has announced a detection of gravitational waves via the effects of gravitational waves on the spectrum on polarization of cosmic microwave background (CMB). What happens that gravitational waves (or possibly some other mechanism) transforms so called E modes which correspond the curl free part of polarization field expressible as gradient to B modes responsible for the divergenceless part of polarization field expressible as curl of vector field.
Interaction of photons with gravitons would induce this polarization changing transformation: this is discussed in earlier post by Lubos. The signal is unexpectedly strong constraints on possible models, in particular to the inflationary models which are currently in fashion. There is excellent popular summary of the physics behing scalar, vector, and tensor perturbations of CMB here. The map produced by BICEP describes the vorticity of the polarization field at the sky and one can clearly see it.
There has been a lot of pre-hype about the finding as proof for inflation, which it is not. Even Scientific American falls in the sin of inflationary hyping which is a pity. Inflationary theory is only the dominating theory which might be able to explain the finding.
In the following the findings are discussed in the framework of TGD based cosmology in which the flatness of 3-space is interpreted in terms of quantum criticality rather than inflation. The key role is played by gradually thickening cosmic strings carrying magnetic monopole flux, dark energy as magnetic energy and dark matter as large heff phases at cosmic strings. Very thin cosmic strings dominate the cosmology before the emergence of space-time as we know it and quantum criticality is associated with the phase transition between these two phases. Later cosmic strings serve as seeds of various cosmological structures by decaying partially to ordinary matter somewhat like inflaton fields in inflationary cosmology. Cosmic strings also explain the presence of magnetic fields in cosmos difficult to understand in standard approch. The crucial point is that - in contrast to ordinary magnetic fields - monopole fluxes do not require for their creation any currents coherent in long scales.
Liam McAllister's summary about the findings of BICEP2 team
Liam McAllister from Cornell University has written an excellent posting about the discovery and its implications in Lubos's blog. McAllister discusses the finding from several points of view. Can one trust that the finding is real? How should one interpret the result? What are its implications? A brief summary is in order before going to details.
Comparison of inflationary models and TGD
- Consideration is restricted to inflationary scenarios but it is made clear that they are not the only option. It is emphasized that a huge amount of inflationary parameter space is excluded by the unexpectedly high strength of the effect. Also the general problems of inflationary models are made explicit - a great favor for those who are not inflationary enthusiasts and might have something else in mind.
- Also other than gravitonic mechanisms transforming E modes to B modes can be imagined. For instance, the signal might not be primordial but caused by polarized foreground sources: BICEP claims that these contributions have been eliminated.
- The most important conclusion is of course that a direct detection of gravitational waves - maybe even quantal ones - has been achieved. Earlier gravitational radiation has been detected only a slowing down of rotation rate of pulsars (Hulse-Taylor binary pulsar).
Further conclusions depend on the cosmological model adopted and McAllister considers the situation in the framework of inflationary models and lists the basic aspects of inflationary model.
- The Universe on large scales should be approximately homogenous, isotropic and flat.
- The primordial scalar density perturbations should be correlated on super-horizon scales and be approximately Gaussian, adiabatic, and approximately scale-invariant.
In TGD framework inflationary cosmology is replaced with a cosmology fixed almost uniquely by the criticality of the mass density when combined with imbeddability to N4
as Lorentz invariant 4- surface. The only free parameter is the finite durationkenotau of the critical period. This kind of critical - it seems even quantum critical - periods are predicted to appear in various scales so that Russian doll cosmology is strongly suggested as in case of inflationary models. Scalar fields (inflaton fields) are replaced with cosmic strings, which evolve by thickening their M4
projections from string world sheets to 4-D ones. Magnetic energy replaces dark energy and has interpretation as counterpart for the energy of inflation field. Dark matter at magnetic flux tubes corresponds to large hbar phases (see this
, and this
- In TGD framework the long range correlations would be due to quantum criticality rather than extremely rapid expansion during inflationary period. The Universe in large scales should be also now homogenous, isotropic, and flat.
- The primordial density perturbations reflect the presence of cosmic strings (see this) before the phase transition period. These cosmic strings have 2-D M4 projection, which is minimal surface, so that these object behave for all practical purposes like strings, and CP2 projection is e 2-D holomorphic surface in CP2. During primordial period cosmic strings dominate and the mass density behaves like 1/a2, where a is proper time coordinate of the light-cone. The mass per comoving volume goes to zero at the moment of big bang so that initial singularity is smoothed out and big bang transforms to "a silent whisper amplified to big bang". For radiation dominated cosmology mass density would behave as 1/a4 giving rise to infinite energy per comoving volume at the moment of Big Bang.
- Cosmic strings gradually thicken their M4 projections and the huge primordial magnetic fields carrying quantized monopole flux weaken. These fields differ crucially from the ordinary magnetic fields in that no current is needed to create them - this is due the fact that CP2 Kähler form defines a self-dual magnetic monopole (instanton). Amazingly, even the magnetic fields penetrating to super-conductors could be this kind and perhaps even those associated with ferromagnets.
This can explain why primordial and recent Universe is full of magnetic fields in length scales, where they should not exist since the currents creating them cannot exist in long scales. The thickening of the remnants of cosmic strings would give rise to birth of galaxies organised like pearls in necklace along big cosmic strings: galaxies are indeed known to be organized into long string like structures and density perturbations would correspond to these strings.
No vacuum expectations of Higgs like scalar fields are needed. Even in elementary particle physics Higgs expectation is replaced with string tension assignable to string like structures accompanying elementary particles.
Cosmic strings would carry dark energy as magnetic energy and dark matter as phases with large values of Planck constant coming as integer multiple of ordinary Planck constant. Ordinary matter would be formed when cosmic strings and dark matter "burn" to ordinary matter: this would be the TGD counterpart for the decay of inflaton field to ordinary matter.
- Cosmic strings would define the density perturbations having correlations on super-horizon scales. In the first approximation they are certainly Gaussian. Whether they are adiabatic (no exchange of heat with environment) is an interesting question: if they correspond to large values of Planck constant, this is certainly what one expects. The perturbations would be approximately scale invariant: p-adic length scale hypothesis would formulate this quantitatively by replacing continuum of scales with a hierarchy of discrete p-adic length scales coming as powers of square root of 2 (half octaves).
- One can of course ask about spectrum of Planck constant coming as integer multiples of ordinary Planck constant: could it realize the presence of large number of length scales characterizing criticality? Could the spectrum of length scales implied by spectrum of Planck constants be the TGD counterpart for the inflationary expansion? Does the average value of Compton length or flux tube length proportional to heff=nh increase with exponential rate during quantum criticality as larger and larger Planck constants emerge?
It seems that at this qualitative level TGD survives basic tests at qualitative level but without assuming inflation fields and exponentially fast expansion since quantum criticality predicting flat 3-space (dimensional parameters such as curvature of 3-space vanish). Cosmic strings would represent the long range fluctuations. A further bonus is that cosmic strings explain dark energy and dark matter, and also the presence of long range magnetic fields in cosmos.
Fluctuations of gravitational field
McAllister gives a nice overall summary about the physics involved if given by inflationary models.
- It is not yet fully clear whether the fluctuations of gravitational field are quantum mechanical or classical. In TGD framework quantum classical correspondence suggests that quantal and classical identifications might be equivalent.
- Just as the quantum fluctuations of inflaton field would give rise to the density fluctuations visible as temperature anisotropies and large scale structures, the quantum fluctuations of gravitational field would give rise to the observed B modes in inflationary scenario. The correlation functions of gravitons in the background metric would tell everything. The problem is that we do not yet have quantum theory of gravitation allowing to really calculate everything except in QFT approximation.
- In TGD framework the fluctuations should physically correspond to cosmic strings and the question is whether gravitons can be identified as massless modes for the cosmic strings so that string like objects would give all. In fact, elementary particles are in TGD framework identified as string like objects! Ironically, TGD as generalization of string model realizes stringy dream in all scales and even for ordinary elementary particles!
Since gravitons couple to energy the formula for the energy density at which inflationary period begins should determine the spectrum of gravitational waves. Inflationary models predict this energy scale as the fourth root of the energy density in the beginning of inflation: the formula is given by in the article of McAllister. This formula contains single dimensionless parameter called r, and BICEP measurements give a rather large value r=.2 for it.
The natural expectation is that any theory explaining the findings in terms of gravitons produces similar prediction but with the energy density of scalar field replaced with something else. In TGD the energy density assignable to cosmic strings so that the square root of the energy density of cosmic string multiplied by some numerical factor should be the relevant parameter now.
Inflation should begin at GUT mass scale
The first implication of the findings is that if inflation explains the findings, it should have begun in GUT scale 1016 GeV, which is very high. The findings cut off a gigantic portion of the parameter space of inflationary models and leaves only inflation potentials that are approximately translationally invariant.
In TGD framework one expects that the energy scale corresponds to that in which quantum critical period begins after string dominated primordial period. This scale should be given by CP2 mass scale apart from some numerical factor. CP2 mass corresponds to m(CP2)=hbar/R(CP2), where R(CP2) is CP2 radius. p-Adic mass calculations predict the value of electron mass and assign to electron the largest Mersenne prime M127 having the property that the p-adic length scales kenosqrtpR(CP2) is not completely super-astronomical. This fixes R(CP2) and m(CP2). The outcome is m(CP2)∼ 4× 1015 GeV.
A numerical constant can be present in the estimate for the energy scale at which quantum critical period begins. In particular, the factor 1/αK1/4 should be present since Kähler action is proportional to 1/αK, which by simple argument is in excellent approximation equal to the inverse of the fine structure constant equal to 137. This would rise the estimate for the energy scale to about 1016 GeV if the same formula for it is used also in TGD (which might of course be wrong!). With a considerable dose of optimism one could say that TGD allows to understand why the measured value of r is what it is.
Difficulties of the inflationary approach
What is nice that McAllister discusses also so the difficulties of inflationary approach.
- So called Lyth bound gives lower bound for the distance that inflaton's vacuum expectation must move in field space in order to generate detectably large primordial waves: that is the duration of the inflationary expansion. The lower bound is given by Planck mass MP: Δ Φ >MP.
- There is however a problem. This distance should be not larger than the cutoff scale Λ of the quantum field theory. But if standard wisdom is taken granted, Λ should be smaller than Planck mass MP giving Δ Φ<MP!
- One can certainly invent all kinds of tricky mechanisms to circumvent the problem: the proposal considered by McAllister is that the couplings of Φ are suppressed to heavy degrees of freedom so that the UV theory respects the approximate shift symmetry Φ→ Φ+Δ Φ. This is true for massless scalar field but this field does not develop vacuum expectation value. McAllister mentions that for V=m2Φ2/2 the approximate shift symmetry is true. Maybe it is for small enough values of m: exact symmetry would require m=0 .
- The physical interpretation of masslessness implied by strict shift invariance would be in terms of conformal invariance. In TGD framework quantum criticality implies conformal invariance also in 2-D sense and quantum criticality corresponds to the absence of dimensional parameters from Higgs potential making Higgs mechanism impossible.
To my humble opinion, this difficulty means a strong blow against the idea about Higgs mechanism as source of vacuum energy density in cosmology. As already mentioned, the decay of the dark energy identifiable as magnetic energy and large heff
dark matter associated with the evolving primordial cosmic strings would produce ordinary matter in TGD Universe.
Also the ordinary Higgs mechanism is plagued by the loss of naturalness and predictivity by the fact that the Higgs particle has too low mass and SUSY has not been found in low enough mass scales to stabilize Higgs mass. In TGD framework the string tension of string like objects assignable to elementary particles would give the dominating contribution to gauge boson masses and p-adic thermodynamics in its original form the dominating contribution to fermion masses (see this and this). The couplings of fermions to Higgs are gradient couplings and the coupling is same for all fermions in accordance with naturality and universality.
The overall conclusion is that TGD survives the new findings at qualitative and even partially quantitative level.
For details see the chapter TGD and Cosmology of "Physics in Many-sheeted Space-time" , or the article BICEP2 might have detected gravitational waves.