Inflation assumes ##\ddot{a}<0## after inflation?

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In summary, the assumption that ##\ddot{a}<0## in introductions about inflation is based on a model assumption that is observationally false.
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I'm reading introductions about inflation and one thing they assume is that presently ##\ddot{a}<0## where ##a## is the parameter in our FRW metric.

We know that this is observationally false, since in fact ##\ddot{a}>0##.

But why do they assume this?

My guess is that in the big-bang model there is a period where radiation and matter dominates over the cosmological constant and it is in this regime that ##\ddot{a}<0##.

Another guess could be that theorists of the time didn't know that ##\ddot{a}>0##. But I don't think this is a good enough answer since people keep talking about inflation so there has to be some reasoning behind the assumption that ##\ddot{a}<0## after inflation.

So, what going on here?

Thanks.
 
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davidbenari said:
I'm reading introductions about inflation and one thing they assume is that presently ##\ddot{a}<0## where ##a## is the parameter in our FRW metric.
I think I'd need more context to understand what's going on here, but I don't think the current accelerated expansion is relevant to inflation at all. It is certainly the case that ##\ddot{a} < 0## for the period immediately following inflation, however, and for a few billion years afterwards.
 
  • #3
Chalnoth said:
It is certainly the case that ##\ddot{a} < 0## for the period immediately following inflation, however, and for a few billion years afterwards.

Thats what I needed to hear. Is your reasoning that matter and radiation dominated over the cosmological constant for those billion years?
 
  • #4
The universe began accelerating again (after inflation) when it was around 10 billion years old. Taking the end of inflation to correspond to the standard hot big bang, t=0, there was therefore a period of 10 billion years during which the expansion of the universe was decelerating in the sense of [itex]\ddot{a} < 0[/itex].
 
  • #5
What caused the flip in the sign? Is it what I said about matter and radiation dominating over dark energy at first?
 
  • #6
Yes. The energy density associated with the CC, or whatever it is that's driving the accelerated expansion, is tiny. It didn't emerge as a dominant component of the energy density of the universe until after the radiation and matter red shifted sufficiently.
 
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Ok thanks. I have a stupid question though that just occurred to me, which is somewhat unrelated to this thread:

what if dark energy is the inflaton field (of course we now sit at the bottom of the well of ##V(\phi)##? Are there any hypothesis about that? Would that hypothesis be wrong?
 
  • #8
davidbenari said:
Ok thanks. I have a stupid question though that just occurred to me, which is somewhat unrelated to this thread:

what if dark energy is the inflaton field? Are there any hypothesis about that? Would that hypothesis be wrong?
There have definitely been many theorists who have explored this possibility. Look up "quintessence" (quintessence is a word used to describe a wide variety of dark energy models, not all of which can be connected to inflation).

So far, though, there aren't really any compelling ideas. Turns out it's quite difficult to connect the rapid accelerated expansion of inflation with the current (comparatively) slow accelerated expansion, while at the same time having an in-between period in the early universe where there is no evidence of dark energy (the evidence of dark energy comes from the last few billion years of expansion). People have come up with possible mechanisms, but they're all very ad-hoc.
 
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What is inflation?

Inflation is a general increase in the prices of goods and services in an economy over a period of time. This results in a decrease in the purchasing power of the currency, meaning that the same amount of money can buy fewer goods and services than before.

Why does inflation assume a negative acceleration after it occurs?

This assumption is based on the theory that inflation is caused by an excess of demand for goods and services in the economy. As prices continue to rise, consumers may slow down their spending, leading to a decrease in demand and a decrease in the rate of inflation.

What are the consequences of a negative acceleration in inflation?

A negative acceleration in inflation can have both positive and negative consequences. On the positive side, it can help stabilize prices and prevent them from rising too rapidly. However, it can also lead to slower economic growth and potentially cause a recession if it continues for too long.

How does the government respond to a negative acceleration in inflation?

The government can use various tools to address a negative acceleration in inflation. This may include controlling interest rates, adjusting monetary policy, and implementing fiscal policies such as tax cuts or government spending to stimulate demand in the economy.

Can inflation ever be beneficial?

Inflation can be beneficial in small amounts, as it can encourage borrowing and spending, which can stimulate economic growth. However, high levels of inflation can have negative effects on the economy, such as reducing the value of savings and causing uncertainty in the market.

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