and what I want to do today talk about inflation gravitational waves spend a bit of time on the cautionary tale of bicep because I think that's a good warning for jumping on bandwagons and data and then turn to at the end talking about the future directions in the field and particularly say in particular say a few words about CMBS for which is the future big CMB experiment planned by the cosmology community so I want to begin by giving you a sense of why people were driven to inflate and think about inflation and why we need something like inflation in some ways to explain the basic properties of the universe so let's begin with who I'll describe the evolution universe we should start with the Friedman equation that relates of course the expansion rate of the universe to its composition before we started thinking about dark energy we thought in the universe having to contain components matter and radiation universe starts out in that standard picture radiation dominated and then becomes matter dominated so let's look at the conformal structure of this universe and to do this we're going to switch from physical time to conformal time that has the advantage of making our metric have this pretty simple form for an frw universe flatter for double universe where it is conformal time this is comoving distance and so this is the radial coordinate and that's just describing the sphere so during matter domination densities goes is 1 over a to the minus 3 we can plug that into Friedman equation and find that oh ignore that - Sun ast goes as T to the 2/3 as the universe expands so da de Rosas ET / a of T so a grows is a 2 squared during radiation domination things are even simpler expansion factor goes is T to the one-half that means that the relationship between the expansion factor and conformal time is just a goes as e de so they can construct a space-time diagram for a universe we're here we look back along our past light cone to the surface of last scattering microwave background we're seeing all these different patches that are would not in causal contact with each other right because if I go to each patch here and look at the what regions it was in causal contact with this point here is only in causal contact with about a degree of the sky and this point here has only been in causal contact with that region yet when I look at the sky things are remarkably uniform right this is the same temperature there and there not only is that homogeneous are very close to homogeneous we see fluctuations whose coherence scale as many degrees so we have fluctuations on scales that were never in causal contact in the standard Theory so without having and accelerating inflate expansion phase as we do in inflation you know I think of this my teaching my bigot you know a big intro freshman class everyone hands in the same answer that suggests communication what's even stranger about our universe is not just that people hand in exactly the their hand in exactly the same answer the questions that the answer is they go you know well give them a question an exam with 10 to the 4 questions they get a different one wrong but this patch of the room gets one question wrong this cash gets a different question wrong and that catch that's a different question wrong you really know there's been communication and that's what we see in the early universe and you know so this is the first problem this origin of fluctuations problem that really drives us to think about inflation the second problem is the flatness problem and that really comes down to why is the universe so big you know there's a couple ways of expressing this problem one way is to say that when we combine general relativity and quantum mechanics there's really only one characteristic scale that characteristic scales the Planck scale our universe is visibly much bigger than the Planck scale the age of the universe is much larger than the Planck time so somehow you need some way of explaining the origin of these big numbers another way of expressing this is looking at the flatness of the universe effectively the curvature scale and we can look at that by looking at the value of Omega today we know Omega this is actually pretty today we know omegas probably within about 0.2% of one that means if I go back to redshift of a thousand when I look at the microwave background Omega the you know RIT which I can either view as the ratio of the kinetic energy to potential energy or as one - you know what over the curvature scale squared was really close to one you know less than a part in 10 to the fourth and if I go back to Big Bang nucleosynthesis Omega was close to one to one part in 10 to the 18 so somehow you have to set up the initial conditions in a very special way to produce the universe we see in this standard cosmology 10 to the minus 18 number oh let's see I think I got that number by saying this is a redshift of 10 to the 10th of 10 to the 10 and you know Omega so if the universe is positively curved we can look at the evolution of a megalith of its time if it's slightly positively curved it deviates like that as one over it has basically 1 over a squared so you just say you know we have we want to go back factor a of 10 to the 9 and that gives you that number 10 to the minus 18 I think it's actually more like closer to 10 to the minus 20 if I was careful about doing it right oh sure yeah so imagine equals one in the standard frw universe is so this is an unstable fixed point so if the you know bagel is slightly greater than one the universe is closed slightly less than one the universe is open and this is a bad color choice okay I'll make the same plot it'll be unstable either way in black or red Omega was slightly less than one the universe is becomes nearly completely open very quickly Omega is slightly greater than one it collapses in a relatively short time so you need to tune the ratio of the kinetic energy to the potential energy to be remarkably close to one at say the time of Big Bang nucleosynthesis so it seems like you have to start with this very special initial condition historically some another and also some that was quite important in the development of the idea of inflation was people thinking about grand unified theories and realizing that when you write down a theory that that breaks to us you three cross suq course you one it's going to produce multiples you know those mana poles are stable the dense is because they're stable the density and mana poles goes as one over a cubed their massive particles remember that the density and radiation goes as one over a to the fourth so if you're producing multiples at the gut scale then they'll quickly grow to dominate the universe and we would live in a universe completely composed of monocles and that's not true so you need some way to get rid of them there are alternatives to inflation where you have the model the model poles can find each other nor annihilate if they're connected by strings but it became pretty hard to find the viable solution to it so back in the 80s people recognized that potentially phase transitions weren't the problem but were the solution and people recognized that the universe started out in a state that that was a false vacuum state so let's go back to or Friedman equation if the energy density is dominated by a vacuum energy so this is a constant then this is easy to solve and a grows exponentially with time and we undergo this period of super expansion and that changes the conformal structure of space-time things are growing so rapidly that that we solved this problem this closed ality problem and [Music] we then have this period in which the radius of the observable universe grows so rapidly that those two points in the sky were once in causal contact so if we can make the universe homogeneous back then we can explain why we live in a homogeneous universe today and as we'll see when we look at the behavior of the universe during the inflationary stage that inflation also ends up generating vacuum fluctuations now we don't want the universe to expand exponentially forever on one inflation to end so we want the field to roll down the hill whatever old is down the hill the field will oscillate that the field then under those what we call reheating during reheating we have the scalar field Phi in the simplest models a coupled to the faith you know one set of fermions the far field the k's produces the fermions and that generates the the heat from the Big Bang I'll get back to the you know this picture has many attractions but I do want to note that there's a lot of unsolved problems here and we'll talk about them a little bit more but just as I've got this picture up you'll notice this potential has to be really flat in order to make this work in order to match observations that potential I think about this as a Lambda Phi 4 theory this was tuned to a point in 10 to the 12 right you this would generally produce fluctuations who took a generic model of order unity so this you require a very special shape for the potential inflation does not really explain why the universe is homogeneous what it does is it takes a whole-body is patch and stretches it to be very large in order for inflation to start we need the patched to begin with to be homogeneous so we haven't fully solved the problems of initial conditions by postulating inflation what we've done is shove things under the rug and reheating what we do have viable ways of doing reheating is not automatic in that it's very easy to end up with a situation where you do not convert all the energy in this five field into our standard sector of electrons positrons radiation and that you have a lot of residual leftover energy so it's it's easy for inflation to not proceed to the end inflation also explains why all neg is equal to one the way I think about this is imagine that we start with a patch that was positively curved inflation takes that patch and stretches it enormous ly so if we take the curvature scale and if we undergo say a hundred a folds of inflation it stretches that scale by e to the hundred it means that we're living in a patch that's going to locally always look flat if we write out the Friedman equation with the curvature term you what happened in the standard frw model is during radiation domination this term went as one over a to the fourth the court this term goes as one over a squared so as I go back in time you know so over time this term all we ends up winning that's what we felt flattered over there so during radiation domination this term always wins to the egg rose but if you've got a scalar field this kind is constant so as the universe evolves this term drops as one over a squared if the universe is growing exponentially during inflation the relative importance of this term compared to this term changes exponentially so we go from what I plotted before where Omega versus a this this is an unstable fixed point to becoming an attractor where the value of Omega is driven the difference between Omega and one drops exponentially so during the inflationary phase Omega minus one is going to drop of e to minus T and we'll we suppress by eat effectively by e to the minus n where n is the number of a fold that the universe undergoes inflation also helps erase the unwanted relics if you generate mana poles or generate cosmic strings or any kind of effect from a phase transition that happens before inflation occurs inflation expands the bottom of the universe so if you have one monopole within your horizon that's not a problem because the horizon size is grown by e to the hundred and that dilutes the number of mana poles by e to the minus 300 so that makes these models relatively insensitive to initial conditions on though not completely so the feature of inflation that when it was proposed in the 80s was in some ways an afterthought people work out the predictions but people were mostly excited about the first three things I've talked about the fact that it explained why the universe was large what Y Omega was close to one it removed relics but this is the feature that now gets the most attention because we can directly observe the fluctuations that we link to this and the basic idea here is that and if we look at the evolution of the universe tiny quantum fluctuations will be enhanced by the inflation and grow to produce the fluctuations that we see in galaxies so let's look at that quantitatively we'll start with the action for a scalar field the MA the model most of us use when we look at inflation is we imagine we have a scalar field coupled with a potential the physics of inflation ends up being embedded in this potential we can look at the evolution of that field couple the fields of gravity what we do is we take the field we split it to a homogeneous piece that's the piece that's undergoing slow-roll plus a fluctuating piece this is going to describe the evolution of the homogeneous piece as it slowly rolls down the hill stuck in B will go back and forth so if we start with this equation in the limit in which that should be double prime or triple on where the U field is changing slowly the equation simplifies to this as the field slowly rolls down the hill the evolution of the fluctuations we can solve for that turn out to be pretty simple the amplitude of fluctuations that are generated just depend upon the slope of the potential and that means when we look at the fluctuations in large-scale structure remember one of the things we did was we related we said that the what we observe that the fluctuations are well described as a Gaussian random field the amplitude of the gas and random field and the potential fluctuations or density fluctuations will be expressed in terms of a power law the slope of that power law can be directly related to the properties of the in photon potential if we take a theory where V is going as far to the N and when I'm looking at inflation I looking at the fluctuations we see picture to have in mind we've got a field slowly rolling down the hill heading towards reheating in order to produce a universe as big as the one we live in we need the universe to undergo at least 50 e folds of inflation so were our fields must have undergone at least 50 equals on this very flat potential here if we look at the relationship between a scale we observe today and when those fluctuations were generated the scale that correspond to the horizon size today so the scales that we see in the microwave background are when the field was an earlier value so this is corresponds to 3000 mega parsecs go to smaller scales that corresponds to later times and inflation so as the field rolls down the hill it's generating fluctuations on different scales because the potential is close to flat we expect the fluctuations to be close to scale invariant x-axis is 5 so when the field so as the field is evolving this is say 50 e fold from the end of inflation this is 45 G folds 40 e folds and so on so that then will correspond today to physical scales that are you know 3000 mega parsecs or 3 bigger parsecs or 3 parsecs I'm only seeing in the microwave background a very small portion of the potential or in large scale structure so I can probably approximate the potential as 5 to the N and then the slope can just directly be related to the power law n times the number of e folds of inflation so for example we took the simplest theory we could write down M Squared Phi squared that says that we expect that the DV and we undergo about 50 e folds of inflation that directly forgets what we should see for the spectral index end up getting values of about 0.96 for the spectral index and that's just about what we see so you know what we see is in the scalar fluctuations is completely consistent with that simplest model now jumping ahead you take that simplest model of M square Phi squared it predicts the gravitational waves background that's actually inconsistent with what we see so we're going to need a theory that looks more like that to fit the observations because you want to make capital and larger than 50 so yeah about 70 folds away and it's the values more uh about 0.9 well the Planck value is more like twenty nine five so I'll show a plot with Webby n is equal to 5 1 and NS of to model clips so just to remind you you're directly relating the slope you see here or recall that when we're looking at this plot here this is the transfer function this is the power spectrum times the transfer function squared the power spectrum is K n to the S and this is 1 plus K over K a quality squared minus 2 so I look at the large-scale structure and can lead off what's going on during a period of inflation now in one hand this is an impressive range of math scales that we look at we're looking at about a factor of a 10 to the 10 and mass scale but that's only a factor of 10 to the 3 and length scale 10 to the 3 is about things about Eva 7 e to the 8th so we observe about 7 or 8 e folds of inflation so we see a piece of it but we don't we only feel a relatively small piece one of the things that we'd like to do in the future is think about ways in which we can probe over a wider range of scales now this is about as big as we could see that the physical size within a horizon but there's actually an intriguing way of trying to get at much smaller scales and see seeing if we can see what's going on at later stages of inflation and that comes from looking at spectral distortions in the microwave background so recall that the microwave background we always talk about it as being a thermal distribution you know so we've got your bows you know you have your Bose Einstein distribution for the Cosmic Microwave Background and all the fluctuations that we've talked about are thermal fluctuations where the spectrum at a given location is the same and what varies is the temperature from place to place one of the things we can measure is how close is the spectrum to a true planck distribution and we can look for deviations from that in two forms one deviation which we talked about already is what's called a Y distortion and that arises when photons scatter off the electrons and if the electrons are hotter the photon gains energy and that scatters the photon up in energy to produce a wider distortion in any energy that you jump into the microwave background below a redshift of about 10,000 will go into heat that heat will scatter photons and that will produce a wide Distortion now if you pump put energy into the universe between a redshift of a million and a redshift of 10,000 it will initially put the energy into the photon that will distort the spectrum but then through a free body interactions you'll actually create more photons you'll read thermalize them and you well you'll redistribute this distribution but you must or you between 10,000 and a million you'll redistribute the distribution but you won't have time to create more enough photons to return to a bose-einstein distribution so you'll end up with a distribution function that has a thermal a plank like a bose-einstein light distribution but with the wrong world number of photons that you expect for a temperature a given temperature that produces a mew distortion in the spectrum and that mute the amplitude of that new distortion is proportional to the amount of energy that you put into the universe between redshift of 10,000 and a million well how does this connect to inflation well by a swab situations on the scale of one solar mass to a thousand solar masses those fluctuations will have entered the horizon at that time produced sound waves just like the sound waves we talked about in the previous lecture those sound waves will damp by inter by colliding with each other and they will dump their energy into the universe of that redshift and produce a new distortion that's proportional to the amplitude of the power spectrum between it turns out roughly one solar mass and a thousand solar masses so one there's a proposed experiment that NASA is considering right now called pixie and what pixie proposes to do is measure the spectrum a fluctuate of the microwave background from 100 gigahertz up to about a thousand gigahertz one of its primary science goals is to look for this deviation in the spectrum due to the mute distortion and that will tell us what the power spectrum is doing on this very small scale now given the sensitivities they aim for they may just get an upper limit that constrains the amplitude of the power spectrum but if the slope is changing we'll actually have a measurement of what's going on over that much wider range of scale they're actually doing this experiment for many other reasons you know one of the things they want to measure is the new distortion you also get to measure this much larger signal from the Y distortion which tells us about how much energy is put into the universe at lower redshifts that tells us a lot about galaxy formation how the galaxies are affect its environment and sorry sir Oh mo dot is solar mass sorry that that is the latex symbol for solar mass you have to put a slash in and if you write your notes up last night and you didn't check them you didn't check your latex you forgot to put the slash in so if you put the back slash and you get that nice little symbol which means solar mass ah because this scales above 10 to the 3 solar masses do not GAMP until you get to red ships of 10,000 or lower so they damp later so they produce Y distortions not new distortions now if nothing else happened in the universe you could measure the widest torsions of this effect the problem is after register 10000 lots of other things happen stars form galaxies form black holes form they also dump energy into the universe the expected signal from a hot gas at redshift 1 turns out to be a hundred times larger than the cosmological signal so there's really no hope of getting cosmological an early universe information from the Y distortion so that's why you look at the new distortion the lower mass cutoff comes from the fact that if you look at fluctuations at say 10 to the minus 6 solar masses those fluctuations enter the horizon and damp it's a redshift of 100 million that's early enough that you can create additional photons by 3 body effects and that means that you thermalize the distribution completely and that removes any distortion at all that energy just goes into raising the microwave background temperature that just makes the microwave baking background temperature instead of being 2.73 it's 2.7 3 plus 10 to the minus 6 and since we have no idea what the temperature should have been without those fluctuations we can't measure things on smaller scales so so why distortion is when you dub in energy increase the energy in a photon but it don't have time to redistribute the energy if you have enough time that the typical photon has undergone and not just an elastic scattering but an inelastic scattering so can scatter an energy that redistributes the photon distribution so that you have a distribution that's shifted like that it's just differently so the new distribution the deviation which is the limestone and green is different from the line shown in blue which is the widest torsion so by making measurements at many frequencies we can distinguish the two yeah thermalize the spectrum right so and that's that really you know if it's and time here really means that you've got enough time for interactions the density in photons is going as one plus a to the fourth destined and so that they're men um things you really want to have your interaction rates are much higher much higher redshift time during radiation domination a goes is T to the one-half so that the time course then goes is a to the -2 from looking at any given reaction the reaction rate and Sigma C T and is growing as a to the minus four time is going to say to the minus two so my reaction rates are always higher for any reaction earlier on so if you have in this case acoustic waves that dumped in energy at redshift of a billion the reaction rates are so high just produces a thermal distribution at redshift of a million there's enough time to redistribute without creating photons so on all right so let me just go back to the basic predictions of inflation and remind you that we've already seen that inflation predicts the flat universe historically when inflation was proposed in the 80s observation suggested the universe wasn't flat observation suggested that Omega in the universe was about 0.2 those observations turned out to be correct in most ways point to two point three in that those observations were measuring the density in matter which is about twenty to thirty thirty percent of the critical density what people didn't realize back then was that there is a vacuum energy that was enough to make the universe flat this is a case where the theorists actually revived the vacuum energy in the 1980s and in the 1980s and 90s theorists were very fond of vacuum energy in cosmology because it was a way of making inflation work and that's one of the reasons when like the supernova data came along and showed there is strong evidence for acceleration that people were so quick to abrasive because it turned out to fit our theoretical preconceptions another thing inflation predicts is nearly scale-invariant fluctuations and we've seen that in the microwave background third important prediction is the fluctuations of Gaussian because we have loss of independent modes where the quantum fluctuations grow to produce fluctuations and we sum over them we expect the distribution to be Gaussian and when we look at the microwave sky the fluctuations are remarkably Gaussian so this shows the PDF of the temperature fluctuations normalized by their variance this is smooth on the 4 degree scale the 1 degree scale and the quarter degree scale and the dashed line is what you expect for a Gaussian distribution once you've normalized this by a variance there are no free parameters in this thin fitting the data right the you expect things to be Gaussian and they're observed to be very close to Gaussian we can quantify that non Gaussian a'ti in a number of different ways the simplest form to write down for non Gaussian ad is to say that instead of just having the potential fluctuations proportional to variations in the scalar field imagine they were proportional to a quadratic term this is what people call local Don Gaussian ad and since the amplitude of the potential fluctuations are about a part in 10 to minus 5 for this term to be important for non Gaussian ad to be of order unity we'd expect F and L to be of what are 10 to the 5 what we know is f NL is consistent with zero once we subtract off a contribution due to lensing the best fit values basic as well too so plus or minus six completely consistent with zero so if we look at that in terms of what the amplitude of non-gaussian 80 is that the amplitude of the non Gaussian a is less than a part in 10 to the 4 so for the that simplest form if I think about this in terms of you know my simple scalar field model and ask what are things that I can do that would modify that model if I start modifying the kinetic term for that scalar field to make it a non-trivial kinetic term that will put produce equilateral orthogonal non-gaussian annuities thank do something that enhances the couplings that tends to produce this local non Gaussian a'ti and people have looked in the planck data for many different forms of non Gaussian a'ti and we don't see any the fluctuations are as simple as they could be I remember Chuck Bennett complaining to me Chuck was the leader of the W math team that how come we work so hard to produce a map of the microwave background and all that you theorists want to do is measure a two-point function there's all this information in a map why can't you get something else out of it and we've we and many others have worked very hard over the years to find something beyond the two-point function but Nature doesn't seem to be providing much much information yep right okay so this is a good lesson in statistics you're measuring lots of things and you expect that one time in 20 there should be something that's 2 Sigma off and there's at least 20 numbers in this table a bunch of these are actually quarterly that these are just measuring things the same way in this particular case you actually want to look at this column I just pulled out the full table this is if I just look at the measure of the non-gaussian 80 without there is an effect actually but I point it out in a paper with a graduate student Dave Goldberg called the ISW lensing effect that is just an effect that happens at low redshift photons have to propagate from the surface of last scattering get deflected by matter fluctuations along the line of sight and we have a deflection that the temperature that I thought was at position n ends up being deflected by the interval of grad Phi along the line of sight that's the effect of gravitational lensing so this is the lensing effect there's another effect called the intervening Sachs Wolf effect that says the temperature fluctuations I see or the temperature fluctuation to the surface of last scattering due to the change in the potential along the line of sight as photons fall into a potential well they gain energy when they climb out of potential while they lose energy if the potential well doesn't change with time those two terms cancel but as what happens in a universe dominated by dark energy our universe since redshift 1 or so that potential fluctuation decays that induces a temperature fluctuation with as a potential fluctuation those same potential fluctuations also distort the photons paths when you work out the three point function take the temperature at three points take its expectation value you can get a cross term between these two terms that produces non-gaussian a T that's is W lensing you have to subtract it because it looks a little bit like primordial non generating when you do that you get this column here and then you end up with and you these three different columns in this case are just three different techniques for measuring it you can take the KSW method which I happen to like for reasons you can might be able to figure out and those are all consistent with even within one Sigma but if there was one that was off by two sigma you shouldn't get excited never get excited by two sigma results you can get excited by 3 Sigma results they'll go off and go away but you could start to get excited another prediction of inflation is recall that inflation says that we've generated the fluctuations during the accelerating phase during the inflation stage and that means we generate fluctuations in a single field and that gives rise to adiabatic fluctuations there is only one source of those fluctuations and when we look at the temperature in the polarization we have enough independent modes we can show that the fluctuations are adiabatic another key test of inflation so that the fluctuations are expected not to be entirely scale-invariant but close to scale-invariant and this is from the Planck that alone will look at the plane plus bicep later this is constraints on the spectral index this is the the black line is the projection of N squared by squared inflation with 50 and 60 E phobes on this is the different ways of cleaning the data don't worry about that detail for the moment this is the current the best bit number from Planck in terms of the spectral index and the amplitude of gravitational waves and as our gate is improved I'll show some recent results towards the end we're no longer consistent with M squared Phi squared so where we are observational e we've seen a whole bunch of the predictions of inflation a flat universe a nearly scale invariant fluctuations Dowson fluctuations adiabatic fluctuations super horizon fluctuations and we're basically just you know waiting on the detection of gravitational waves and in some ways on the observational side if we were to see that I think people would be declared victory for inflation but before we declare a victory I think we should be mindful of some of the challenges for inflation um in many ways this is more a scenario than a theory I get to write down a free function V of Phi that you think that's not doesn't come from first principles it's not constrained by any other observations so I get to see what value of spectral index or RIC and then come up with the BFI that fits it doesn't solve the initial conditions problem and a big you know we have these fine-tuning problems in the shape of initial convention and put on potential and the initial conditions the problem which some people view is a feature rather than above that's also attracted a great deal of attention just discussion is the idea of the multiverse if we take we go back to our feel rolling down the hill the more inflationary model the homogeneous part rolls down the hill each in homogeneous part this is fluctuation sometimes it goes up the hill sometimes it goes down the hill if I have two different patches in the universe one patch where the fluctuation goes up in this region V of R plus Delta Phi is larger this region B is smaller recall that the expansion rate of the universe during inflation is proportional to Z this region expands faster this region expands slower because this region expands faster that has the effect unlike of take when we average over this volume the region with the larger field value dominates more of the volume that tends to drive the field value upwards this is not an important effect at the late stages of inflation that we observe in the left final 60 efj olds of inflation but if we take the inflation model seriously and look at what happens in earlier times at earlier times this dominates that means that the field does does not evolve down the hill that in fact most of the universe ends up eternally inflating up at the top of the hill and there are only small rare patches that roll down the hill so in this picture we live in one small rare patch that happened to have the right conditions to roll down the hill this is one of many causally disconnected patches people call this you are the multiverse but it's not just one causal you're causally connected patch but many causally disconnected patches if we're exploring some large space of models then the laws of v we could be living in one patch that has represents one vacuum solution there could be other patches that have found their way into other vacuum solutions and if you know the laws we you know there may not be one unique vacuum solution and we just and to live in the vacuum leaf solution we find ourselves in you know this is a path that leads you to discussions of things like the entropic principle the idea that we happen to live in the patch that has the right conditions for our survival this isn't you know an intellectually viable solution from my hat as a Bayesian a statistician I look at that and say that's really Oh if that if your model can predict everything it's not a very that's not a great success for the model doesn't mean the models wrong but does mean if someone had an alternative model that could could be more predictive you would favor that alternative model over a model that produces a multiverse there's been you know a Paul Steinhardt Neil Turok have been I think the most effective proponents for one of the alternatives to inflation and that's an idea where you broadly speaking what you do is you generate the you solve the solution to these problems of homogeneity and flatness and generating the fluctuations not during the expanding phase of the universe but instead postulate that the universe went through a box and solve these problems during the collapsing phase and if you generate the fluctuations during the collapsing phase you can also generate a newly scale-invariant spectrum of fluctuations you can explain homogeneity it's a model that avoids the problems of a multiverse avoid some of these initial condition problems but the trade-off is you then have to get through the initial singularity and we don't have a good theory for getting to the initial singularity doesn't mean we shouldn't develop one but I think it's a very interesting alternative to consider from the observational point of view one of the big differences is the exper attic model does not predict traffic a tional waves but in flip for inflation gravitational waves is are actually a generic prediction that that during mass inflation any massless field is going to experience quantum fluctuations and these massless fields will require fluctuations at the de sitter temperature so we'll just depend on the expansion rate that's right yeah so yet parodic model things happened verse you produce gravitational waves by having things change rapidly that's how you produce gravitational waves well you know by having a you know the source term change rapidly when you have two black holes spiral together in the early universe you produce gravitational waves by having this rapidly evolving expansion term there's one way to think about it but in the egg product model you don't have gravitational waves in the you know if you look at this in the slow roll limit the amplitude of the scalar fluctuations and the gravitational fluctuations on just differ by this slow roll parameter so it just depends upon the shape of the in photon potential and the fact that gravitational waves with such a generic prediction of inflation is why people that's so excited when there was this claim detection of gravitational waves made the front page of the New York Times and generated hundreds of papers so let me go into a spend the next 15 minutes just saying a little bit about those measurements it'll be a chance to talk about some of the relevant astrophysics but also a little warning to not jump on every claim so quickly so in many ways this is some heroic science the people who do this go to places like the South Pole and winterover to make measurements they build very sensitive measurements experiments so these are the array of experiments that they build to make these measurements and this is the plot that got everyone really excited so this plot shows the amplitude of fluctuations in B modes as a function of multiple scale right so remember this multiples correspond to one over angle so we're looking at fluctuations here in about the two degrees scale on the sky and these are fluctuations in B modes the red curve is what you expect in a theory if there were no gravitational waves you'll notice that even if there are no gravitational waves we still have some B modes and that's because of gravitational lensing so at the surface of last scattering my pattern of fluctuations was purely alike but the photons have to get from the surface of last scattering a and as they do that they have has get deflected and we take this pattern and we map it in a way at this point well this point maps to here and this point maps to there and when Z maps this point to here and by distorting that pattern that takes the e light pattern and generate the B light pattern and that becomes most important on small scales high L and that's why we get the red curve here the dashed line corresponds to what you expect when you have the combination of gravitational lensing producing emotes and gravitational waves producing a gravitational wave signal and this dashed line corresponds to the signal that you would get if or the ratio of scalars cancer modes was point two and that's pretty close to what you expect for a theory like M squared Phi squid so this seemed pretty exciting and you know just remind you that you know this would be the glimpse into the universe pencil - 30 seconds after the Big Bang you're really seeing physics near the Planck scale these are actually gravitons that it become classical right you're actually would be observing graviton if you were to see this and would really open up a a new area of cosmology so the question then is this correct is this real and the problem is the galaxy if we live in a galaxy in the galaxy is hardly polarized emission and the galaxy has two sources of polarization one comes from synchrotron emission remind you that synchrotron emission comes when you've got a magnetic field an electron moving along the magnetic field would knit synchrotron emission our galaxy has a magnetic field of about ten to the minus six Gauss it's filled with cosmic rays on those cosmic waves are bombarding us one of the sources of cancer no sorts of things like that mutation these cosmic ray electrons produce a pattern of synchrotron emission across the sky and this shows a map of the synchrotron emission 23 gigahertz where synchrotron dominates you can see emission from the Galactic plane but you'll notice there's a lot of synchrotron emission above and below the plane the second source of polarized emission from the galaxy comes from dust grains much of the carbon and silicon in our galaxy is tied up in tiny dust grains the characteristic size of these dust grains are about one micron on these dust grains are what Redden's emission from the Stars historically these dust grains were why astronomers in the 19th century thought we were in the center of onion the universe we happen to live in the disk of the Milky Way little we're here this is our galaxy here's the galactic center galaxies filled with dust more dust towards the center when we look out we have relatively little dust towards the galactic poles but towards the Galactic claim there's a lot of dust absorption that actually blocks us from seeing stars 19th century astronomers counted the Stars found that the star countless stars around us were nearly isotropic because in the plane they were blocked by dust and conclude we were in the center of the universe and it wasn't to the 1920s when people realized that we were not located in the center of our galaxy these dust grains both absorb light and emit they absorb opt upon UV light and that heats up the dust grains and these dust grains are heated up and have a temperature about 20 Kelvin so warmer than the microwave background but still pretty cold so there they have a lot of emission at the frequencies we use to study the microwave background and these dust grains are not spherical they tend to be elongated so that you can think of them as the first order so the classical radiators you know in classical antennas from your Jackson E&M class and that means if you're looking at their emission or their absorption at wavelengths longer than the size of the brain and that's what we're doing what we're looking at the microwave background they're the power they admit is suppressed by lambda over D squared so the emission from grains goes as nu squared D nu of T rather than the usual thermal distribution and that's because they're such inefficient radiators and they're in a they emitted at microwave frequencies and they admit polarized emission because the dust grains tend to align with the Galactic magnetic field what happens is hydrogen atoms come along they hit these dust grains they spill ate them they pull off charges the dust grains apply a slight positive charge these charge grains then align with the Galactic magnetic field and as a result when you observe the dust grains you see a pattern a polarized dust emission well you've got a charged brain that spins and there's a little bit of dissipation that dissipates the energy and spinning and ends up aligning the field so I was immediately pretty doubtful about this result and I pulled this slide out of a talk I gave 15 years ago on what it would take to see the gravitational waves and the thing that makes this hard is we're looking for a thermal signal in the microwave background and we have a synchrotron that's dropping this way we have the dust that's dropping this way and the amplitude of the dust and synchrotron signal can easily be larger than the galactic signal the bicep experiment operated a single frequency so you really could not easily distinguish between the two they had some data at 90 gigahertz but that was quite noisy and at 90 gigahertz you have to worry about the fact that you have both synchrotron and dust making a significant contribution another reason to worry was the Planck team had already reported their results on the dust grains and the dust signal and they had shown that the polarization fraction the ratio of the polarized signal to the intensity signal was could be as large as 20% in regions and all depended which way the magnetic field pointed and in fact the you know the maps of galactic foregrounds showed that the four grounds can extend that but for and this shows from the Planck data a combination of W map and Planck data what the Galactic foregrounds do and you can see that there's significant correlated foreground emission from the various components yep carbon and silicon Brits are mostly carbon carbon silicon every galaxy every galaxies star stars at the later stages of this evolution blow off winds asymptotic giant branch stars in the expanding envelopes of those stars on the dust grain but gas cools and Carbet carbonaceous grades and silicate grains freeze out the grains these dust grains are actually quite important they can when you form a star the dust grains tend to condense in the disk they coagulate and form rocks those rocks coagulate and form planets you'll notice that the earth is made of things like carbon and silicon it's we're basically made up of dust grains and in fact you know this is you know we are actually all Stardust I will not sing the challenge with dust is that when you look at the predicted of dust spectrum this blue dashed line is what you expect the foregrounds to do so when you combine the blue dashed line and the lens C&B signal that we know is there you get the solid blue line gravitational waves plus the lens signal gives you the solid red line and with this data you can't distinguish at a single frequency between the blue line and the red line and you can go and fit the data and including fitting the limited data the head of 90 gigahertz and the red curve is with gravitational waves the blue curve has no gravitational waves and assumes there's dust there now the team knew about dust and they tried to model the dust and they construct a bunch of different dust models the most realistic one was - blue one hidden in there paper was the line that said we're assuming that the dust polarization is 5 percent and that's not a crazy number but there's no reason to assume it I asked Clem trike as you analyze a gas clamp right at the meet talk here at red sky McCall said why don't you marginalize over the dust polarization fraction since we don't know what it is and he said if we do that the signal goes away that's why some of us aren't Asians this is why some of us are beige ins you don't know something you need to marginalize over it they made some estimates of it by doing something remarkably Swezey and you know too little unfair to hit on people at lectures but this was so sleazy it's worth complaining about and they took the plank maps that were shown at conferences and people upload conference slides to the web they scan the slide of what the polarization fraction is and read off the polarization fraction it basically went to the packs in the sky and just read off from the color scheme what the polarization fraction is so that's sleazy what was stupid was not reading the slide which said this phrase on top not Cid subtracted which may not mean much to people who haven't doesn't work in this field but it means you haven't removed the effect of the cosmic infrared background some would had asked earlier do other galaxies have dust the answer is yes the other galaxies have dust and they contribute to the cosmic infrared by the infrared background as well with individual galaxies on those each of those have polarization directions that are different so when you average over many many galaxies it does not produce a polarized signal but does produce some intensity signal so you know something when you're measuring the polarization fraction in that map it's the Galactic polarization fraction divided by the Galactic fraction plus the extra galactic fraction so you're under estimating it a common Hill who was doing as part of his thesis was looking at the cosmic infrared background I knew the two signals were the same so you can just correct for that that makes the polarization fraction not 5% but twice as high 10% a variance goes as polarization squared you get to take this blue curve multiplied by four it nicely fits the data here so the whole thing ends up going away and this was seen most clearly in the joint analysis of the Planck data and the bicep data the two teams got together eventually and the Planck experiment had measurements of many frequencies so it had measurements that characterize included dust if you took the Planck measurements use them to remove the dust signal from the bicep measurements the black points dropped to the blue points and they all Wylie on that red line and when you reanalyze the results as the youth they were able to do using the planck data you now no longer have a detection but now have an upper limit let's pull up the upper limit and this is the current upper limit here in blue and we based on the current data we have a value of R less than about 0.1 at the two Sigma level and that's enough to actually rule out theories like M Squared Phi squared so at the end of the day we made significant progress and remain important progress these experiments are able to rule out some of the simplest theories of inflation but we don't have gravitational waves so where we go from here well the next steps or we want to make more sensitive maps and we want to make sure we make these maps at many frequencies so what we'd like for example while the things we're doing here was we have a survey led by Susanne Staggs called the advance AK poll survey and we're surveying the sky at five frequencies and also making use of the Planck data and the goal is to be able to if we see something have enough multi frequency information that we can separate out the two sources of galactic for grams and the primordial signal and be sensitive to gravitational waves with this data down to about R of 0.01 so that's a signal of that of the tenth we look at the program for the field advance that together with the the Simon's array and the South Pole telescope upgraded experiment SPD or 3G or what people like to call stage 3 experiments with roughly 10,000 detectors and they're pushing towards sensitivities of about you know 0.01 or so in sensitivity to our what the cosmology community is proposed to do e is to get together combine all the groups in the u.s. build a single experiment with roughly half a million detectors and that will let us push down to better than sensitivities to gravitational waves of better than apart in 10 to the minus 3 and we'll do that at five or six frequencies and this will represent basically as far as we could go because at that point we're completely dominated by four grams and our uncertainties and for ground removal will limit us from pushing further so the hope is that the gravitational wave signal is above this level it depends on the inflationary model what we predict so it could be there or we could not get lucky and not see it all notices on this product the same time will actually make a number of other interesting measurements will be putting increasingly a better constraints on the mass of the neutrino we should be able to achieve the sensitivity of sometime in the next five to ten years that the combination of C and B experiments and large-scale structure experiments will measure the mass of the neutrino will measure the sum of the neutrino species by their effects on large-scale structure another thing that we'll get increasingly good limits on is the number of relativistic this is something I talked about me earlier lecture that neutrinos and any other relativistic species contributes to the expansion rate of the universe and has an effect on the microwave background and if in the early universe if there's any other light species that's stable that was created we ought to be able to see its effects on the watch on the microwave background so that doesn't represent another opportunity for discovering new physics so I'll conclude once this on one hand this is a boring list of numbers and charts and sensitivity goals to the do-e on the other hand I think this represents you know outside of the LHC one of the great opportunities for experimental breakthroughs in the next decade giving us some some hints about something really fundamental I mean we have a chance you know our limits on gravitational waves a little improve by a factor of a hundred our sensitivity to extra relativistic species won't improve by that amount and we'll be able to determine the nature of the neutrino hierarchy and you know and then we may discover just upper limits in the next 10 years but while the reasons we're trying to do all this is we're hoping that stuff will be a real opportunity for discovery so let me in there [Applause]
