A reader asks this question, testing the boundaries between physics culture and religious belief:
How hostile do you think a learning institution would be to someone in their Physics department looking at the Horizon problem via the Universe being an Ex Nihilo creation of God, where matter was purposefully set in place and then a God-caused spacetime expansion? (As opposed to the thought experiment of assuming a singularity and a "Theistic or Non-Theistic Big-Bang" requiring another speculation (inflation) to explain one of the shortcomings of the theory.)
— Dean C
Most physicists aren't actually militant atheists, but all of us (whatever our views on religion) have been exposed to numerous "crackpots" who think that they have found major flaws in conventional physics and have a completely new and revolutionary way of doing things. I discussed this pathology here and here. At least 99.99% of time, outsiders making such grandiose claims are totally wrong (or "not even wrong", because their ideas aren't precise enough to be testable), and so we filter out pretty automatically anything which pattern-matches onto typical crackpot-seeming claims and behaviors.
But this is not to say that simply criticizing inflation, all by itself, would get you lumped into the "crackpot" category. Even among respectable mainstream physicists, inflation isn't completely uncontroversial. While most of us believe it is true, this hasn't been established with total certainty.
A lot of the original arguments for inflation (e.g. the flatness and horizon problems) are a little bit philosophical in nature, and it's understandable if you don't find them completely convincing. But it's not just generic arguments like that. Inflation also makes some very specific predictions about the state of the universe after inflation ends, and these predictions seem to match very closely to what we actually observe (as the graph in that article shows). There are respectable researchers (such as Neil Turok and Paul Steinhardt) who have philosophical objections to inflation (not based on religion) and are working on alternatives which may predict the same features in the microwave background. But they are able to do that only because they fully understand the mathematics of inflation and the observational tests that it passes.
If somebody said something like "For philosophical reasons I am skeptical of inflation, and therefore I am interested in exploring alternatives to inflation such as X, Y," and if this person understood the mathematics of inflation (so they weren't just criticizing something they didn't know well enough), and if X and Y were mathematically-precise models with equations (such that even somebody who didn't believe in God could manipulate the equations and work out the predictions of the model), and if there was some hope that in the future, that model could be confirmed by empirical observations, then if all of these conditions are met, I think at most places this would be regarded as acceptable though eccentric. Even if the "philosophical reasons" included some religious considerations.
It would be even better if this person had the ability to "suspend their disbelief" by sometimes having useful conversations with other people that presupposed the truth of inflation, without bringing up their reasons for skepticism every single time. (Because that would make them a more useful colleague, and its scientifically it's an important skill to be able to work out the consequences of hypotheses even if you aren't convinced by them yet, as a way of keeping a open mind and understanding the relationship between ideas.) Such a person would be capable of interfacing with other scientists who don't share his conviction.
(Which is not to say you could actually obtain a research job simply by working on X, Y, since there also need to be a sufficiently large number of other people who think work on X, Y is valuable enough to pay somebody money to do it. In practice, people who work on long-shot alternatives to standard physics also need to work on more conventional topics, in addition, to be viable. There are limited resources and funding in science, and not everyone can be supported. But not getting a job is quite different from being excommunicated as a heretic!)
On the other hand, if X and Y can't be understood without reference to a Creator, and have phrases like "and then God miraculously caused this to happen" in them, or if the model doesn't lead to any mathematically precise predictions that could in principle be tested by future experiments, then this would not be anything like Science as it is traditionally practiced, and it would be dismissed off-hand by almost all scientists as a scientific theory.
And rightly so, because it would, at the very least, involve an enormous paradigm shift in what it even means to practice the scientific method, and justifying such a change would require overwhelmingly convincing evidence. Of course, as a Christian I believe that miracles have happened in history, and that the universe was created by God. But in the field of Cosmology as practiced in Physics departments, the job is to mathematically model the universe using a set of natural processes described by equations.
It's hard to see how "matter was purposefully set in place and then a God-caused spacetime expansion" could, all by itself, be a mathematically predictive theory. Because if the matter was just spontaneously created, there are almost an infinite number of configurations it could have appeared in. Without some physical process or principles to limit it, it could have been anything! And a "God-caused spacetime expansion" must either be described by a set of specific equations like that of Einstein's (in which case, an atheist could also use those same equations, while denying the existence of God) or else it means we (not having access to God's "hidden counsels") simply can't predict exactly how the size of the early universe changed with time. But then how do you get any quantitative predictions for what you see when you point your telescope into the sky?
But if all you mean is that, in the ordinary course of doing science, scientists should not a priori rule out mathematically well-defined hypotheses (such as the fine-tuning of the constants of nature in a way that happens to permit life, or a net nonzero number of baryons coming out of an initial singularity), simply because those hypotheses seem "unnatural" in the absence of an intelligent creator, then I agree with this. Nor, obviously, should a theist rule out the possibility that God might have created our universe using inflation (I don't see why not). Such scientific hypotheses should stand or fall on their own individual merits, as the case may be. It's okay (and indeed essential) to be guided by our own individual sense of parsimony, but we shouldn't be so biased that we rule out sensible models which explain the facts better.
(Incidentally, if inflation did happen, then the hypothesis that the universe just "started off" with more matter than antimatter can't work. Even if there were more baryons than antibaryons coming out of the initial singularity, the universe expanded so rapidly during inflation that the initial baryons would have been diluted to homeopathic proportions. For this reason, physicists generally prefer models of baryogenesis, in which the baryons are created by some specific physical process some time after inflation ends.)
This reminds me of Frank Tipler's Omega point theory, although he meets the requirement of understanding inflation, his idea is still crazy. He tries to build a mathematical based theorem/model for God but he does really make a lot of philosophical-theological claims that are no where in the equations.
Yeah, the Omega Point model is totally fruit-cake bonkers!
It feels a bit redundant to add that Tipler's model presupposed that the universe would recollapse on itself, and is inconsistent with the current model in which the universe's expansion accelearates forever. Since the model was already inconsistent with any sane understanding of physics or theology.
It should be noted that there are different kinds of untestability. As elegant and successful as the inflationary framework has been it has one really big problem: It's based on the inflaton--a scalar field (or fields possibly) about which we know pretty much nothing. And that leaves us with a theoretical brush that's almost as broad as the canvas itself. These days inflationary models are a nickel per baker's dozen, and while these models are easy enough to observationally test (on a case by case basis) they're even easier to tweak until they fit virtually any observation we could make. The Standard Model seems to offer little hope that we'll discover any new physics that might turn up a more definitive inflaton candidate until we can probe near GUT/Planck energy scales--which isn't likely to happen in our lifetimes--and the same applies to string/M-theory, which some have claimed leads naturally to inflation. On top of that, as Steinhardt, Penrose and others have pointed out (rightly IMHO), inflation solves flatness, isotropy, and other fine-tuning issues only to have them return with a vengeance via inflaton fine-tuning. Thus, even though it has a well-defined mathematical framework from which specific predictions can be made, the inflationary framework is effectively untestable. This is of course, different from "God-just-did-it-that-way" untestable, which is of course, why one wouldn't be lumped into the "crackpot" category for criticizing it. But in the end, untestable is untestable.
I suppose I'm splitting hairs here Aron... none of this changes anything you said. But I think the distinction is important because there is a growing community of folks [I'm looking at you Sean Carroll!] who claim that we should indiscriminately lump the two together and dispense with testability as a requirement for meaningful physics and cosmology... as long as it's "elegant" (and of course, politically correct), then testable or not, it's science. These days it seems that "Science as it is traditionally practiced" is no longer fashionable.
Ironic, isn't it...? For centuries atheists have been bludgeoning Christians for allegedly basing our faith on "belief without proof" instead of facts. Now they're bludgeoning us for not doing so! Go figure...
Yes, although the situation is not completely bleak. Many specific models of inflation can be ruled out by the current data. It's just, that leaves a large number of different models of inflation which can't be distinguished by the current data. And while there are theoretical limits to the amount of data which can reasonably be extracted from cosmology (due to problems such as cosmic variance), we aren't yet at the point where we can't get more data with more funding!
Physics seems to be asymptoting, not to a state where we know everything, but to a state where we know everything except the stuff which is too hard to measure. But we aren't at the end yet.
Anyway, there's a difference between saying we can't test which model of inflation is correct, and saying we can't test whether inflation is correct. The proposition that some kind of inflation happened is supported by quite a bit of evidence, and although I'm not an expert on this, I'm given to understand that the rivals to inflation all have even more serious problems.
I don't think any scientist wants to throw out testability in cases where we can test. The question is what should we do when we can't? I think there is a time and a place for, what you might call, "scientifically informed elegant speculations involving math, inspired by the attempt to explain observable facts". If something is only loosely based on observation, but satisfies the other five Pillars of Science, perhaps this process shouldn't be called scientific, and it certainly shouldn't be considered Established Scientific Fact (TM). But that's different from saying that scientists shouldn't speculate, just that we should be self-aware and honest about what we are doing and why.
At the level of academic culture, if such speculations are worth doing at all, and if doing them well requires formal training in physics, then it makes sense for the people who do it to be in the Physics Department. But that doesn't mean we can't call people out when they smuggle in naturalistic presuppositions unfairly without argumentation, and then call that Science!
I have a question. Like you and our blog writers, I believe God created the universe and all matter. Staring with this premise, supported by many plausible arguments, such as the ones in Undivided Looking, would you not think that unless physicists knew God’s mind, or had a direct call from God, no amount of modelling will be able to explain creation, or bring us any closer to the explanation. So whatever models we construct on the origin of the universe, how matter came into being, they would all be speculative because(a) the models would be incomplete (missing variables, missing parameters, incorrect specification of functions, etc. etc) and (b) untestable due to lack of clean data ruling "noises".
One eminent mathematical physicist who is skeptical of inflation is Roger Penrose. See "The Road to Reality", pp. 753-757. His objections do not seem to be based on philosophical grounds. "As stated above my basic objections to this idea have mainly to do with the underlying motivations for it." (Namely, overcoming the horizon and flatness problems.)
Physics and philosophy are overlapping fields; indeed Science used to be called "Natural Philosophy" [i.e. the Philsophy of Nature]. That's why, like most other professional physicists, my diploma says I've got a Doctorate of Philosophy (Ph.D.)! So there isn't a hard and fast line separating the two. When somebody looks at a theory, and says "Sure this theory is consistent with the data, but does it REALLY explain it? We need a better theory", and then when all the physicists argue with each other about it, what are they doing if not philosophy?
Penrose's main objection is that inflation doesn't actually explain flatness etc. unless the universe started in an even lower entropy state. (In fact, inflation probably doesn't even begin unless the initial state of the universe is highly special.) That is a valid objection if we misinterpret inflation as a theory about why the universe started out in a low entropy state. But I would reply that this is holding the theory to unrealistic expectations. Let us concede that inflation does not explain why the universe began with low entropy. Neither does FRW cosmology, or our theories of stellar formation, or Darwinian evolution, or any other established theory in physics. Yet we don't reject those theories, just because they require the additional assumption that the universe began with low entropy, so why should we reject inflation on the same grounds? Given certain assumptions, it explains what we see. That is the best we can expect from a physical theory of the universe.
Even if we found a so-called "Theory of Everything" in physics, there would still be a lot of deep philosophical mysteries which wouldn't be explained, such as why the laws are that way, the interpretation of QM, the nature of consciousness, and so on. But so far, we aren't anywhere close to a T.O.E., and it seems unlikely we will have enough data to really know what happened at the absolute beginning of the Big Bang (or if there was time before the Big Bang, what happened before that).
"Where were you when I laid the earth’s foundation?
Tell me, if you understand.
Who marked off its dimensions? Surely you know!
Who stretched a measuring line across it?
On what were its footings set,
or who laid its cornerstone—
while the morning stars sang together
and all the angels shouted for joy?"
Amen and Amen to that, Aron. You always have the right words.
I agree Aron... and Ty is right. You always do seem to have the right words! :-) My comments above notwithstanding, I also think inflation is an elegant framework and that some variant of it is probably right. And as you said, it is testable to the extent that many inflation models can be observationally ruled out, and also that (if you'll forgive the worn-out phrase) it is "the best game in town" regarding the observations it accounts for. The real problem I was alluding to is more that neither the inflationary framework nor its rivals can be falsified. [Actually, falsifiable would've been a better term to use in my last than testability.] Apart from the whole mystery inflaton issue, consider for instance what is probably its most specific and striking success: prediction of the CMB running Gaussian power spectrum. Steinhardt claims ekpyrotic models can account for this as well, and so can a few other theories. Granted, inflation is far and away the best explanation for these things, and thus the most likely. But it can't be confirmed until the others are definitively ruled out. And ekpyrotic models in particular are based on string/M-theory, the L'Enfant Terrible of untestable frameworks.
The bottom line is this: Eternal inflation, string/M-theory, and the multiverse... this trinity almost certainly stands or falls with our ability to probe on GUT/Planck scales. But unless some entirely new physics comes along that no one can even imagine much less foresee, we're left pinning our hopes for doing so on collider technology... and all indications are that we're going to need one the diameter of the solar system, and that with all the resulting luminosity problems overcome. Needless to say, that ain't gonna be happening any time soon!
Ergo, this trinity isn't just untestable... it never will be testable. In the very least, it won't be during our lifetimes. This, more than anything else, is why the "Post-Empiricists" are saying that at least as far as high energy physics and cosmology are concerned, we should dispense with falsifiability as a criteria of science. True, no one is nutty enough to argue that we shouldn't test our theories where we can. But as far as this topic is concerned that's moot... everything relevant to questions of ultimate theories, God, and the origin of the universe is being played out on the inflation/string/multiverse stage, where philosophical and theological issues are unavoidable and falsifiability is a pot of gold at the end of the rainbow. I find it telling that most, if not all of Post-Empiricism's most ardent torch bearers are atheists, and some of its most ardent detractors are Christians (e.g. George Ellis).
Btw, there's another issue here I haven't mentioned... this isn't just a philosophical/theological problem, it's a practical one as well. I was in jr. high school when string theory first appeared on the scene, and it was more than a decade old and all the rage when you were born. By some accounts, since its inception it has produced more than 50,000 papers but no definitive predictions we can test. That's 40+ years and 50,000 papers... without a single unambiguous, testable prediction and no sign of one on the horizon. Yes it's elegant, and it has proven useful for dealing with many otherwise intractable toy model problems. But is it a wagon to hitch all our hopes and dreams for an understanding of the universe to...? It seems to me that 40+ years of tossing every kind of power-bait imaginable into the same trout pond without a single nibble is a pretty clear indication that one needs to pack up and find another pond. But in spite of these failures string/M-theory still seems to be all the rage and drawing the lion's share of high energy physics resources. You'll know a lot more about this than I of course, but according to Peter Woit, these days it's almost impossible to get a HEP postdoc gig unless one is willing to work on string/M-theory. That's a problem. It seems blindingly obvious to me that if we ever want to get out of this rut we should be exploring a wide range of theoretical avenues, not restricting ourselves to only one or two no matter how pretty they are. If there's a better pond out there... one that might actually have some trout in it... how are we ever going to find that pond if no one is willing to fund anyone looking for it? And I haven't even gotten yet to the issue of public perceptions of science, and how we're going to motivate anyone to support our efforts based on nothing more than promises of greater "beauty" without verifiability. Perhaps this is overly pessimistic... I certainly hope it is. If so, by all means correct me! Either way, we should bear in mind that philosophy and theology aren't the only things at stake.
Good comment Aron! ...you admit that philosophical assumptions ground physics! Or do you? There's a quote from Pierre Duhem that's apropos:
"Therefore, if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics..." Pierre Duhem, The Aim and Structure of Physical Theory.
I agree with you that explaining the Second Law, i.e. explaining the very limited initial conditions of the beginning should not be a requirement for a theory, but I think Penrose's point is that if Inflation is to be an inclusive theory it should explain that feature. I think that Penrose may not be willing to admit that there is a Creator who set up creation with special conditions. He has tried to justify a cyclic type of cosmology that depends on conformal mapping. To his credit he tried to adduce experimental evidence for this--the "rings" in the cosmic microwave background radiation. What are your thoughts on that?
I tried to sketch a moderate view about the relationship between physics and metaphysics here.
I don't know what you mean by an "inclusive theory". If you mean that the theory is supposed to explain everything, I don't think that's a reasonable expectation to hold inflationary models too!
Penrose is willing to make some very creative long-shot proposals. It's good that there are some physicists willing to do that, but most of the time they don't pan out!
Not all inflationary models predict eternal inflation, but I understand that most models people cook up do... eternal inflation seems a lot more speculative though, since it refers to stuff outside our lightcone.
I think falsifiabiltiy is slightly overrated, while normally it is a criterion of good science, there are some exceptional cases where it is possible to verify an idea without being able to falsify it.
For example, suppose that inflationary models are so broad that we can cook up a model to explain practically anything we see. (This isn't really true, it's not hard to imagine cosmological observations that would make it so we'd never have considered inflation a reasonable explanation in the first place. But suppose for the sake of argument.) Then that sounds really bad, from a scientific perspective. It's unfalsifiable! But now suppose that, in addition, every reasonable rival theory we can cook up is soundly defeated by the evidence. In that case, I would be willing to say that inflation has been scientifically verified even though (in this hypothetical) it couldn't be falsified. Which seems just as good. (Until we start asking the question which theory of inflation is true; then we might get stuck if there are multiple models with the same predictions. But nobody ever promised us we'd be able to answer all the questions.)
Needless to say, that's a parody of the real situation. In fact, the Steinhardt-Turok model has not yet been falsified by experimental data (although I find it implausible for other reasons), although it could be falsified if we ever detect the effects of primordial gravity waves on cosmology. This would also narrow down the field of inflationary models. Unfortunately, there are also models of inflation in which the gravity waves are too small to be realistically detected.
As a person working in high energy physics who is skeptical about the actual truth of string theory, I strongly agree that the community should hire more people who work on alternative approaches (which is one of the reasons Peter Woit's Not Even Wrong is on my sidebar, despite its somewhat strident tone). However, I am also in a good position to see the payoff which has emerged from the string theory, and I would say we've learned quite a large number of things from the extravaganza, which are extremely useful. For example we've learned an enormous amount more about Conformal Field Theories, including things which are useful for studying real physical substances in the laboratory, near phase transitions. I'm actually pretty grateful to be interfacing with this community at this point, I feel that it has enhanced my work on things like black hole thermodynamics, rather than inhibited it, and I'm glad my advisor (Ted Jacobson) steered me gently towards that direction. I'm pretty sure this isn't just me cravenly reprogramming my priorities in order to get a job, although having a reasonable hope of getting a faculty position is kind of nice.
By instinct I'm more sympathetic to LQG, but so far this approach is at least as unverifiable, and I think in practice there haven't been nearly as many spin-off benefits from that research community.
I think it's a shame there isn't more research on 3rd party Quantum Gravity candidates. It's easy to say there should be more approaches, but it's harder to actually do it in a way that is good. Quantum Gravity is hard!
I sincerely apologize for having asked that question and quite frankly we are surprised that you took the time to answer it. When I say we, I mean myself and three other Physicists I work with. Despite the fact the two of us are Theists and the other two Agnostics, we agree on a great many things. We've had far too many conversations with someone who presupposes the truth of inflation. He's the only one in our department who is a somewhat "militant Atheist", to borrow your phrase. I'm surprised to hear anyone say that inflation helps to match closely with what we observe, this not only takes liberty with the word closely, but is problematic in other ways. The world of Physics is guilty of adding extraneous hypotheses to save a particular theory from being falsified. We all rule out inflation as a sound and viable explanation with Mathematics and Physics, we may be wrong in the end, nonetheless our Theism or Agnosticism didn't drive us to this conclusion. As a practical joke, we did work out a mathematically precise model, that was militantly Theistic, involving spacetime expansion with no singularity. We went so far as to enlist support from others in Academia. After this little prank, our victim actually converted from absolute Atheism, to a neutral position.
After this prank, we came to realize a truth. Secular Humanism, which rules Academia and government with an iron fist, forbids historical science to be viewed from any viewpoint, other than the religion of Secular Humanism. Aron, it is refreshing to see a fellow Physicist boldly speak out and proclaim Jesus Christ as Lord and Savior. Speaking of funding, we're all grouchy old men, who worked at one time or another on Bosonic String Theory. As you pointed out, because that's where the money was. Our attitude towards this concept is no friendlier than that of Peter Woit.
By asking this question, we were simply trying to get you to admit, that no hypotheses which presumes the existence of God is tolerated. Oddly enough it was the Agnostics in our little group who first pointed out this truth to the two Christians, back in the '80s. Perhaps you're not feeling the hostility yet, but this is because you're brilliant and you have God's protection. On a serious note, two of us pray all the time for men and women in Physics, Chemistry and Mathematics who boldly proclaim the Gospel of Jesus Christ. If you're a Christian, you can not logically escape Ex Nihilo creation. We hope you join us in our search for X and Y.
Aron, I reread your "exceptional cases" link again ( I enjoyed it just as much this time as before) and I see its relevance to falsifiability here. Thanks!
It's interesting that you mentioned inflation models with gravity waves too faint to detect. Remember a few years back when everyone was using the phrase "smoking gun" to describe how inflation could be confirmed with broad spectrum primordial gravity waves (PGW's)? Last year when the BICEP2 results were first released, every news outlet from here to Mars had "smoking gun" in their headlines and YouTube went viral with that video of Linde having what can only be called a religious experience when he got the news. But... no sooner had the results been found questionable than he started having press conferences all miffed over the term "smoking gun." Didn't we all know that there were inflation models that didn't result in detectable PGW's...? Specific models aside, that was when I first started thinking that the inflationary framework may not be verifiable after all...
But that said, speaking of specific models being testable BICEP2 set upper thresholds on PGW's that do rule out a ton of them, and interestingly, chaotic (eternal) inflation models now seem to be among those disfavored. In conjunction with Planck, the data seems to fit best with Starobinsky models. In coming years it'll be interesting to see how all this falls out, and how it will impact the string landscape/anthropic multiverse--which pretty much requires chaotic inflation to generate an anthropically significant number and variety of bubble universes.
Btw, did I understand you right... that string/M-theory aside, the discovery of PGW's would rule out ekpyrotic models? I'd love to hear more of your thoughts on that, and on ekpyrotic models in general... maybe a post dedicated to them? :-)
Dean, thank you also for a very intriguing and revealing story! I would love to hear more about your "prank" model, and how it led your atheist colleague to agnosticism! Do tell...!
If we adopt a rule that the media running wild with a new supposed discovery discredits the underlying theory, I'm not sure how much of Science will be left... ;-)
With respect to the ekpyrotic model and PGW's, all I know is that the absence of PGW's is claimed as a prediction of the model by its proponents. I haven't done the calculation myself.
Regarding inflation, I'd like to call your attention to some recent statements by Paul J. Steinhardt, one of the architects of inflationary cosmology, in his new year article at
"The failure to detect the B-mode pattern means that there is something very wrong with the picture of a violent Big Bang followed by a period of high energy-driven inflation. Whatever processes set the large-scale structure of the universe had a to be a gentler, lower-energy process than has been supposed.
Simply lowering the energy concentration at which inflation starts, as some theorists have suggested, only leads to more trouble. This leaves more time after the Big Bang for the non-uniform distribution of matter and energy to drive the universe away from inflation. Starting inflation after the Big Bang and having enough inflation to smooth the universe becomes exponentially less likely as the energy concentration is lowered. The universe is more likely to emerge as too rough, too curved, too inhomogeneous compared to what we observe.
Something more radical is called for. Perhaps an improved understanding of quantum gravity will enable us to understand how the Big Bang and inflation can be discarded in favor of gentler beginning."
Sure enough, he then mentions as a potential way out of this problem his current pet model of a cyclic universe. But cyclic cosmological models are wholly implausible for the simple reason that since 1998 it has been demonstrated beyond discussion that the expansion of the universe is accelerating, which obviously implies that the universe will expand forever. Therefore, if the "current instance" of the universe will expand forever, actually at ever faster rates, why would a hypothetical "previous instance" have slowed its expansion to a full stop and then started to contract? What changed between that "previous instance" and this "current instance"? Clearly the only rational answer is that there were no such previous instances.
Therefore, if current observations show the need to discard "the picture of a violent Big Bang followed by a period of high energy-driven inflation [...] in favor of gentler beginning", and such gentle beginning cannot logically be a bounce from a previous contraction, we biblical theists can posit that the universe was created at the start of the inflationary epoch, empty of matter and radiation and with only the inflaton scalar field that drives inflationary expansion. If we couple this assumption with that of a closed (spherical) geometry (which, as you correctly point out in your current latest article, can never be discarded from observations of zero curvature), it is easy to show that the scale factor a(t) starts to evolve as:
a(t) = a0 cosh(Hi t)
Hi = asymptotical Hubble parameter of the inflationary epoch = c sqrt(Lambda_i / 3)
a0 = sqrt(3 / Lambda_i)
Lambda_i = effective cosmological constant at the start of the inflationary epoch
As H(0) = Hi tanh(Hi 0) = 0, you just cannot get a gentler beginning than that.
The reason why this currently wholly plausible hypothesis of "creation at the start of the inflationary epoch" is attractive for biblical theists is that it has a most remarkable concordance with the Genesis narrative of the first day of creation, as I explain in the article linked above. (In the article I then go on with day 2, which also has a remarkable level of concordance independent of this hypothesis, and days 3 to 6, for which the concordance is much weaker.)
Clarification: the article mentioned in the last paragraph of my previous comment is linked to my nickname. Just in case, it is this:
Do you have a post regarding the ultimate fate of the universe and philosophycal and theological implications it might have? I just saw your discussion here about the Big Bang and the infamous Craig-Carroll debate, yet I haven't found anything about Big Rip and Big Crunch. It'll be very interesting to hear your thoughts!
Neither a Big Crunch nor a Big Rip are plausible in light of our current knowledge of physics. Rather, cosmologists currently expect the universe to exponentially expand forever, and get very cold and empty. See here for a description.
The science has changed on this a few times already, but on pretty much any materialistic view, one expects the Second Law of thermodynamics to eventually result in a lifeless universe. Of course as a Christian I think Christ is going to return sometime before that happens, and as the Bible says there will be a new Heaven and a new Earth, that operates on different principles than the current one.
For a biblical perspective on the futility of our current cosmos, see Ecc 2:11, Romans 8:20).
Isn’t the scenario described in the article, actually, a Big Rip? I thought that Big Rip is expected, more or less, given our current knowledge, - so I’ve read. What’s the difference between it and the scenario you provided?
Also, the idea that our universe can be, actually, dead for quite a long, with everything around being a result of quantum fluctuations, gives me chills.