact that the density parameter $\Omega(t)$ has an unstable equilibrium point at $\Omega = 1$ (which corresponds to a Euclidean universe). ...
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### What if cosmological inflation never stopped?

If inflantionary theory is correct, the universe ceased to expand after just $10^{−32}$ seconds. Imagine a scenario where cosmic inflation never actually stopped. At the extremely accelerated ...
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### What does it mean that gravitation separated from the four forces at $10^{-36}$ seconds?

Physicists have used math to calculate that gravitation separated from the 4 forces at 10^-36 seconds after the big bang, which is even before the inflationary period. The universe was still smaller ...
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### How does the tensor-to-scalar ratio depend on the prior adopted?

A reviewer for one of my papers made the comment that the "tensor-to-scalar ratio is sensitive to the prior adopted" and asks if I'm able to work out the prior using the methods in the paper....
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### Does whether or not inflation occurred change the estimated age of the universe?

When we say "age of the universe," I assume this means the time interval for the Euclidean FLRW metric $$ds^{2} = -dt^{2} + a^{2}(t)\Big(dx^{2}+dy^{2}+dz^{2}\Big)$$ from when the scale ...
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### Trying to understand the horizon problem

I'm trying to understand the horizon problem better. For the record, I have read this post and this post, which have been tremendously helpful. My understanding of the problem is that even if we ...
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### What are the appropriate densities and temperatures of constituents of the universe after reheating?

In slow roll inflation, the inflaton field has to decay into the currently observed constituents of the universe at the end of inflation. This process is called reheating. What are the experimental ...
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### Ratio of a given co-moving length scale to the horizon

How does the quantity $aH = \dot{a}$ measures the ratio of a given comoving length scale to the horizon (during inflation say)?
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### Numerical solution to the equation of curvature perturbation

Numerical solution to Mukhanov-Sasaki equation In the above link, an equation is given which is the evolution equation of curvature perturbation as a function of $N$ (number of e-folds). In order to ...
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### What is the reason for density fluctuations in the primary matter of the early Universe? [duplicate]

After a period of inflation and nucleosynthesis, small density fluctuations appeared in the primary gas, which became the "seeds" of the first stars and galaxies. What led to the appearance ...
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### Number of e-foldings in inflationary cosmology

Is there a physical principle limiting the number of e-foldins during cosmological inflation? What is the upper bound on the possible number of e-foldings?
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### Are density fluctuations during inflation unitary?

One of the popular ways of introducing initial density fluctuations (which are necessary for structure formation amongst other things) in $\Lambda_{CDM}$ is to use quantum fluctuations of an inflaton ...
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### Is there empirical evidence supporting a universe expanding faster than light?

We receive no light from galaxies beyond the cosmological horizon, but if they were moving away only at light speed, it seems to me their light wouldn't reach us. Is there any observations or ...
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### Would very high energy density (like in Back holes) give a non-zero value to inflation field?

I have been watching some PBS SpaceTime about inflation, and it is explained that there is an inflation field that at high energy density makes space expand, it then fell into a false vacuum state, ...
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### Discovery of 3C273 as black holes

In Stephen Hawkings book "Brief History Of Time", in chapter 6 Black holes, on page 102, it is written "He found it was too large to be caused by a gravitational field:if it had been ...
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### Is the inflation rate of the universe uniform throughout?

Is inflation constant at any given moment throughout the entire observable universe? I realize inflation was once much more prevalent, so at the edge of the observable universe, we would observe a ...
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### Why in the first Friedmann equation quantity $ρ$ is directly proportional to Hubble's constant despite the fact that gravity counteracts expansion?

Here is the first Friedmann equation: $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}$$ We know that matter and energy through gravity slow ...
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### Distribution of matter in the Universe

My teacher explained today that quantum fluctuations in the early Universe (in particular, during inflation) determined the spatial distribution of small mass inhomogeneities, which, in turn, due to ...
How does varying the boundary action $$S = \int_{t_0} d^3 x \sqrt{g}\left(-{\textstyle\frac12}\kappa\phi^2\right)\tag{5}$$ eq. 5 of of https://arxiv.org/abs/astro-ph/0503458, lead to $$\partial_n \phi ... 2 votes 1 answer 82 views ### Fokker-Planck equation from Langevin equation in stochastic inflation I'm reading this paper by Starobinsky and Yokoyama where they give the coarse-grained equation of motion,$$ \dot{\bar{\phi}}({\bf x},t ) = -\frac{1}{3H}V'(\bar{\phi}) + f({\bf x},t) $$where f({\bf ... 6 votes 4 answers 343 views ### Did the universe need the presence of matter and radiation to start expanding? I have read this question: Hence it is not possible that photons generated by stars is contributing to dark energy. Could photons generated from the many trillions of stars be some how contributing ... 0 votes 0 answers 27 views ### Calculating Φ(t) during inflation I am trying to solve for \Phi(t) during inflation for a given metric,$$ ds^2 = dt^2 - a^2dx^2 - b^2dy^2 - c^2dz^2. $$I just wanted to know how should I proceed while taking Lagrangian L as  L =... 0 votes 0 answers 50 views ### Quantum fluctuations in the early universe A Quanta Magazine article on the relationship between inflation and the large-scale structure of the universe mentions the relationship between the spatial distribution of galaxies and quantum ... 3 votes 0 answers 20 views ### Which inflation models does BICEP3 rule out? Polarization data from BICEP3 combined with BICEP2 and Keck in a recent analysis is reported to rule out several simpler categories of inflation models. Which are these? e.g. single-inflaton models? -4 votes 1 answer 129 views ### Is Universe expansion means that speed of time flow is increasing? The massive objects compresses the space-time around themselves and it leads to slow down the time. If we are moving with speed that is close to speed of light, we are moving through much amount of ... 0 votes 0 answers 25 views ### Can be the observed Universe expansion be explained by different speed of light in the past? We see the redshift at spectres of all objects around us that was interpreted as space-time expansion. But could we see the same effect in case if speed of light was different in the past? 0 votes 0 answers 14 views ### Squeezing and classicalization of inflationary perturbations Is there a simple physical picture of how/why the primordial modes (once they exit the Hubble radius) undergo squeezing and classicalize? 0 votes 1 answer 129 views ### Schrodinger versus Interaction Pictures for Mukhanov Field \hat{v}(\eta,\mathbf{x}) in inflation? EDIT: This is more than anything else, a question about how to define Schrodinger-picture operators, if you are given an Interaction picture set of operators (with a time-dependent potential: in this ... 2 votes 1 answer 103 views ### Why do some diagrams of the particle horizon, observable universe etc show the past light cone as hitting ~20glyr out from us at time zero? This question is mainly in reference to this question: Is the observable universe equivalent to 'our' light cone?, and the answer, which is great. But what I can't wrap my head around is why ... 0 votes 1 answer 55 views ### A fire at the end of inflation? In their article at bigthink.com "Surprise: the Big Bang isn't the beginning of the universe anymore", the writer articulated an alternative theory that suggests inflation didn't begin at a ... 0 votes 1 answer 59 views ### Is it possible that the the Big Bang is still taking Place? [closed] My question is the same mechanism by which particles formed at the big bang still active here and now? To clarify the lambda CDM model fir instance say the observable universe was very dense at the ... 0 votes 2 answers 53 views ### Are there introductory reviews of trans-Planckian physics and inflation? Looking for something similar to Daniel Baumann's cosmology notes Are there introductory reviews of trans-Planckian physics and inflation? Looking for something similar to Daniel Baumann's cosmology notes - things are explained assuming minimal background. 5 votes 3 answers 438 views ### Inflation and gravitational interaction In a new article, Cosmological constraints on slow-roll inflation, the authors write: "Notice that this theory is said to be “minimal coupled to gravity” because there is not a direct coupling ... 5 votes 2 answers 975 views ### Inverse Laplacian I have seen the following operator somewhere in a paper on cosmology$$ \frac{\partial_i \partial_j}{\nabla^2} - \frac{1}{3} \delta_{ij}. $$What is the definition of the inverse Laplacian? What is ... 5 votes 4 answers 256 views ### What particles are thought to have existed before Inflation? What fundamental particles do most Grand Unified and Inflationary theories predict existed before the Inflationary period? Basically, what do we expect the family of particles existing during the ... 1 vote 1 answer 65 views ### Entropy and large-scale structure of the universe In their article Disturbing Implications of a Cosmological Constant, Leonard Susskind and others write: Certainly, given enough time and a suitable inflaton, recurrences will eventually bring the box ... 1 vote 2 answers 79 views ### Cosmic inflation and how does it stop? What conditions make out the probability for the Cosmic Inflation once began to stop. For instance quantum physics says that once the inflation started there was a probability say 80% for it to stop ... 8 votes 7 answers 1k views ### Are Laws of nature independent of time? [duplicate] There are certain laws that govern the universe and these laws make up the fundamentals of any physical observation. But were these laws present the way there are now since the beginning of space time,... 0 votes 3 answers 79 views ### Is there a specific reason that the universe is precluded from expanding into anything? Or is it simply not required in the mathematics? [closed] We know that the universe doesn't need to expand into anything to support current theories, but is there a reason that it is specifically precluded from doing so? In other words, is there any evidence ... 0 votes 1 answer 50 views ### Space expansion explainable by a 4D universe? Could our universe be finite, but in 4D? Basically that the universe that we experience is a 3D slice of a 4D body that moves through our 3D "plane". The "big bang" then occured ... 0 votes 1 answer 65 views ### What, exactly, is meant by 'effective number of neutrino species'? As stated above... How can the the physics of early cosmology (articles about which are where I usually come across mentions of such) be affected by an 'effective' number of neutrino types, rather ... 0 votes 0 answers 18 views ### How do quantum fields in the emptiest parts of space fall into a local minimum? A potential energy well? What constitutes the walls of the barrier? Somehow, in all my reading, I don't remember coming across a specific explanation of what the barriers or walls of potential energy wells/minima are made of, so to speak.... Most recently, I've read ... 2 votes 2 answers 118 views ### How should we deal with interactions not from a “fundamental force”? [closed] Question Should the cosmological constant and/or vacuum energy be listed as one of the fundamental interactions? If not, how can we have actual energy and forces that are not assignable to one of the ... 0 votes 1 answer 36 views ### Inflation parameter value One of slow-roll Inflation condition is$$ \ddot{\phi} \ll H\dot{\phi}. $$When i performed numeric calculation, I got a value:$$ \ddot{\phi} = -2, \\ H\dot{\phi} = -120. $$I got confused because ... 1 vote 1 answer 128 views ### Stress energy tensor and scalar field [closed] The lagrangian for a scalar field \phi is$$\mathcal{L}=\frac12 \partial_{\mu}\phi \partial^{\mu} \phi -V(\phi)$$From Noither's theoreme we got stress energy tensor as$$T^{\mu \nu}=\partial^\mu \...
I am trying to derive the equation of motion for a scalar field in flat and homogenous space time where the metric is $g_{\mu \nu}=diag(-1,a^2(t),a^2(t),a^2(t))$ and the Lagrangian is given by \...