I recently heard a lecture from prof Ruth Durrer (who unlike me, is a real expert on this) that the correlation function of the temperature fluctuations of the Cosmic Microwave Background is the best test for the inflation hypothesis. In particular it contains peaks that are strong indications of in-phase Alfven waves and the most natural explanation is that they were coherent and in causal contact before inflation. These lecture notes http://arxiv.org/abs/astro-ph/0109522 are quite old (for this subject anyway) but seem to contain the same kind of pictures for the correlation spectrum on figure 4.2 as I saw in the lecture although it seems that they are purely theoretic in the notes but are now reconstructed in detail by measurements from the Planck satellite.

I'm just a casual observer, but as I understand the justification for inflation theory is the difficulties presented by observed conditions such as the horizon problem, the flatness problem and the magnetic-monopole problem. Since the theories' specifications are now based on observational data regarding the CMB, and other indications, that they are consistent with these observations does not seem to satisfy requirements for making independent predictions. I agree that some testable predictions of conditions that have not yet been identified should be independently derived from inflationary models so that they can be properly evaluated - rather than simply judging them on the basis of how well they fit the observed conditions from which they are derived...

One of the fundamental presumptions of big bang theory that seems to require inflation to produce observed conditions is that the universe originated from a singularity. This seems to be simply a maximal reverse extrapolation of observed expansion. Alternatively, if the universe originated as a confined dimensional space containing all of the universe's energy, the horizon and flatness issues might be explained without inflation...

Another way to think about this is to consider other ways to solve the horizon / flatness problem, and the experimental means of testing those alternatives. There are such theories, including Moffat's MOG and the variable speed of light theories, such as Doubly Special Relativity and Rainbow gravity (see http://arxiv.org/pdf/gr-qc/0305055v2.pdf http://arxiv.org/abs/0807.1689 http://arxiv.org/pdf/astro-ph/9811018v2.pdf ). Tests of these theories (including tests of the anisotropy of c) are thus really also tests of inflation.

I really never understood the flatness problem very well. I am going to pose this in a seperate question.

1.

To calculate temperature of CMBR one uses several experiments to

plot the Plank distribution curve of this black-body radiation. Several

experiments are required to measure intensity at different wavelengths.

After the curve is plotted from the position of its peak we can say the

the temperature of black-body.

2.

Next investigation is the temperature of black-body CMBR from different

directions of the sky.

Combining answers of 1 and 2 one concludes that whatever is the

direction from which CMBR is coming, temperature of balck-body

source of CMBR is the same. This is horizon problem.

Flatness problem is that if we draw a triangle then sum of all three

angles is 180 degrees. This is a property of flat space. The problem

is why it is so regarding the geometry of 3D space. We see that

when we inflate a balloon, and draw a triangle on its surface, sum

of angles comes closer and closer to 180 degrees as the balloon

is inflated.

What are in phase alfven waves ?

Biswajoy,

Regarding flatness, I don't think we can determine the angles of a triangle in space, since we can only estimate distances to luminous points in space, presuming that their light linearly traversed intervening spacetime. If light was actually uniformly curved by spacetime, we'd actually be estimating its traversal distance - not the linear distance to its source.

The caption to the image inset at the top of http://en.wikipedia.org/wiki/Flatness_problem states:

"The local geometry of the universe is determined by whether the relative density Ω is less than, equal to or greater than 1. From top to bottom: a spherical universe with greater than critical density (Ω>1, k>0); a hyperbolic, underdense universe (Ω

@James this definition of flatness applies only to FRW universes.

The matric need not be FRW, even though most of the time

we work with it.

This seems to be a crucial and nice confirmation of inflation,

https://www.simonsfoundation.org/quanta/20140317-possible-echo-of-big-bang-detected

Recent discovery of the gravitational waves imprint in the cosmic background radiation constitues a solid support of the inflation concept as proposed by Andrei Linde to solve some cosmological problems of the Big Bang model.

http://www.space.com/25091-cosmic-inflation-gravitational-waves-discovery-images.html

Once the inflation is proven the flatness of the space comes out in a natural way, I think.

Effects of gravitational waves are imprinted in CMBR. That

is what an American group found in a nine year long

experiment at south pole. How does that prove inflation ?

Is there some more involved arguments with various

Fourier modes of CMBR ?

Juan,

Nice reference article. The Bicep2 results do seem to provide compelling experimental evidence supporting some inflation theories, but those results still require independent experimental confirmation.

There are already many who suggest that this evidence also supports many multiverse theories and the existence of gravitons (see http://arxiv.org/pdf/1309.5343v2.pdf - referenced by your article - and https://www.researchgate.net/post/Does_the_detection_of_primordial_gravitational_waves_really_imply_that_gravity_is_a_quantum_particle_interaction_and_the_existence_of_gravitons).

There is still room for healthy skepticism, despite the attractiveness of inflation in fitting the observed properties of the universe to the standard big bang model. I think the most important consideration is that the Planck full-sky dust maps will be available late this year and may provide additional information important to the evaluation of the Bicep2 results. Also see http://physicsworld.com/cws/article/news/2014/mar/18/neil-turok-urges-caution-on-bicep2-results http://blankonthemap.blogspot.com/2014/03/b-modes-rumours-and-inflation.html and http://blankonthemap.blogspot.com/2014/03/bicep2-reasons-to-be-sceptical-part-2.html.

Thanks James Dwyer for the interesting references. I fully agree in that independent confirmation is required. Whatever the final interpretation of the experimental facts I don't doubt this is a great, Great finding.

We know that E = -grad phi and B= curl A

Here phi is a scalar function and A is a vector function.

E and B are two different types of vector fields.

E has zero curl whereas B has zero divergence.

Now polarization pattern is a vector field which

is decomposed into a curl free mode (E) and a

divergence free mode (B).

B modes are caused by gravity waves. Gravity

waves are caused by inflation. So detection of

B modes in CMB anisotropy will say that inflation

happened. Again, this is because B modes are

caused by gravity waves whereas gravity waves

are caused by inflation.

Dear Biswajoy,

I think a few of your statements above are unduly generalized, specifically:

"B modes are caused by gravity waves. Gravity waves are caused by inflation."

Please see http://physicsworld.com/cws/article/news/2014/apr/10/have-galactic-radio-loops-been-mistaken-for-b-mode-polarization - which begins:

""Radio loop" emissions, rather than signatures of the early universe, could account for the observation of B-mode polarization announced by the BICEP2 collaboration earlier this year. That is the claim of a trio of cosmologists that has found evidence that local structures in our galaxy generate a polarized signal that was previously unknown to astronomers studying the cosmic microwave background (CMB). The new foreground, which can be detected in the radio and microwave frequencies, is present at high galactic latitudes and could potentially be misinterpreted as a B-mode polarization signal caused by primordial gravitational waves, thus casting doubt on the BICEP2 finding."

There are also concerns that intervening dust clouds could also produce such signals, and there are concerns that the signal has only been identified in emissions of a singly frequency. See http://physicsworld.com/cws/article/news/2014/mar/18/neil-turok-urges-caution-on-bicep2-results.

Also, http://blankonthemap.blogspot.com/2014/03/b-modes-rumours-and-inflation.html the blog author discusses primordial gravitational waves as primordial tensor fluctuations - I think the result of rapid amplitude modulation of the stress-energy tensor describing universal spacetime - that is why they're referred to a 'gravitational waves'...

I think its more precise to say that inflation theories predict that primordial gravitational waves should produce B mode polarization signals in the cosmological background microwave spectrum. Detection of such primordial signals would not prove inflation theories, but would provide compelling supporting evidence...

CMBR undergoes scattering with a tensor field in early

universe. That can produce B mode polarizations in CMBR.

Therefore a precise statement would be that discovery of

B mode polarization in CMBR indicates that microwave

photons have undergone scattering with tensor fields

prior to their exit from the surface of last scattering.

But commonly, scattering with a tensor field is being

called as `interaction with gravity waves' . I do not know

whether this is proper.

Any signal in experimental physics has some

backgrounds. Here the background comes from scattering

from interstellar dust.

The article http://physicsworld.com/cws/article/news/2014/apr/10/have-galactic-radio-loops-been-mistaken-for-b-mode-polarization concludes:

"Fortunately, Sarkar, Coles and Spergel all agree that all eyes are now on the upcoming polarization data from the Planck satellite, which should clarify the situation within the year. "Planck has polarization measurements across the whole sky at multiple frequencies, so it will provide both a detailed characterization of galactic emission and should hopefully also confirm the BICEP2 results and show convincingly that the emission is cosmological," says Spergel."

If I recall correctly, the Planck satellite dust data will be available late this year (perhaps early next year). Until this more complete data is available, there remains some real possibility that the identified B mode polarization was produced by dust clouds...

Also see http://arxiv.org/abs/1404.1899.

Thank you James for these references. Both galactic radio loops

as well as interactions with dust clouds could be alternative

explanations for the B mode polarizations. We have to wait and

watch how scientific community reaches an uniform view

after polarization data from Planck satellite is available.

FYI - the BICEP2 primordial gravitational wave - CMB polarization results may be confirmed (or not) in Oct. See http://www.nature.com/news/milky-way-map-skirts-question-of-gravitational-waves-1.15181.

At what point of time did CMBR photons interact with a tensor

field ? Perhaps that is not answered by BICEP2 results. But

I have still not grasped the relevance of "r" parameter, which

gives the ratio of strengths of tensor interactions to the scalar

interactions. BICEP2 is quoting r=0.2. What is this value saying

about inflation. Possibly it will rule out a few candidate models.

For example phi^4 model with 50 e folding.

I am uploading a figure with summarizes experimental

status of inflationary models. In this plot the y axis represents

tensor/scalar ratio of perturbations, in the x axis it is nr. Note

that nr appears in (k)^(nr-1), which measures deviation from

absolute scale invariance. The shaded regions are the allowed

regions. Note that r=0.2 is outside orange shaded regions.

source of figure:

http://lambda.gsfc.nasa.gov/product/map/pub_papers/sevenyear/cosmology/wmap_7yr_cosmology_images.cfm

Biswajoy,

I think one has to put this chart in context to consider it properly. It and the other images in your source are included in the 2011 research report "SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP *) OBSERVATIONS: COSMOLOGICAL INTERPRETATION" - freely available at http://dx.doi.org/10.1088/0067-0049/192/2/18. To quote that report, on page 38 it refers to the chart you referenced as Figure 20:

"1. Gravitational waves and primordial power spectrum.

Our best estimate of the spectral index of a power-law primordial power spectrum of curvature perturbations is ns = 0.968 ± 0.012 (68% CL). We find no evidence for tensor modes: the 95% CL limit is r < 0.24.41 There is no evidence for the running spectral index, dns/d ln k = −0.022±0.020 (68% CL).Given that the improvements on ns, r, and dns/d ln k from the five-year results are modest, their implications for models of inflation are similar to those discussed in Section 3.3 of Komatsu et al. (2009a). Also see Kinney et al. (2008), Peiris & Easther (2008) and Finelli et al. (2010) for more recent surveys of implications for inflation. In Figure 20, we compare the seven-year WMAP+BAO+H0 limits on ns and r to the predictions from inflation models with monomial potential, V (φ) ∝ φα."

Obviously, this research was reporting the researchers' conclusions based primarily on the their incremental findings of the 7 year WMAP data and do not include the recently reported BICEP2 results. As I understand, the Tensor-Scalar Ratio (r) describes the ratio of tensor signals to scalar signals they found in their CMB data - it says nothing about when those signals were encoded.

I think the answer to that and other questions may be found in http://arxiv.org/abs/astro-ph/9706147 and http://background.uchicago.edu/~whu/polar/webversion/node1.html - which states:

"The polarization probes the epoch of last scattering directly as opposed to the temperature fluctuations which may evolve between last scattering and the present."

I interpret everything I've seen to indicate that detected CMB photons were emitted no earlier than the surface of last scattering - which was triggered by the recombination event. As http://en.wikipedia.org/wiki/Cosmic_microwave_background states very succinctly:

"The CMB is a cosmic background radiation that is fundamental to observational cosmology because it is the oldest light in the universe, dating to the epoch of recombination."

"CMB Polarization primer" Hu and White is pretty much insightful.

Specially it describes polarization signals; peak of the

signal when we plot power as a function of `l'. The peak has two

properties (i) location of the peak (ii) height of the peak.

Location of the peak gives information on the horizon size at

the point of last scattering. Height of the peak (peak power)

gives information on the time duration of last scattering.

I am summarizing discussion on this question till now;

Three major predictions of inflation, which are being

experimentally tested are,

(1) flatness

(ii) spectrum of density perturbations

(iii) existence of b modes.

Finally also the inflationary consistency

condition which is

r = -8 n_T

here n_T is the spectral index of tensor fluctuations.