# Higgs inflation

1. Mar 24, 2013

### mitchell porter

I figure that we need a thread specifically for this topic, while we try to sort out just how minimal physics could be, in the wake of the Moriond conference on the Higgs and the data release from the Planck collaboration. Fedor Bezrukov has written many papers on Higgs inflation, and curiously, the lower bound on the range of possible Higgs masses is quite close to the zone of metastability where the measured Higgs mass actually resides.

2. Mar 24, 2013

### ftr

A quick question. Was higgs field there at the start of BB? did it have any role in inflation at that time?

3. Mar 24, 2013

### garrett

As a proponent of unification I favor models in which the Higgs is or relates to the inflaton. But these models aren't nailed down yet. A big open question is what the potential and coupling to the gravitational curvature is. I'm expecting the Planck data to winnow the field of options a bit, and more when the polarization data comes in.

4. Apr 14, 2013

### ftr

5. Apr 15, 2013

### brianhurren

I was thinking that..I am thinking that at the instant after the big bang. everything was energy and all forces are unified and everything was at plank temperature. at this temperature it was far to hot for the Higgs field to have broken symetry or condensed out of space. this means there was no mass to restrain the expansion of space so it inflated at thousands of times the speed of light. expansion caused the space to cool. eventually it got cold enough for the first symitry break to occur and this was when the Higgs field condensed out of space. This suddenly gave a lot of the particle (heavy hadrons mostly at this stage) mass and everything suddenly became subluminal, expansion slows right down. as the universe continues to expand, it cools and other particles condense out of the space.....essentially, matter is frozen radiation.

mind you, this is just a guess based loosely on what i have read...please feel free to correct it....or is it more or less right?

6. May 1, 2013

7. May 2, 2013

### ohwilleke

While perhaps this is looking too big picture for this post, I'll have at regarding the question of whether the question of an inflaton is one that we should be asking at all, or if it is really a category error. (If this needs to be kicked into its own thread, no hard feelings.)

As I understand it, inflation is basically necessary to explain why the universe at t=fraction of a second after the Big Bang, is as homogeneous as it is. The end of inflation is the point at which phenomena like the speed of light speed limit of the physics we know kicks in.

It isn't at all obvious to me why we can't have a cosmology that simply starts at a putative end of inflation and says that at that point which constitutes the initial conditions of the universe: (1) at proper time arbitrarily set at zero, the radius of the universe is approximately "X", (2) the universe is homogeneous, (3) the observed matter-antimatter asymmetry of the universe is already in place, (4) the universe has its current baryon number and lepton number which is conserved at all points thereafter except as the Standard Model permits this number to vary (if at all), (5) all known laws of physics including the speed of light apply at that point and all points thereafter. If you want a fancy name for it, call it the "Big Bang event horizon."

Cosmology after this point is just reverse engineering from the universe we know based on straight-forward application of the known laws of physics. It is definitely science.

To go back before the Big Bang Event Horizon, one needs a lot of BSM physics, all of which is necessary simply to get to a point that is maybe a second earlier and a few meters smaller (as I understand it, at the end of inflation in most models were are still a mere fraction of a second after the Big Bang and the universe is still smaller than a typical single family house) which gets highly speculative. Most of this is endeavor to go back further is motivated by the assumptions that (1) the Big Bang was a point-like singularity, (2) the initial condition baryon number and lepton number was zero, (3) the initial conditions of the universe has balance between matter and anti-matter.

Those assumptions seem rather presumptuous to me in the absence of any experimental data points that says they must be true. It may not be theology (particularly if one can devise an inflaton that integrates well with the Standard Model and GR), but it gets pretty speculative.

Point (1) flows from the continous classical form of GR which is a feature of GR that is far less definitively established than say, the universality of the speed of light speed limit.

Point (2) is purely an aesthetic consideration because including a particular baryon number and lepton number for the universe seems arbitrary and ugly. But, nobody seriously argues that mass-energy conservation is violated at any post-Big Bang point in time and the total amount of mass-energy in the universe is essentially as arbitrary as the B and L numbers are except that it comes on a discrete rather than a continous scale. It becomes even more of a distinction without a difference in any theory of quantum gravity where everything is fundamentally discrete anyway. (Incidentally, is there any good experimental evidence that B-L=0 exactly (it is, of course, trivially true that B-L=constant is necessarily true in any scenario where B and L are separately conserved and it is also easily concluded from the observation that most matter comes in the form of electrically neutral atoms and that the net electromagnetic charge of the universe is neutral at a quite fine grained level that B-L<<B+L).

Point (3) is even more presumptuous. While matter equals anti-matter is very natural, a starting point of 100% matter and 0% antimatter with antimatter arising only emergently thereafter (and in a form that lasts very long at all before being annihilated after crashing into ordinary matter in the vicinity pretty much only in the neutrino sector) is almost as natural as matter=antimatter. To start at matter=antimatter and get the universe we see today and requires elaborate B-L conserving but B or L violating processes that we haven't observed despite looking very hard for them.

At some point simply conceding a set of irreducible initial conditions does less injustice to the overall beauty and coherence of the theory than the contortions necessary to go back beyond the Big Bang Event Horizon, and even if you do go back from t=fraction of a second at end of inflation in a matter only universe with B=L=0 to t=0 and an inflaton your still stuck with lots of intial conditions including the total mass-energy of the universe and all of the constants and equations of GR and the Standard Model that can't be determined from first principles with additional complications to accomodate B/L/Flavor Changing Neutral Current interaction, and the equations and constants of an inflaton (assuming that you can't use an unmodified Higgs field to get an inflaton which does partially vindicate the attractiveness of a Higgs inflaton relative to other possibilities).

8. May 2, 2013

### ftr

ohwilleke,

can you elaborate on point 1 please, I am not getting it.

9. May 2, 2013

### Haelfix

Ohwilleke, i'm not sure I understand your post, but it *is* perfectly legitimate to simply say 'these are the initial conditions and regular laws of physics' and then be done with it... Certain laws and the particular initial conditions seems peculiar, but they simply are what they are.

You then don't need any mechanism to drive baryogenesis, and you don't need inflation.

However, this is essentially equivalent to believing in a miracle. It is a miracle that one side of the universe knows about the temperature distribution and energy density of the other side of the universe, to better than 10^60 decimal points, even though they couldn't have ever been in causal contact.

It also seems weird that out of all the universes that could have existed, we happen to live in one where there is 10^10 nuclei, for every anti proton or somesuch.

It's a little bit like if you walked out to the park, and everyone you saw was wearing red socks. You might think, oh well everyone happened to pick red socks when they woke up in the morning. That is a perfectly consistent initial condition and dynamical evolution. However, I think most people would guess that there was something else to it. Perhaps that it might be a holiday or some other event.

Now the analogy is faulty in the sense that a holiday is a known quantity, and inflation requires new physics, but then it's not so surprising that new physics shows up in places where you haven't tested things as thoroughly (and the Planck era is most certainly a potential spot where by dimensional analysis, certain extrapolations seem to go wrong).

10. May 2, 2013

### Haelfix

This is nothing new. Higgs inflation has always required a nonrenormalizable interaction that has no reason to be there by symmetry considerations, and is finetuned through many orders of magnitude.

Contrary to some threads, this is actually a highly nonminimal solution to inflation, and why it was quickly disfavored in the early literature in favor of more natural, simpler proposals like new inflation (even though the latter introduces a new particle).

If this is indeed the physics of inflation, it seems highly anthropic in nature and strikes me as maximally ugly in terms of predictivity.

11. May 2, 2013

### marcus

http://arxiv.org/abs/1207.4353
Inflation from non-minimally coupled scalar field in loop quantum cosmology
Michal Artymowski, Andrea Dapor, Tomasz Pawlowski
(Submitted on 18 Jul 2012)
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by critical matter energy density, (ii) the Planck scale physics features the "mexican hat" trajectory with two consecutive bounces and rapid expansion and recollapse between them. Furthermore, for physically viable coupling strength and initial data the subsequent inflation exceeds 60 e-foldings.
14 pages, 5 figures

My comment: Loop cosmology makes inflation look pretty good---suggests that adequate inflation, with simple generic assumptions, occurs with high probability. So some of Steinhardt's objections to inflation do not apply--fine-tuning obviated. Here's a paragraph from page 1
==quote Artymowski Dapor Pawlowski==
...
While the considered model is very successful on the classical level it still suffers the standard problems related with the presence of initial singularity, which are expected to be solved by quantum gravity. One of the leading approaches to provide quantum description of spacetime itself is Loop Quantum Gravity (LQG) [9–11]. The cosmological application of its symmetry reduced version, known as Loop Quantum Cosmology (LQC) [12], has indeed provided a qualitatively new picture of early Universe dynamics. The prediction of the so-called big bounce phenomenon [13] offered a new mechanism of resolving long standing cosmological problems. For example, the existence of a pre-bounce epoch of the Universe evolution provides an easy solution to the horizon problem, while preliminary studies indicate that the dynamics in the near-bounce superinflation epoch prevents the catastrophic entropy increase [14, 15] usually considered a danger to bouncing cosmological models (following the consideration of [16]). What’s even more important, the spacetime discreteness effects amount to a dramatic increase of the probability of inflation in the models with standard m2φ2 potential scalar fields [17] (see also [18]). Indeed for such models the probability of inflation with enough e-foldings to ensure consistency with 7 years WMAP data happens with probability greater than 0.999997. These results make the loop approach very attractive in inflationary cosmology.
==endquote==

Last edited: May 2, 2013
12. May 2, 2013

### fzero

To add to this, the paper by Xianyu et al (1305.0251) attempts to derive a unitarity bound on the nonminimal coupling by studying scattering of W-bosons. They somewhat refine the standard argument that unitarity is violated at a center-of-mass energy $E$ when $\xi E/M_P\sim 1$. It's not clear that their discussion really adds much to the arguments presented by Hertzberg, who clearly demonstrated how the unitarity violation for multiple scalars in the Einstein and Jordan frames, using the scalar-scalar channels.

As explained in either of these papers, for any $\xi\geq 1$, the EFT breaks down before we reach the Planck scale, implying that new physics must be present. This new physics would inevitably change the Higgs potential, invalidating the very assumption that you can compute Higgs inflation from the low-energy SM+gravity. In models where naive Higgs inflation seems to "work," $\xi \sim 10^4$ (including the LQC paper that marcus cited). In these models the unitarity bound is violated at a scale around $10^{-4}M_P$, whereas the energy scale at the end of inflation is bounded by around $10^{-6}M_P$. This last number comes from an old paper by Liddle based on COBE. I'm not sure that there's a better bound available, but the point is that the new physics arises at a scale that happens to fall right in the middle of inflation. So it's always impossible to use the low-energy EFT to study inflation in these models.

13. May 2, 2013

### mitchell porter

In an earlier paper by De Simone, Hertzberg, and Wilczek, "Running Inflation in the Standard Model", I have finally found (page 8) something like an explanation of why the threshold of vacuum instability would coincide with the threshold of Higgs inflation's viability:
And:
When I read that, the first thing I think of is Bousso and Polchinski's implementation of Weinberg's anthropic prediction of a small cosmological constant: lots of possible vacua with different c.c., and a small window (see their page 22) in which observers can live. Here, it's as if we're scanning over inflationary initial conditions distinguished by the mass of the inflaton and the size of the nonminimal coupling, with heavier inflatons being more improbable; so the mass favored is the lightest one that will allow a universe of a decent size to form.

I don't especially like anthropic arguments, I would rather have some causal mechanism (asymptotic safety? self-organized criticality?) which produced a Higgs mass on this threshold. But a more important question would be, is there a microphysical implementation of this scenario - some stringy or other landscape, which contains the required range of masses and couplings for the inflaton?

As for what fzero said (these models can't be valid all the way back to the start of inflation), I suppose the question is whether you can introduce extra physics in a way which doesn't spoil the logic, whether causal or anthropic, of whatever scenario is being advanced.

14. May 3, 2013

### ftr

Why would this be anymore mysterious than the laws of physics being the same in both parts of the universe?

15. May 3, 2013

### ohwilleke

Of course, you still have conventional nucleosynthesis even in a no new physics plus initial conditions approach. You don't lose much predictive and explanatory power from the model by truncating its beginning slightly.

Also, it isn't so much a matter of believing in a miracle (any more than the Big Bang theory, or the hypothesis that inflation violating the ordinary law of physics happened) as it is acknowledging that there may be mysteries in the universe that we can definitively solve even in principle.

Speculation about what happens before that point in time is different in kind from speculation about what happens after that point in time.

16. May 3, 2013

### ohwilleke

"Most of this is endeavor to go back further is motivated by the assumptions that (1) the Big Bang was a point-like singularity . . . Point (1) flows from the continous classical form of GR which is a feature of GR that is far less definitively established than say, the universality of the speed of light speed limit."

The usual approach in cosmology with general relativity, is to start with your initial conditions and trace them all of the way back to t=0 where the size of the universe is point-like, producing a singularity. Voila, when you do that, you get a Big Bang singularity.

This is a very natural limit to take. But, there isn't really any profound reason, if you are going to have a Big Bang where all the mass-energy in the universe magicially appears at the point of creation for it to have volume zero, as opposed, for example, to the post-inflation volume of the universe which is roughly the size of a house. A non-zero Big Bang volume does no injustice to GR in any other part of the theory with no new physics - and the question of a zero v. non-zero Big Bang volume at t=0 is one that is pretty much impossible to resolve.

Indeed, for example, if you have a discrete structure of space-time with Planck scale nodes, and each node can only carry at most X much mass-energy by the mechanism of your theory, then there is a minimum Big Bang volume built right into the theory. This is somewhat analogous to what you do when you run into a singularity in complex analysis - you integrate on a path integral around the point-like singularity to keep your equations well defined rather than trying to trace your equations all the way back to the singularity itself.

The natural thing to do in a maximum mass-energy per node scenario is to calculate the minimum size of the universe at the Big Bang moment, rather than t=0, volume of the universe=0 conditions.

We have no real solid experimental evidence that resolves the question of whether space-time is continous or merely really fine grained, or put another way, whether singularities in GR are true physical singularities or merely look like singularities because we are using continous space-time approximations of a very fine grained discrete space-time reality. In contrast, we have overwhelming direct evidence that the speed of light limit applies even in quite extreme conditions. So, maybe we should be more worried about relaxing the speed of light limit than other parts of the theory as we look at very early cosmology.

17. May 3, 2013

### fzero

I am getting the impression that you have an issue with superluminal expansion. If I have misread your posts, I apologize in advance.

Superluminal expansion or, more directly, superluminal recession, is not just a feature of inflationary models, but is in fact a feature of the observationally favored $\Lambda$CDM model of our current epoch. Objects with redshifts greater than $z\sim 1.5$ are presently receding superluminally (c.f., http://arxiv.org/abs/astro-ph/0310808). I believe there is already a FAQ here on PF explaining why this is consistent with special relativity, else it is discussed in the reference I just gave.

18. May 4, 2013

### Haelfix

There is no reason that two regions of space should have the same average temperature distribution, if they haven't had time to settle into thermal equilibrium. Yet we know they are not, and never have been, in causal contact under the assumptions ofthe standard theory. So that's very odd. It's either the greatest coincidence ever created, or it simply means that an assumption in the theory has broken down.

http://en.wikipedia.org/wiki/Horizon_problem

19. May 4, 2013

### Haelfix

The theory of inflation makes testable and falsifiable predictions, that we can directly measure. No one would believe in the somewhat crazy idea unless it had passed a number of nontrivial tests. So many in fact, that it has convinced the majority of physicists. So yea, if it was just relying on its theoretical arguments (and they are very good reasons), I very much doubt it would be the standard bearer that it is today amongst cosmologists..

20. May 5, 2013

### ftr

Of course you are right in the sense of inflation. But what I was alluding to is that in the sense of
ohwilleke proposal the different parts of the universe is expected to behave the same and not the other way around.